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This document discusses the numerical calculation of observational parameters for inflationary cosmology models, specifically tachyon inflation models and Randall-Sundrum braneworld models. The author develops software to solve the dynamical equations for tachyon scalar fields and radion fields during inflation. The software allows calculation of the scalar spectral index, tensor-to-scalar ratio, and number of e-folds for different model parameters. The best fitting results are obtained for tachyon potentials with 60 ≤ N ≤ 90 e-folds and dimensionless parameter 1≤ κ ≤ 10. The software provides a tool to test a wide range of inflationary models by inputting the corresponding Hamiltonian and Friedmann equations.

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Observational Parameters in a Braneworld Inlationary Scenario

This document describes a study of observational parameters in a braneworld inflationary scenario. It provides background on standard cosmological models, inflationary theory, and observational parameters measured by Planck. It then discusses tachyon inflation models and the Randall-Sundrum braneworld model. The study extends the RS model to include a dynamical radion field and examines the dynamics and observational predictions of tachyon inflation in this braneworld model through numerical simulations.

Braneworld Cosmology and Tachyon Inflation - RSII Numerical Models

This document summarizes a numerical model of tachyon inflation in the context of braneworld cosmology and the Randall-Sundrum II model. The model considers a tachyonic scalar field minimally coupled to gravity on a positive tension brane embedded in an anti-de Sitter bulk. Nondimensional equations are derived and solved numerically. The results show that including the radion field and bulk effects significantly extends the duration of inflation compared to standard tachyon inflation models.

Tachyon inflation in DBI and RSII context

This document summarizes research on tachyon inflation in the context of Dirac-Born-Infeld (DBI) and Randall-Sundrum type II (RSII) models. It introduces tachyon fields which arise in string theory, describes how they can drive inflation in various scenarios, and presents numerical solutions of the equations of motion. Key aspects covered include tachyon potentials, equations for tachyon inflation, extending the analysis to an anti-de Sitter braneworld model based on RSII, and calculating observational parameters like the scalar spectral index and tensor-to-scalar ratio from the solutions.

Numerical inflation: simulation of observational parameters

The CERN – SEENET-MTP - ICTP PhD Training Program
"Computational Methods in Theoretical Physics"
24 - 27 September 2020 (online / Craiova, Romania)

Observational parameters of Inflation in Holographic cosmology

Workshop on Quantum Fields and Nonlinear Phenomena, 27 September 2020. Organized by University of Craiova.

Dragoljub Dimitrijević "Tachyon Inflation in the RSII Framework"

This document summarizes research on tachyon inflation in an anti-de Sitter (AdS) braneworld framework. The researchers study a tachyon field on a dynamical 3-brane embedded in a 5-dimensional AdS bulk spacetime. They derive the equations of motion for the tachyon field and radion field in this braneworld cosmology. Dimensionless equations are obtained and numerical results show that the model can produce over 60 e-folds of inflation with observable parameters consistent with current data. The analysis provides a novel mechanism for tachyon inflation distinct from standard 4D models, with predictions depending on only one free parameter related to the AdS curvature scale.

Prediction of the daily global solar irradiance received on a horizontal surf...

This document presents a new approach for predicting the daily global solar irradiance received on a horizontal surface as a function of local daytime and the maximum daily value. An exponential distribution function is suggested and compared to experimental data from several locations. The maximum daily value (qmax) is estimated theoretically in terms of the solar constant adjusted for earth-sun distance variation. Computed values using the new approach show good agreement with experimental data, within 16% error except for some extreme points.

Quantile regression ensemble for summer temperatures

This document presents research on using quantile regression and ensembles to model summer temperatures in London from 1961-2010. It finds that quantile regression can better capture relationships between temperature and weather variables like wind speed and cloud cover at extreme quantiles. An ensemble approach is also proposed, combining 50 quantile regression models to generate synthetic weather data for use in built environment studies rather than using complete observed years. Further work would expand these quantile methods and test their use with other weather data.

Observational Parameters in a Braneworld Inlationary Scenario

This document describes a study of observational parameters in a braneworld inflationary scenario. It provides background on standard cosmological models, inflationary theory, and observational parameters measured by Planck. It then discusses tachyon inflation models and the Randall-Sundrum braneworld model. The study extends the RS model to include a dynamical radion field and examines the dynamics and observational predictions of tachyon inflation in this braneworld model through numerical simulations.

Braneworld Cosmology and Tachyon Inflation - RSII Numerical Models

This document summarizes a numerical model of tachyon inflation in the context of braneworld cosmology and the Randall-Sundrum II model. The model considers a tachyonic scalar field minimally coupled to gravity on a positive tension brane embedded in an anti-de Sitter bulk. Nondimensional equations are derived and solved numerically. The results show that including the radion field and bulk effects significantly extends the duration of inflation compared to standard tachyon inflation models.

Tachyon inflation in DBI and RSII context

This document summarizes research on tachyon inflation in the context of Dirac-Born-Infeld (DBI) and Randall-Sundrum type II (RSII) models. It introduces tachyon fields which arise in string theory, describes how they can drive inflation in various scenarios, and presents numerical solutions of the equations of motion. Key aspects covered include tachyon potentials, equations for tachyon inflation, extending the analysis to an anti-de Sitter braneworld model based on RSII, and calculating observational parameters like the scalar spectral index and tensor-to-scalar ratio from the solutions.

Numerical inflation: simulation of observational parameters

The CERN – SEENET-MTP - ICTP PhD Training Program
"Computational Methods in Theoretical Physics"
24 - 27 September 2020 (online / Craiova, Romania)

Observational parameters of Inflation in Holographic cosmology

Workshop on Quantum Fields and Nonlinear Phenomena, 27 September 2020. Organized by University of Craiova.

Dragoljub Dimitrijević "Tachyon Inflation in the RSII Framework"

This document summarizes research on tachyon inflation in an anti-de Sitter (AdS) braneworld framework. The researchers study a tachyon field on a dynamical 3-brane embedded in a 5-dimensional AdS bulk spacetime. They derive the equations of motion for the tachyon field and radion field in this braneworld cosmology. Dimensionless equations are obtained and numerical results show that the model can produce over 60 e-folds of inflation with observable parameters consistent with current data. The analysis provides a novel mechanism for tachyon inflation distinct from standard 4D models, with predictions depending on only one free parameter related to the AdS curvature scale.

Prediction of the daily global solar irradiance received on a horizontal surf...

