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

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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 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.

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.

Soil Dynamics

This document provides an overview of soil dynamics and vibratory motion. It discusses periodic and non-periodic motion, describes simple harmonic motion using trigonometric and complex notation, and defines displacement, velocity and acceleration for vibratory systems. Fourier series are also summarized, including their trigonometric, exponential and discrete transform forms. Examples are provided to illustrate Fourier analysis and the power spectrum.

Basics1variogram

This document provides an overview of geostatistics and variogram analysis. It discusses how the variogram describes the spatial correlation of a phenomenon through parameters like the nugget effect and range. Experimental variograms are calculated from data and theoretical models like spherical, exponential, and power models are fitted. The variogram can identify different correlation scales through nested models. Components at different scales can be extracted through kriging. As an example, fertility data from France is analyzed to filter its large-scale spatial structure.

Soil dyn __3 corr

This document discusses wave propagation in soils and geologic materials. It begins by outlining the topics to be covered, which include waves in unbounded media, waves in a semi-infinite body like the Earth's surface, and waves in layered bodies. For unbounded media, it derives the one-dimensional and three-dimensional wave equations and solves them for different wave types. It also examines Rayleigh and Love waves that propagate along the surface of a semi-infinite solid. The goal is to describe dynamic soil response in terms of wave propagation.

Introduction geostatistic for_mineral_resources

This document provides an agenda for a presentation on geostatistics for mineral deposits. The presentation will cover topics such as sampling, geostatistics part 1 and 2, and estimations. It will include breaks between sessions and conclude with a discussion period. Sampling topics include an overview of sampling theory and nomographs, while geostatistics sessions will cover variograms, kriging, and simulations. Estimation methods like inverse distance, kriging, and recoverable resources will also be discussed.

Soil dyn __2

This document discusses dynamics of discrete systems, including:
- Single degree of freedom systems (SDOF), their equations of motion, and response to forced and free vibrations
- Damping mechanisms like viscous damping and how they affect system response
- Multiple degree of freedom systems and their equations of motion
It provides examples of undamped and damped SDOF system responses to different loading conditions.

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 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.

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.

Soil Dynamics

This document provides an overview of soil dynamics and vibratory motion. It discusses periodic and non-periodic motion, describes simple harmonic motion using trigonometric and complex notation, and defines displacement, velocity and acceleration for vibratory systems. Fourier series are also summarized, including their trigonometric, exponential and discrete transform forms. Examples are provided to illustrate Fourier analysis and the power spectrum.

Basics1variogram

This document provides an overview of geostatistics and variogram analysis. It discusses how the variogram describes the spatial correlation of a phenomenon through parameters like the nugget effect and range. Experimental variograms are calculated from data and theoretical models like spherical, exponential, and power models are fitted. The variogram can identify different correlation scales through nested models. Components at different scales can be extracted through kriging. As an example, fertility data from France is analyzed to filter its large-scale spatial structure.

Soil dyn __3 corr

This document discusses wave propagation in soils and geologic materials. It begins by outlining the topics to be covered, which include waves in unbounded media, waves in a semi-infinite body like the Earth's surface, and waves in layered bodies. For unbounded media, it derives the one-dimensional and three-dimensional wave equations and solves them for different wave types. It also examines Rayleigh and Love waves that propagate along the surface of a semi-infinite solid. The goal is to describe dynamic soil response in terms of wave propagation.

Introduction geostatistic for_mineral_resources

This document provides an agenda for a presentation on geostatistics for mineral deposits. The presentation will cover topics such as sampling, geostatistics part 1 and 2, and estimations. It will include breaks between sessions and conclude with a discussion period. Sampling topics include an overview of sampling theory and nomographs, while geostatistics sessions will cover variograms, kriging, and simulations. Estimation methods like inverse distance, kriging, and recoverable resources will also be discussed.

Soil dyn __2

This document discusses dynamics of discrete systems, including:
- Single degree of freedom systems (SDOF), their equations of motion, and response to forced and free vibrations
- Damping mechanisms like viscous damping and how they affect system response
- Multiple degree of freedom systems and their equations of motion
It provides examples of undamped and damped SDOF system responses to different loading conditions.

Parabolic Restricted Three Body Problem

Dynamical generation of bridges and tails between galaxy close encounters using the Parabolic RTBP model

The Shifting Seasonal Mean Autoregressive Model and Seasonality in the Centra...

Changli He, Jian Kang and Timo Teräsvirta
Tianjin University of Finance and Economics
CREATES, Aarhus University
C.A.S.E., Humboldt-Universität zu Berlin
Seminar at Eesti pank
21 September 2017

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.

Ground Response Analysis - Geotechnical Earthquake engineering

This document discusses ground response analysis and one-dimensional ground response analysis approaches. It covers linear and non-linear approaches. The linear approach uses transfer functions to directly solve for site response but does not account for soil non-linearity. The non-linear approach uses an equivalent linear approach or fully non-linear approach. The equivalent linear approach performs multiple iterations to determine equivalent linear soil properties representing average shear response.

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.