This document presents a new approach for predicting the daily global solar irradiance received on a horizontal surface as a function of local daytime and the maximum daily value. An exponential distribution function is suggested and compared to experimental data from several locations. The maximum daily value (qmax) is estimated theoretically in terms of the solar constant adjusted for earth-sun distance variation. Computed values using the new approach show good agreement with experimental data, within 16% error except for some extreme points.

Quantile regression ensemble for summer temperatures

This document presents research on using quantile regression and ensembles to model summer temperatures in London from 1961-2010. It finds that quantile regression can better capture relationships between temperature and weather variables like wind speed and cloud cover at extreme quantiles. An ensemble approach is also proposed, combining 50 quantile regression models to generate synthetic weather data for use in built environment studies rather than using complete observed years. Further work would expand these quantile methods and test their use with other weather data.

Seismic velocity analysis in Anisotropic media

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The document summarizes key concepts and developments in seismic velocity analysis in transversely isotropic (TI) media over several decades, beginning with Thomsen's (1986) seminal work introducing parameters to characterize TI anisotropy. Subsequent work expanded on non-hyperbolic moveout (Tsvankin and Thomsen 1994), dipping reflectors (Tsvankin 1995), and velocity analysis techniques for TI media (Alkhalifah and Tsvankin 1995). Later contributions improved modeling of non-hyperbolic moveout using rational functions (Douma and Calvert 2006) and the generalized moveout approximation (Fomel and Stovas 2010). The document outlines the theoretical underpinnings of seismic analysis in anisotQuality factor of seismic coda waves in garhwal himalayas 2

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CLIM Fall 2017 Course: Statistics for Climate Research, Analysis for Climate ...

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1. The document describes an experiment measuring the length of a moving object using two synchronized clocks, one stationary and one moving with the object.
2. As the moving clock moves away from the stationary clock at a constant velocity, it emits an image of itself at the starting time to the observer.
3. By the time the image reaches the observer, both clocks have ticked forward in time, but the image remains fixed at the starting time.
4. Comparing the times on the clocks and the distances traveled allows calculating the observed length as contracted from the true rest length by a factor related to the object's velocity.

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GP-B

The Gravity Probe B experiment tested two predictions of general relativity using gyroscopes in a satellite orbiting Earth. It measured the geodetic precession and frame-dragging precession predicted by Einstein to within 0.2% and 18.4% accuracy, respectively, confirming his theory of gravitation. Technical challenges arose from the gyroscopes not being perfectly spherical, leading to greater errors than anticipated. The experiment was a decades-long effort involving NASA, Stanford University, and collaboration with other institutions.

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3. The document provides an example application of MTLS to estimate the power spectrum of a red giant star using Kepler telescope lightcurve data, finding an improvement over the standard Lomb-Scargle method.

Berlin - Conceptual Aspects of Gauge-Gravity Duality

The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms for those who already suffer from conditions like depression and anxiety.

Acoustic Model.pptx

The document discusses acoustic modeling techniques for underwater sound propagation. It provides an overview of several common modeling approaches, including ray theory models, normal mode models, multipath expansion models, fast field models, and parabolic equation models. It also discusses how these approaches relate to solving the acoustic wave equation and Helmholtz equation. The key steps of ray theory modeling are outlined, including derivation of the eikonal and transport equations from the Helmholtz equation.

Seismic velocity analysis in Anisotropic media

Seismic velocity analysis in Anisotropic mediaInistute of Geophysics, Tehran university , Tehran/ iran

The document summarizes key concepts and developments in seismic velocity analysis in transversely isotropic (TI) media over several decades, beginning with Thomsen's (1986) seminal work introducing parameters to characterize TI anisotropy. Subsequent work expanded on non-hyperbolic moveout (Tsvankin and Thomsen 1994), dipping reflectors (Tsvankin 1995), and velocity analysis techniques for TI media (Alkhalifah and Tsvankin 1995). Later contributions improved modeling of non-hyperbolic moveout using rational functions (Douma and Calvert 2006) and the generalized moveout approximation (Fomel and Stovas 2010). The document outlines the theoretical underpinnings of seismic analysis in anisotQuality factor of seismic coda waves in garhwal himalayas 2

This document analyzes seismic coda wave attenuation in the Garhwal Himalayan region using data from 75 earthquakes recorded between 2004-2006. Coda quality factor (QC) values were estimated at different frequencies using a lapse time of 50 seconds and four coda window lengths. QC was found to fit a power law relationship with frequency, with exponents ranging from 0.967 to 1.016. Lower QC values at lower frequencies indicate higher attenuation, while higher QC values at higher frequencies indicate lower attenuation, suggesting heterogeneity decreases with depth in the study region.

on Thomesn's strange anisotropy parameter

In this presentation I tried to talk about Thomesn parameters based on published papers and related documents.

Anisotropic Bianchi Type-III Dark Energy Model with Time-Dependent Decelerati...

An anisotropic Bianchi type-III cosmological model is investigated in a Saez-Ballester scalar-tensor theory of gravitation. Three different time-dependent skewness parameters along spatial directions are introduced to represent the deviation of pressure from isotropy. To get deterministic solutions of the field equations, we choose variation law of scale factor 𝑆= (𝑡𝑟𝑒𝑡)1𝑙 which yields a time-dependent deceleration parameter (DP) representing a model that generates a transition of the universe from the early decelerating phase to the present accelerating phase. Some physical and geometrical properties of the model are also discussed.

CLIM Fall 2017 Course: Statistics for Climate Research, Analysis for Climate ...

CLIM Fall 2017 Course: Statistics for Climate Research, Analysis for Climate ...The Statistical and Applied Mathematical Sciences Institute

This document discusses models used in climate science and uncertainty quantification. It begins by introducing the types of models, including general circulation models (GCMs) that simulate the climate system. A key point is that climate models provide probability distributions of weather rather than single predictions. The document emphasizes that uncertainty quantification is essential in climate science given the complexity of the climate system and imperfections in both models and observations. It presents a Bayesian framework for combining information from multiple models and data sources to obtain probability distributions of climate projections and quantify associated uncertainties. Gaussian process emulation is discussed as a method for approximating computationally expensive climate models to facilitate Bayesian calibration and inference.Cosmic Adventure 5.6 Time Dilation in Relativity

1) Time dilation describes the phenomenon where time passes at different rates for observers in different reference frames that are in motion relative to each other.
2) The proper time between two events is the time interval measured by an observer in the rest frame of the events. For observers in different frames, the time interval is dilated compared to the proper time.
3) Experiments have verified time dilation, such as atomic clocks on airplanes or the lifetime of muons. The twin paradox describes how a twin that travels in a rocket will age less than their identical twin who remains on Earth, even though each twin was stationary in their own reference frame.

Cosmic Adventure 5.10 Length Contraction on the Move in Visonics

1. The document describes an experiment measuring the length of a moving object using two synchronized clocks, one stationary and one moving with the object.
2. As the moving clock moves away from the stationary clock at a constant velocity, it emits an image of itself at the starting time to the observer.
3. By the time the image reaches the observer, both clocks have ticked forward in time, but the image remains fixed at the starting time.
4. Comparing the times on the clocks and the distances traveled allows calculating the observed length as contracted from the true rest length by a factor related to the object's velocity.

CLIM: Transition Workshop - Activities and Progress in the “Parameter Optimiz...

CLIM: Transition Workshop - Activities and Progress in the “Parameter Optimiz...The Statistical and Applied Mathematical Sciences Institute

This document summarizes the activities of a working group on parameter optimization in climate models. It discusses the group members and their interests. The group is exploring methods for calibrating climate model parameters using observations, with a focus on computationally expensive models. They plan to test calibration approaches on simplified climate model experiments focusing on extreme events like hurricanes. The group discussed challenges like choosing the right calibration method and formulation of the cost function. Ongoing activities include emulating models to alleviate computational costs and exploring statistical tools to generate heavy-tailed extremes.CA 5.12 Acceleration Transformation

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Aspects Of Higher-Spin Conformal Field Theory

This document provides an overview of higher-spin conformal field theory. It discusses the need for CFT in quantum field theory, the AdS/CFT correspondence, unfolded dynamics, Fronsdal equations, higher spin algebras, Vasiliev theory, 3D conformal equations, actions for higher spin theories, and Coleman-Mandula no-go theorem. The document outlines how interacting theories of massless higher spin particles can be constructed using unfolded dynamics and how Vasiliev theory in AdS space is conjectured to be dual to simple vector models in conformal field theory.

Quantum Statistical Geometry #2

This document discusses developing a quantum-statistical geometry by measuring lengths using a simple ruler. It considers the ruler and its measurements as observables and operators. Measurements of a wandering curve with a ruler will have uncertainty since the ruler only measures straight lines. This introduces errors when comparing the measured length to the true curve length. The document explores how probability, entropy, and statistics relate to the measurements and derives equations involving parameters like length, true length, and alpha, which may be related to measurement variance. It considers how concepts like the normal curve, Raleigh distribution, and Fourier transform could apply to the probability density functions that arise from the measurements.

CA 5.11 Velocity Transform in Relativity & Visonics

The kinematic entity of velocity is transformed in the Theory of Relativity by the Lorentz transformation of frames; in visionics, by delayed images. Simpler results in visonics.

002 uniform circularmotionlab

This document describes an experiment to investigate the relationship between force and velocity of an object moving in a circular path. Students will use a string, rubber stopper, washers, and timer to rotate the stopper in a circle with varying masses attached. They will measure the time it takes for 20 revolutions and calculate the period for different numbers of washers. By plotting force versus the inverse of period squared, students can determine if centripetal force is inversely proportional to the period squared as predicted.

Dynstoch (presented)

The document discusses first and second order estimation for a periodic Poisson process. It introduces the concepts of mean and intensity functions for an inhomogeneous Poisson process. The empirical mean function is presented as the simplest estimator for the mean function. A key equality shows the empirical mean function achieves the optimal convergence rate of root-n and has an asymptotic variance equal to the integral of the mean function. The document explores whether estimators can achieve better rates of convergence or lower asymptotic variance than the empirical mean function.

Critical Overview of Some Pumping Test Analysis Equations

This document provides a critical overview of equations used to analyze pumping test data to determine aquifer parameters. It discusses the assumptions and limitations of the commonly used Theis equation. Three alternative mathematical solutions to the exponential integral in the Theis equation are derived: self-similar, separable variable, and travelling wave. Further analysis of the self-similar solution provides an alternative approach using a normal graph of drawdown versus time intervals in log cycles to determine transmissivity. This method is applied to pumping test data from two aquifers in Nigeria, yielding transmissivity values that align with known properties of the aquifers. The analysis suggests the normal graph approach provides a good alternative or supplementary method to traditional curve-matching techniques for

GP-B

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Spherical harmonics

The presentation presents to the reader an understanding of Scalar and Vector Spherical Harmonics, it's origin and application to various engineering fields.

AGU 2012 Bayesian analysis of non Gaussian LRD processes

Contributed talk at American Geophysical Union Fall Meetinfg, San Francisco, 2012.
Part of work now submitted to Bayesian Analysis, 2014, see eprint: http://arxiv.org/abs/1403.2940

Seismic velocity analysis in Anisotropic media

Seismic velocity analysis in Anisotropic media

Quality factor of seismic coda waves in garhwal himalayas 2

Quality factor of seismic coda waves in garhwal himalayas 2

on Thomesn's strange anisotropy parameter

on Thomesn's strange anisotropy parameter

Anisotropic Bianchi Type-III Dark Energy Model with Time-Dependent Decelerati...

Anisotropic Bianchi Type-III Dark Energy Model with Time-Dependent Decelerati...

CLIM Fall 2017 Course: Statistics for Climate Research, Analysis for Climate ...

CLIM Fall 2017 Course: Statistics for Climate Research, Analysis for Climate ...

Cosmic Adventure 5.6 Time Dilation in Relativity

Cosmic Adventure 5.6 Time Dilation in Relativity

Cosmic Adventure 5.10 Length Contraction on the Move in Visonics

Cosmic Adventure 5.10 Length Contraction on the Move in Visonics

CLIM: Transition Workshop - Activities and Progress in the “Parameter Optimiz...

CLIM: Transition Workshop - Activities and Progress in the “Parameter Optimiz...

CA 5.12 Acceleration Transformation

CA 5.12 Acceleration Transformation

Aspects Of Higher-Spin Conformal Field Theory

Aspects Of Higher-Spin Conformal Field Theory

Quantum Statistical Geometry #2

Quantum Statistical Geometry #2

CA 5.11 Velocity Transform in Relativity & Visonics

CA 5.11 Velocity Transform in Relativity & Visonics

002 uniform circularmotionlab

002 uniform circularmotionlab

Dynstoch (presented)

Dynstoch (presented)

Critical Overview of Some Pumping Test Analysis Equations

Critical Overview of Some Pumping Test Analysis Equations

GP-B

GP-B

Spherical harmonics

Spherical harmonics

AGU 2012 Bayesian analysis of non Gaussian LRD processes

AGU 2012 Bayesian analysis of non Gaussian LRD processes

D. Vulcanov: Symbolic Computation Methods in Cosmology and General Relativity...

Lecture form Spring School on Strings, Cosmology and Particles (SSSCP2009), March 31-4 2009, Belgrade/Nis, Serbia

Gwendolyn Eadie: A New Method for Time Series Analysis in Astronomy with an A...