Introduction to second gradient theory of elasticity - Arjun Narayanan

This document introduces higher gradient theories of elasticity. It begins with an overview of how gradients appear in classical field theories like Newtonian gravity and Einsteinian gravity. It then discusses how higher gradients are relevant to continuum mechanics. The remainder of the document outlines the mathematical and variational framework for developing higher gradient elasticity theories. This includes discussions of geometric notions, variational principles, obtaining the strong form of the governing equations, and finite element discretization methods.

Kgeppt spvm 0_try1

This document summarizes work exploring the Klein-Gordon field near the event horizon of a Schwarzschild black hole. Near the horizon, the radial equation of motion for the scalar field is approximated and shown to have oscillatory solutions. Using Eddington-Finkelstein coordinates, the solutions are recast into outgoing and ingoing waves with different properties on each side of the event horizon. Future work is outlined to examine the parametrized wave solutions, Fourier components, and derive Hawking radiation and temperature from the black body spectrum at infinity.

CLIM: Transition Workshop - Overview and New Modeling Directions - Dorit Hamm...

CLIM: Transition Workshop - Overview and New Modeling Directions - Dorit Hamm...The Statistical and Applied Mathematical Sciences Institute

This document discusses climate change detection and attribution (D&A). The goal of D&A is to determine whether observed climate changes are caused by internal variability or external forcings like human activities. Regression models are commonly used to attribute observed temperature changes to different forcings, but there are challenges due to uncertainties in observations and model simulations. The document proposes a Bayesian hierarchical model to account for these uncertainties and estimate the contribution of each forcing factor while representing climate variability. This approach frames D&A as a Bayesian statistical inference problem to provide probabilistic attribution statements.Soil Dynamics - Local Site Effects - Ground response - Geotechnical Earthquak...

Soil Dynamics - Local Site Effects - Ground response - Geotechnical Earthquak...Cristian Soriano-Camelo

Soil dynamics, site efects, DEEPSOIL examples, earthquake geotechnical engineering, ground response, local site effects.Comments_on_Paper_Shuey_1985

Shuey's 1985 paper rewrote Aki and Richards' equation for reflection coefficients using Poisson's ratio σ instead of shear velocity Vs. This allowed the equation to be expressed as a function of increasing incident angle θ. Shuey's equation separates elastic parameters from angular functions, showing which parameter combinations are effective at different θ values. It explains and justifies Koefoed's empirical rules from 1955. Today, Shuey's equation is commonly approximated linearly for θ < 30° and used to extract information about subsurface properties like ∆σ from AVO analysis.

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.Outgoing ingoingkleingordon spvmforminit1 - copy - copy

This document summarizes the solutions to the Klein-Gordon equation of motion for a scalar field in the background of a Schwarzschild spacetime metric near a black hole. Very near the event horizon, the radial equation is approximated as an oscillatory solution in the Regge-Wheeler coordinate. These solutions are then expressed as outgoing and ingoing waves using Eddington-Finkelstein coordinates. While the outgoing waves have regular behavior at the future event horizon, the ingoing waves hit the future event horizon in finite coordinate time as the radial coordinate approaches negative infinity.

GSA-BBO HYBRIDIZATION ALGORITHM

IT IS ABOUT FUSION OF TWO NATURE INSPIRED OPTIMIZATION ALGORITHM(S).THE FIRST ONE IS GRAVITATIONAL SEARCH ALGORITHM(GSA) BASED ON NEWTONS UNIVERSAL LAW OF GRAVITATION AND OTHER ONE i.e; BIOGEOGRAPHY BASED OPTIMIZATION(BBO) BASED ON BIOGEOGRAPGY (THE STUDY OF SPECIES IN A PARTICULAR HABITAT).

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.

Application of vector integration

This document discusses the application of vector integration in various domains. It begins by defining vector calculus concepts like del, gradient, curl, and divergence. It then presents several theorems of vector integration. Next, it explains how vector integration can be used to find the rate of change of fluid mass and analyze fluid circulation, vorticity, and the Bjerknes Circulation Theorem regarding sea breezes. It also discusses using vector calculus concepts in electricity and magnetism.

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.

Trends in daily rainfall erosivity in relation with NAO, MO and WeMO for Spai...

The document discusses trends in daily rainfall erosivity in northeastern Spain from 1955 to 2006 and its relationship to atmospheric teleconnection patterns. It finds increasing rainfall erosivity at annual and seasonal scales over this time period. At the daily scale, there was an increase in high erosivity events and a decrease in low erosivity events. These trends are likely related to changes in atmospheric circulation patterns like the North Atlantic Oscillation, Mediterranean Oscillation, and Western Mediterranean Oscillation, which influence rainfall characteristics and erosivity. The phases of these teleconnection patterns impact average daily erosivity.

Wd equation

This document summarizes Juan M Guerra's presentation on the Weyl-Dirac equation in condensed matter physics and graphene. It discusses Dirac's original equation, the Dirac and Weyl Lagrangians, the massless Weyl equation and its two uncoupled components. It also covers Weyl's gauge theory formulation, the Klein paradox of chiral tunneling, applications to graphene and nanotubes where electrons behave as Dirac particles, and ongoing research on electric transport in graphene nanostructures.