1. The document describes a new method called Multitaper + Lomb-Scargle (MTLS) for estimating the power spectrum of unevenly sampled time series data, such as that from astronomical observations.
2. MTLS combines the Multitaper method, which reduces spectral leakage and variance, with the Lomb-Scargle method, which can handle uneven sampling times.
3. The document provides an example application of MTLS to estimate the power spectrum of a red giant star using Kepler telescope lightcurve data, finding an improvement over the standard Lomb-Scargle method.

Berlin - Conceptual Aspects of Gauge-Gravity Duality

The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms for those who already suffer from conditions like depression and anxiety.

Acoustic Model.pptx

The document discusses acoustic modeling techniques for underwater sound propagation. It provides an overview of several common modeling approaches, including ray theory models, normal mode models, multipath expansion models, fast field models, and parabolic equation models. It also discusses how these approaches relate to solving the acoustic wave equation and Helmholtz equation. The key steps of ray theory modeling are outlined, including derivation of the eikonal and transport equations from the Helmholtz equation.

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Oxford slides on Duality and Emergence

Talk given at Oxford Philosophy of Physics, LSE's Sigma Club, the Munich Center for Mathematical Philosophy, Carlo Rovelli's 60th birthday conference.
I construe dualities in physics as particular cases of theoretical equivalence. The question then naturally arises whether duality is compatible with emergence. For the the focus of emergence is on novelty rather than on equivalence.
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Geneva Emergence in Gauge/Gravity Dualities

Talk given at the University of Geneva, 14 January 2016,
on emergence of space, gravity in gauge/gravity dualities.

Reduction and Emergence in Holographic Scenarios

Talk given at the Munich Center for Advanced Studies, conference Reduction and Emergence in the Sciences, Nov. 15, 2013.

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Slideshow summarizing the findings of a project to investigate the impact of dark matter and dark energy on large scale structures in the universe.

Program on Mathematical and Statistical Methods for Climate and the Earth Sys...

Program on Mathematical and Statistical Methods for Climate and the Earth Sys...The Statistical and Applied Mathematical Sciences Institute

Physical processes in the earth system are modeled with mathematical representations called parameterizations. This talk will describe some of the conceptual approaches and mathematics used do describe physical parameterizations focusing on cloud parameterizations. This includes tracing physical laws to discrete representations in coarse scale models. Clouds illustrate several of the complexities and techniques common to many physical parameterizations. This includes the problem of different scales, sub-grid scale variability. Discussions of mathematical methods for dealing with the sub-grid scale will be discussed. In-exactness or indeterminate problems for both weather and climate will be discussed, including the problems of indeterminate parameterizations, and inexact initial conditions. Different mathematical methods, including the use of stochastic methods, will be described and discussed, with examples from contemporary earth system models.Seismic Imaging using wave theory

Yasir Bashir is proposing research on using wave theory to improve seismic imaging of fractured basement in the Malay Basin. The research will develop and apply depth migration algorithms to better define faults and fractures in the heterogeneous basement. Preliminary results show wave equation migration provides better illumination of dipping layers than Kirchhoff PSTM. The research aims to identify the best methods for imaging complex fractured basement and boundaries poorly resolved by current techniques.

Dynamical Systems Methods in Early-Universe Cosmologies

The document discusses applying dynamical systems methods to develop models of the early universe. Specifically, it discusses:
1. Applying these methods to the Einstein field equations to obtain cosmological models that are spatially homogeneous but anisotropic.
2. Describing the process of analyzing the dynamics of these models, which involves identifying invariant sets, equilibrium points, monotone functions, and bifurcations in the parameter space.
3. The importance of numerical methods in understanding the global behavior of these systems, since analytical methods are often limited to local analysis near equilibrium points.

TuckerHEDPSummer2016Presentation

This document summarizes research applying self-similarity constraints to Reynolds-averaged turbulence models for modeling Rayleigh–Taylor turbulent mixing. Key points include: developing a framework to derive self-similar solutions for turbulence model equations; verifying self-similar solutions in simulations; using expressions for the mixing layer growth parameter alpha to determine sensitivity to model coefficients and bounds on values. Ongoing work includes completing modeling of Richtmyer-Meshkov instabilities and incorporating additional constraints from Kelvin-Helmholtz instabilities.

Wave Mechanics and Large-scale Structure

Short talk given at the Osservatorio Astronomico di Bologna on Thursday 18th May 2017 on the use of wave mechanics in cosmology to study the formation and evolution of large-scale structure in the Universe.

Maths Investigatory Project Class 12 on Differentiation

This document provides an overview of differentiation and its applications. It defines differentiation as finding the slope of the tangent line to a function's graph at a given point, which provides the instantaneous rate of change. The document then lists the group members working on the topic, outlines the contents to be covered, and gives a brief history of differentiation. It provides definitions and graphical understandings of derivatives, discusses some basic differentiation formulas and their applications in mathematics, sciences, business, physics, chemistry and more. It concludes that derivatives are constantly used to measure rates of change in various everyday and professional contexts.

E03503025029

The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.

Cfd notes 1

This document provides notes for an introduction to computational fluid dynamics (CFD) course. It outlines the course organization, learning objectives, and contents. The key points are:
- The course grade is based on homeworks, a report, and a final exam. Interaction is extremely important.
- The learning objectives are to understand the role of C programming in fluid dynamics and numerical methods, learn various CFD terminology and best practices, and be able to set up and analyze simple aerodynamic problems.
- The contents include introductions to partial differential equations, finite difference methods, grids/boundaries, Euler/RANS equations, and case studies. Hands-on lab sessions make up a large part of

quantum gravity

Causal set theory is an approach to quantum gravity that represents spacetime as a locally finite partially ordered set of points with causal relations. It is a minimalist approach that does not assume an underlying spacetime continuum. There are two main methods to reconstruct a manifold from a causal set: 1) extracting manifold properties like dimension from causal sets that can be embedded in a manifold, and 2) sprinkling points randomly into an existing manifold to produce an embedded causal set. To study dynamics, an action must be defined on causal sets that reproduces the Einstein-Hilbert action in the continuum limit. Several proposals have been made to define nonlocal operators on causal sets that approach the d'Alembertian operator in the limit. Overall causal set

Physics Serway Jewett 6th edition for Scientists and Engineers

This document provides an overview of a physics textbook. It is the 6th edition of Physics for Scientists and Engineers by Raymond Serway and John Jewett. The textbook has 1296 pages and covers topics in classical mechanics, oscillations and mechanical waves, thermodynamics, electricity and magnetism, light and optics, and modern physics. It uses the international system of units and includes worked examples, end-of-chapter problems, and a solutions manual.

D. Vulcanov: Symbolic Computation Methods in Cosmology and General Relativity...

D. Vulcanov: Symbolic Computation Methods in Cosmology and General Relativity...

Gwendolyn Eadie: A New Method for Time Series Analysis in Astronomy with an A...

Gwendolyn Eadie: A New Method for Time Series Analysis in Astronomy with an A...

Berlin - Conceptual Aspects of Gauge-Gravity Duality

Berlin - Conceptual Aspects of Gauge-Gravity Duality

Acoustic Model.pptx

Acoustic Model.pptx

2021 icse reducedsylabiix-physics

2021 icse reducedsylabiix-physics

CFD PPT.ppt

CFD PPT.ppt

Oxford slides on Duality and Emergence

Oxford slides on Duality and Emergence

Geneva Emergence in Gauge/Gravity Dualities

Geneva Emergence in Gauge/Gravity Dualities

Reduction and Emergence in Holographic Scenarios

Reduction and Emergence in Holographic Scenarios

The Dark Side of the Universe

The Dark Side of the Universe

Program on Mathematical and Statistical Methods for Climate and the Earth Sys...

Program on Mathematical and Statistical Methods for Climate and the Earth Sys...

Seismic Imaging using wave theory

Seismic Imaging using wave theory

Dynamical Systems Methods in Early-Universe Cosmologies

Dynamical Systems Methods in Early-Universe Cosmologies

TuckerHEDPSummer2016Presentation

TuckerHEDPSummer2016Presentation

Wave Mechanics and Large-scale Structure

Wave Mechanics and Large-scale Structure

Maths Investigatory Project Class 12 on Differentiation

Maths Investigatory Project Class 12 on Differentiation

E03503025029

E03503025029

Cfd notes 1

Cfd notes 1

quantum gravity

quantum gravity

Physics Serway Jewett 6th edition for Scientists and Engineers

Physics Serway Jewett 6th edition for Scientists and Engineers

Inflacija, crne rupe i Fizika u Nišu

Predavanje održano 4. aprila 2022. godine u okviru programa CERN Masterclass.

Observational tests of Tachyonic and Holographic Models of Inflation

- The document discusses inflationary cosmology and tachyon fields. It provides details on analytic calculations of spectra for different inflationary models using the first order approximation and the slow-roll and Dirac-Born-Infeld approximations.
- Tables in the document show the mean, standard deviation, median and range of values for the spectra calculated using the different approximations for various inflationary potentials in different cosmological models. The tables also show the relative distance between the approximations and the exact first order result.

Kako smo videli nevidljivo - od crne rupe do Nobelove nagrade za fiziku

Predavanje održano 27. septembra 2021. godine u okviru serije naučno-popularnih predavanja povodom obeležavanja 50 godina studija fizike, hemije i matematike na Univerzitetu u Nišu i dana Prirodno-matematičkog fakultetu u Nišu.

Sunce - zvezda iz Sunčevog sistema

24. decembar 2020
Drugo predavanje u okviru serije predavanja "Ekskurzija kroz Sunčev sistem" koju organizuje AD Alfa u okviru projekta "Malim koracima ka astronomiji" uz podršku Centra za promociju nauke

Od crne rupe do Nobelove nagrade za fiziku

Predavanje održano 23. novembra 2020. godine u Regionalnom centru Niš, u okviru programa Noć istraživača.

Od velikog praska do Nobelove nagrade za fiziku za 2019. godinu

Predavanje održano 12. decembra 2019. godine na Prirodno-matematičkom fakultetu u Nišu.

Evolucija zvezda i nastanak crnih rupa - kako smo videli nevidljivo

Predavanje održano 6. novembra 2019. godine u gimnaziji u Zaječaru u okviru projekta "Apolo na mreži" koji realizuje AD Alfa uz podršku centra za promociju nauke.

Kako videti nevidljivo? - prva fotografija crne rupe

Predavač Milan Milošević.
Predavanje održano 31. oktobra na Prirodno-matematičkom fakultetu u Nišu, u okviru projekta “Između redova i van okvira: Seminar za mlade i ambiciozne fizičare” sekcije Young Minds Section Niš, čije finansiranje je odobrilo Evropsko društvo fizičara (EPS).

Kako preživeti internet?

10. oktobar 2019, PMF
Obeležavanje Svetske nedelje svemira, u okviru projekta "Apolo na mreži" koji realizuje AD Alfa uz podršku Centra za promociju nauke.

CERN mesto gde je nastao "internet"

8. oktobar 2019, PMF Niš
Obeležavanje Svetske nedelje svemira, u okviru projekta "Apolo na mreži" koji realizuje AD Alfa uz podršku Centra za promociju nauke.

Kako je svet postao globalno selo?

30 godina nastanka World Wide Weba
23. jula 2019, EU info kutak Niš

NETCHEM CPD: Audio prezentovanje jednosmerna i dvosmerna komunikacija

Predavanje održano 17. aprila 2019 na Prirodno-matematičkom fakultetu u Nišu, u okviru CPD kursa "Virtual Learning Environment in University Laboratory Classes" koji se realizuje kao deo aktivnosti NETCHEM projekta.

NETCHEM CPD: Video konferencijsko povezivanje

Predavanje održano 10. aprila 2019 na Prirodno-matematičkom fakultetu u Nišu, u okviru CPD kursa "Virtual Learning Environment in University Laboratory Classes" koji se realizuje kao deo aktivnosti NETCHEM projekta.

Fizika mobilnog telefona

Predavanje održano u okviru programa Smotre najboljih radova prijavljenih na Konkurs za učenike srednjih škola „Mobilni telefon u fizičkom eksperimentu“
20. april 2019, Prirodno-matematički fakultet u Nišu

30 godina World Wide Web-a

Predavanje održano 4. aprila 2019. godine na Prirodno-matematičkom fakultetu u Nišu u okviru CERN Masterclass programa

"Svet nauke" o svetu nauke

Prezentacija sajta "Svet nauke" održana u Naučnom klubu (Regionalni centar u Nišu), 24. januar 2019.

NETCHEM Forum

The document discusses a project funded by the European Commission on remote access to analytical chemistry instrumentation. It provides an overview of remote access data collected from the NETCHEM consortium. Important links to the NETCHEM website and a remote session request form are included. The project aims to overcome technical and social barriers in instrumental analytical chemistry education.

Overview of collected WARIAL data from NETCHEM consortium

ERASMUS+ PROJECT NETCHEM: ICT Networking for Overcoming Technical and Social Barriers in Instrumental Analytical Chemistry Education
University of Niš, Serbia, 24-25 September 2018

Agreement of protection of intellectual property

ERASMUS+ PROJECT NETCHEM: ICT Networking for Overcoming Technical and Social Barriers in Instrumental Analytical Chemistry Education
University of Niš, Serbia, 24-25 September 2018

Invision power. Visual design of Forum. Demo

This document discusses the history and features of internet forums. It begins by explaining how forums originated from bulletin boards and early online discussion sites. It then covers key aspects of forums like their hierarchical structure, user permissions, and moderation. The document also compares forums to other social media, noting forums allow more control over content. It concludes by providing an overview of Invision Power Board, a popular forum software.

Inflacija, crne rupe i Fizika u Nišu

Inflacija, crne rupe i Fizika u Nišu

Observational tests of Tachyonic and Holographic Models of Inflation

Observational tests of Tachyonic and Holographic Models of Inflation

Kako smo videli nevidljivo - od crne rupe do Nobelove nagrade za fiziku

Kako smo videli nevidljivo - od crne rupe do Nobelove nagrade za fiziku

Sunce - zvezda iz Sunčevog sistema

Sunce - zvezda iz Sunčevog sistema

Od crne rupe do Nobelove nagrade za fiziku

Od crne rupe do Nobelove nagrade za fiziku

Od velikog praska do Nobelove nagrade za fiziku za 2019. godinu

Od velikog praska do Nobelove nagrade za fiziku za 2019. godinu

Evolucija zvezda i nastanak crnih rupa - kako smo videli nevidljivo

Evolucija zvezda i nastanak crnih rupa - kako smo videli nevidljivo

Kako videti nevidljivo? - prva fotografija crne rupe

Kako videti nevidljivo? - prva fotografija crne rupe

Kako preživeti internet?

Kako preživeti internet?

CERN mesto gde je nastao "internet"

CERN mesto gde je nastao "internet"

Kako je svet postao globalno selo?

Kako je svet postao globalno selo?

NETCHEM CPD: Audio prezentovanje jednosmerna i dvosmerna komunikacija

NETCHEM CPD: Audio prezentovanje jednosmerna i dvosmerna komunikacija

NETCHEM CPD: Video konferencijsko povezivanje

NETCHEM CPD: Video konferencijsko povezivanje

Fizika mobilnog telefona

Fizika mobilnog telefona

30 godina World Wide Web-a

30 godina World Wide Web-a

"Svet nauke" o svetu nauke

"Svet nauke" o svetu nauke

NETCHEM Forum

NETCHEM Forum

Overview of collected WARIAL data from NETCHEM consortium

Overview of collected WARIAL data from NETCHEM consortium

Agreement of protection of intellectual property

Agreement of protection of intellectual property

Invision power. Visual design of Forum. Demo

Invision power. Visual design of Forum. Demo

3D Hybrid PIC simulation of the plasma expansion (ISSS-14)

3D Particle-In-Cell (PIC) algorithm,
Plasma expansion in the dipole magnetic field.

Nucleic Acid-its structural and functional complexity.

This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.

Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water

Sharlene Leurig - Enabling Onsite Water Use with Net Zero WaterTexas Alliance of Groundwater Districts

Presented at June 6-7 Texas Alliance of Groundwater Districts Business MeetingTHEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...

THEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...Abdul Wali Khan University Mardan,kP,Pakistan

hematic appreciation test is a psychological assessment tool used to measure an individual's appreciation and understanding of specific themes or topics. This test helps to evaluate an individual's ability to connect different ideas and concepts within a given theme, as well as their overall comprehension and interpretation skills. The results of the test can provide valuable insights into an individual's cognitive abilities, creativity, and critical thinking skills如何办理(uvic毕业证书)维多利亚大学毕业证本科学位证书原版一模一样

原版纸张【微信：741003700 】【(uvic毕业证书)维多利亚大学毕业证】【微信：741003700 】学位证，留信认证（真实可查，永久存档）offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原海外各大学 Bachelor Diploma degree, Master Degree Diploma
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留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
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8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才

Thornton ESPP slides UK WW Network 4_6_24.pdf

ESPP presentation to EU Waste Water Network, 4th June 2024 “EU policies driving nutrient removal and recycling
and the revised UWWTD (Urban Waste Water Treatment Directive)”

bordetella pertussis.................................ppt

Bordettela is a gram negative cocobacilli spread by air born drop let

NuGOweek 2024 Ghent programme overview flyer

NuGOweek 2024 Ghent programme overview flyer

The binding of cosmological structures by massless topological defects

Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.

Applied Science: Thermodynamics, Laws & Methodology.pdf

When I was asked to give a companion lecture in support of ‘The Philosophy of Science’ (https://shorturl.at/4pUXz) I decided not to walk through the detail of the many methodologies in order of use. Instead, I chose to employ a long standing, and ongoing, scientific development as an exemplar. And so, I chose the ever evolving story of Thermodynamics as a scientific investigation at its best.
Conducted over a period of >200 years, Thermodynamics R&D, and application, benefitted from the highest levels of professionalism, collaboration, and technical thoroughness. New layers of application, methodology, and practice were made possible by the progressive advance of technology. In turn, this has seen measurement and modelling accuracy continually improved at a micro and macro level.
Perhaps most importantly, Thermodynamics rapidly became a primary tool in the advance of applied science/engineering/technology, spanning micro-tech, to aerospace and cosmology. I can think of no better a story to illustrate the breadth of scientific methodologies and applications at their best.

Bob Reedy - Nitrate in Texas Groundwater.pdf

Presented at June 6-7 Texas Alliance of Groundwater Districts Business Meeting

What is greenhouse gasses and how many gasses are there to affect the Earth.

What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.

EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...

Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.

20240520 Planning a Circuit Simulator in JavaScript.pptx

Evaporation step counter work. I have done a physical experiment.
(Work in progress.)

Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...

Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.

Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf

Sickle cell in children

Nucleophilic Addition of carbonyl compounds.pptx

Nucleophilic addition is the most important reaction of carbonyls. Not just aldehydes and ketones, but also carboxylic acid derivatives in general.
Carbonyls undergo addition reactions with a large range of nucleophiles.
Comparing the relative basicity of the nucleophile and the product is extremely helpful in determining how reversible the addition reaction is. Reactions with Grignards and hydrides are irreversible. Reactions with weak bases like halides and carboxylates generally don’t happen.
Electronic effects (inductive effects, electron donation) have a large impact on reactivity.
Large groups adjacent to the carbonyl will slow the rate of reaction.
Neutral nucleophiles can also add to carbonyls, although their additions are generally slower and more reversible. Acid catalysis is sometimes employed to increase the rate of addition.

Equivariant neural networks and representation theory

Or: Beyond linear.
Abstract: Equivariant neural networks are neural networks that incorporate symmetries. The nonlinear activation functions in these networks result in interesting nonlinear equivariant maps between simple representations, and motivate the key player of this talk: piecewise linear representation theory.
Disclaimer: No one is perfect, so please mind that there might be mistakes and typos.
dtubbenhauer@gmail.com
Corrected slides: dtubbenhauer.com/talks.html

3D Hybrid PIC simulation of the plasma expansion (ISSS-14)

3D Hybrid PIC simulation of the plasma expansion (ISSS-14)

Nucleic Acid-its structural and functional complexity.

Nucleic Acid-its structural and functional complexity.

Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water

Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water

THEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...

THEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...

Oedema_types_causes_pathophysiology.pptx

Oedema_types_causes_pathophysiology.pptx

如何办理(uvic毕业证书)维多利亚大学毕业证本科学位证书原版一模一样

如何办理(uvic毕业证书)维多利亚大学毕业证本科学位证书原版一模一样

Thornton ESPP slides UK WW Network 4_6_24.pdf

Thornton ESPP slides UK WW Network 4_6_24.pdf

bordetella pertussis.................................ppt

bordetella pertussis.................................ppt

NuGOweek 2024 Ghent programme overview flyer

NuGOweek 2024 Ghent programme overview flyer

The binding of cosmological structures by massless topological defects

The binding of cosmological structures by massless topological defects

Applied Science: Thermodynamics, Laws & Methodology.pdf

Applied Science: Thermodynamics, Laws & Methodology.pdf

Bob Reedy - Nitrate in Texas Groundwater.pdf

Bob Reedy - Nitrate in Texas Groundwater.pdf

What is greenhouse gasses and how many gasses are there to affect the Earth.

What is greenhouse gasses and how many gasses are there to affect the Earth.

EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...

EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...

20240520 Planning a Circuit Simulator in JavaScript.pptx

20240520 Planning a Circuit Simulator in JavaScript.pptx

Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...

Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...

Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf

Topic: SICKLE CELL DISEASE IN CHILDREN-3.pdf

Chapter 12 - climate change and the energy crisis

Chapter 12 - climate change and the energy crisis

Nucleophilic Addition of carbonyl compounds.pptx

Nucleophilic Addition of carbonyl compounds.pptx

Equivariant neural networks and representation theory

Equivariant neural networks and representation theory

- 1. NUMERICAL CALCULATION OF THE HUBBLE HIERARCHY PARAMETERS AND THE OBSERVATIONAL PARAMETERS OF INFLATION MILAN MILOŠEVIĆ Department of Physics Faculty of Sciences and Mathematics University of Niš, Serbia 10th International Conference of Balkan Pysical Union (BPU10) Sofia, 26 - 30 August 2018 In collaboration with N. Bilić (Zagreb), G. S. Đorđević, D. D. Dimitrijević, M. Stojanović (Niš)
- 2. INTRODUCTION • The inflation theory proposes a period of extremely rapid (exponential) expansion of the universe during the very early stage of the universe. • Inflation is a process in which the dimensions of the universe have increased exponentially at least times. • Although inflationary cosmology has successfully complemented the Standard Model, the process of inflation, in particular its origin, is still largely unknown.
- 3. INTRODUCTION • Over the past 35 years numerous models of inflationary expansion of the universe have been proposed. • The simplest model of inflation is based on the existence of a single scalar field, which is called inflaton. • The most important ways to test inflationary cosmological models is to compare the computed and measured values of the observational parameters.
- 4. OBSERVATIONAL PARAMETERS • Hubble hierarchy (slow-roll) parameters • Length of inflation • The end of inflation • Three independent observational parameters: amplitude of scalar perturbation , tensor-to-scalar ratio and scalar spectral index Hubble expansion rate at an arbitrarily chosen time At the lowest order in parameters 𝜀 and 𝜀
- 5. OBSERVATIONAL PARAMETERS • Satellite Planck (May 2009 – October 2013) • Planck Collaboration • Latest results are published in year 2018. Planck 2015 results. XX. Constraints on inflation, Astronomy & Astrophysics. 594 (2016) A20
- 6. INFLATIONARY MODELS • The dynamics of a classical real scalar field ϕ minimally coupled to gravity • G – the gravitational constant, R - the Ricci scalar, g - the determinant of the matric tensor, and is the Lagrangian, with kinetic term • We will assume the spatially 4-dimensional flat space-time with the standard FRW metric
- 7. LAGRANGIAN OF A SCALAR FIELD - • In general case – any function of a scalar field and kinetic energy • Canonical field with potential , • Non-canonical models • Dirac-Born-Infeld (DBI) Lagrangian • Special case – tachyonic
- 8. TACHYONS • Traditionally, the word tachyon was used to describe a hypothetical particle which propagates faster than light. • In modern physics this meaning has been changed: • The effective tachyonic field theory was proposed by A. Sen • String theory: states of quantum fields with imaginary mass (i.e. negative mass squared). • However it was realized that the imaginary mass creates an instability and tachyons spontaneously decay through the process known as tachyon condensation. • Quanta are not tachyon any more, but rather an ”ordinary” particle with a positive mass.
- 9. TACHYON INFLATION • Properties of a tachyon potential • The corresponding Lagrangian and the Hamiltionian are • The Friedmann equation
- 10. DYNAMICS OF INFLATION 1. The energy-momentum conservation equation . 2. The Hamilton’s equations ℒ ̇ is the conjugate momentum and the Hamiltonian
- 11. TACHYON INFLATION • Nondimensional equations • Dimensionless constant , a choice of a constant (brane tension) was motivated by string theory ,
- 12. CONDITIONS FOR TACHYON INFLATION • General condition for inflation • Slow-roll conditions • Equations for slow-roll inflation
- 13. INITIAL CONDITION FOR TACHYON INFLATION • Slow-roll parameters • Number of e-folds
- 14. RANDAL-SUNDRUM MODELS • Randall-Sundrum (RS) model was originally proposed to solve the hierarchy problem (1999) • Later it was realized that this model, as well as any similar braneworld model, may have interesting cosmological implications • Two branes with opposite tensions are placed at some distance in 5 dimensional space • RS model – observer reside on the brane with negative tension, distance to the 2nd brane corresponds to the Netwonian gravitational constant • RSII model – observer is placed on the positive tension brane, 2nd brane is pushed to infinity
- 15. RSII MODEL • The space is described by Anti de Siter metric • Extended RSII model include radion backreaction • Total action , , , , where the second term is the action of the brane, and is the inverse of AdS5 curvature radius, ϭ is the brane tension, the is tachyon field and is the rescaled radion field .
- 16. RSII MODEL • The Lagrangian and the Hamiltonian • Conjugate momenta , , • In flat space, FRW metrics
- 17. RSII MODEL • The Hamilton’s equations • The modified Friedman equation
- 18. NONDIMENSIONAL EQUATIONS • Substitutions: 4 8 2 8 2 2 8 2 10 2 5 8 2 1 / 4 3 / 3 2 1 / 4 3 / 3 1 / h h 2 2 2 2 8 1 3 12 Gk a h a 2 2 2 2 2 2 2 2 3 4 2 2 4 2 3 1 , sinh , 6 2 sinh , 6 3 1 1 / , 2 1 1 2 1 / d d p Nondimensional constant Hubble parameter Preassure Energy density 2 2 ( ) 1 2 6 h p N h Additional equations, solved in parallel 2 4 / , / ( ), / ( )), , / ( ) h H k k k k k
- 19. INITIAL CONDITIONS FOR RSII MODEL • Initial conditions – from a model without radion field • “Pure” tachyon potential • Hamiltonian • Nondimensional equation 4 8 2 5 8 2 1 4 3 . 1 h
- 20. THE SOFTWARE • Calculation: • Programming language: C/C++ • GNU Scientific Library • Visualization and data analysis • Programming language: R
- 21. THE SOFTWARE The model The initial conditions
- 22. THE SOFTWARE Test mode = 0 IZLAZ = 0 MCM = 1 MODEL = 2 INTC = 0 NoMAX = 10000 Nmin = 45.00 Nmax = 120.00 kmin = 1.00 kmax = 12.00 phimin = 0.00 phimax = 1.00 init.conf
- 23. RESULTS
- 24. OBSERVATIONAL PARAMETERS • Scalar spectral index and tensor-to-scalar ratio (the first order of parameters ) • The second order of parameters different • Always constant , however constant for tachyon inflation in standard cosmology, and for Randall- Sundrum cosmology • Planck results ( ) .
- 25. TACHYION POTENTIAL 30 ≤ N ≤ 150, 0 ≤ κ ≤ 15
- 26. TACHYION POTENTIAL 30 ≤ N ≤ 150, 0 ≤ κ ≤ 15
- 27. TACHYION POTENTIAL 30 ≤ N ≤ 150, 0 ≤ κ ≤ 15
- 28. RSII MODEL 30 ≤ N ≤ 150, 0 ≤ κ ≤ 15,
- 29. THE BEST RESULTS: 60 ≤ N ≤ 90, 1≤ κ ≤ 10,
- 30. CONCLUSION • The software we developed and used has been applied to a limited set of models, mainly to pure tachyonic and RSII inflationary cosmological models. • In the present form it is written in such a way that its only inputs are the Hamilton’s equations and the Friedmann equation, as well as the corresponding parameters. • The program can readily be used for a much wider set of models. • To apply the program to a new model one must determine its corresponding equations and include these equations in the program only • The next steps are: to extend the program to be applicable for new and different types of inflationary models, to improve the program in such a way that only the Hamiltonian or the Lagrangian of a model are their inputs. • The corresponding system of differential equations would be determined by symbolic computation.
- 31. CONCLUSION • After these improvements the program will be published as a free software followed by appropriate documentation. • The best fitting result is obtained for . It opens good opportunity for further research based on this potential in the contest of the RSII model and the holographic cosmology. This work is supported by the SEENET-MTP Network under the ICTP grant NT-03. The financial support of the Serbian Ministry for Education and Science, Projects OI 174020 and OI 176021 is also kindly acknowledged.
- 32. THE MOST IMPORTANT REFERENCES • N. Bilic, G.B. Tupper, AdS braneworld with backreaction, Cent. Eur. J. Phys. 12 (2014) 147–159. • D. Steer, F. Vernizzi, Tachyon inflation: Tests and comparison with single scalar field inflation, Phys. Rev. D. 70 (2004) 43527. • P.A.R. Ade, N. Aghanim, M. Arnaud, F. Arroja, M. Ashdown, J. Aumont, et al., Planck 2015 results: XX. Constraints on inflation, Astron. Astrophys. 594 (2016) A20. • L. Randall, R. Sundrum, Large Mass Hierarchy from a Small Extra Dimension, Physical Review Letters. 83 (1999) 3370–3373; L. Randall, R. Sundrum, An Alternative to Compactification, Physical Review Letters. 83 (1999) 4690– 4693. • N. Bilic, D.D. Dimitrijevic, G.S. Djordjevic, M. Milosevic, Tachyon inflation in an AdS braneworld with back-reaction, International Journal of Modern Physics A. 32 (2017) 1750039. • M. Milosevic, D.D. Dimitrijevic, G.S. Djordjevic, M.D. Stojanovic, Dynamics of tachyon fields and inflation - comparison of analytical and numerical results with observation, Serbian Astronomical Journal. 192 (2016) 1–8. • M. Milosevic, G.S. Djordjevic, Tachyonic Inflation on (non-)Archimedean Spaces, Facta Universitatis (Niš) Series: Physics, Chemistry and Technology. 14 (2016) 257–274. • N. Bilic, D.D. Dimitrijevic, G.S. Djordjevic, M. Milosevic, M. Stojanovic, Dynamics of tachyon fields and inflation: Analytical vs numerical solutions, AIP Vol 1722 No 1 (2016) 50002. • G.S. Djordjevic, D.D. Dimitrijevic, M. Milosevic, On Canonical Transformation and Tachyon-Like ”Particles” in Inflationary Cosmology, Romanian Journal of Physics. 61 (2016) 99–109. • D.D. Dimitrijevic, G.S. Djordjevic, M. Milosevic, Classicalization and quantization of tachyon-like matter on (non)archimedean spaces, Romanian Reports in Physics. 68 (2016) 5–18.