ABOUT MODELLING OF THE GRAVITATIONAL FIELDS

Within the framework of the general theory of relativity (GR) the modeling of the central symmetrical
gravitational field is considered. The mapping of the geodesic motion of the Lemetr and Tolman basis on
their motion in the Minkowski space on the world lines is determined. The expression for the field intensity
and energy where these bases move is obtained. The advantage coordinate system is found, the coordinates
and the time of the system coincide with the Galilean coordinates and the time in the Minkowski space.

Chapter 1: Physical Quantities Unit, And Vectors

This document provides an overview of foundation and materials science studies, including physics and mathematics. It covers topics such as physical quantities and units, scalars and vectors, and multiplication of vectors. Specifically, it defines basic and derived physical quantities and their SI units. It also describes vector addition and subtraction graphically using parallelograms and triangles. Vector components are resolved into x- and y-axes and unit vectors. Scalar (dot) and vector (cross) products are defined, with scalar products providing the parallel component between two vectors and vector products determining the perpendicular component. Formulas for various physical quantities like work and momentum are also presented.

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.

Numerical Calculation of the Hubble Hierarchy Parameters and the Observationa...

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.

Parabolic Restricted Three Body Problem

Dynamical generation of bridges and tails between galaxy close encounters using the Parabolic RTBP model

The Shifting Seasonal Mean Autoregressive Model and Seasonality in the Centra...

Changli He, Jian Kang and Timo Teräsvirta
Tianjin University of Finance and Economics
CREATES, Aarhus University
C.A.S.E., Humboldt-Universität zu Berlin
Seminar at Eesti pank
21 September 2017

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.

Ground Response Analysis - Geotechnical Earthquake engineering

This document discusses ground response analysis and one-dimensional ground response analysis approaches. It covers linear and non-linear approaches. The linear approach uses transfer functions to directly solve for site response but does not account for soil non-linearity. The non-linear approach uses an equivalent linear approach or fully non-linear approach. The equivalent linear approach performs multiple iterations to determine equivalent linear soil properties representing average shear response.

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.

Introduction to second gradient theory of elasticity - Arjun Narayanan

This document introduces higher gradient theories of elasticity. It begins with an overview of how gradients appear in classical field theories like Newtonian gravity and Einsteinian gravity. It then discusses how higher gradients are relevant to continuum mechanics. The remainder of the document outlines the mathematical and variational framework for developing higher gradient elasticity theories. This includes discussions of geometric notions, variational principles, obtaining the strong form of the governing equations, and finite element discretization methods.

Kgeppt spvm 0_try1

This document summarizes work exploring the Klein-Gordon field near the event horizon of a Schwarzschild black hole. Near the horizon, the radial equation of motion for the scalar field is approximated and shown to have oscillatory solutions. Using Eddington-Finkelstein coordinates, the solutions are recast into outgoing and ingoing waves with different properties on each side of the event horizon. Future work is outlined to examine the parametrized wave solutions, Fourier components, and derive Hawking radiation and temperature from the black body spectrum at infinity.

CLIM: Transition Workshop - Overview and New Modeling Directions - Dorit Hamm...

CLIM: Transition Workshop - Overview and New Modeling Directions - Dorit Hamm...The Statistical and Applied Mathematical Sciences Institute

This document discusses climate change detection and attribution (D&A). The goal of D&A is to determine whether observed climate changes are caused by internal variability or external forcings like human activities. Regression models are commonly used to attribute observed temperature changes to different forcings, but there are challenges due to uncertainties in observations and model simulations. The document proposes a Bayesian hierarchical model to account for these uncertainties and estimate the contribution of each forcing factor while representing climate variability. This approach frames D&A as a Bayesian statistical inference problem to provide probabilistic attribution statements.Soil Dynamics - Local Site Effects - Ground response - Geotechnical Earthquak...

Soil Dynamics - Local Site Effects - Ground response - Geotechnical Earthquak...Cristian Soriano-Camelo

Soil dynamics, site efects, DEEPSOIL examples, earthquake geotechnical engineering, ground response, local site effects.Comments_on_Paper_Shuey_1985

Shuey's 1985 paper rewrote Aki and Richards' equation for reflection coefficients using Poisson's ratio σ instead of shear velocity Vs. This allowed the equation to be expressed as a function of increasing incident angle θ. Shuey's equation separates elastic parameters from angular functions, showing which parameter combinations are effective at different θ values. It explains and justifies Koefoed's empirical rules from 1955. Today, Shuey's equation is commonly approximated linearly for θ < 30° and used to extract information about subsurface properties like ∆σ from AVO analysis.

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.Outgoing ingoingkleingordon spvmforminit1 - copy - copy

This document summarizes the solutions to the Klein-Gordon equation of motion for a scalar field in the background of a Schwarzschild spacetime metric near a black hole. Very near the event horizon, the radial equation is approximated as an oscillatory solution in the Regge-Wheeler coordinate. These solutions are then expressed as outgoing and ingoing waves using Eddington-Finkelstein coordinates. While the outgoing waves have regular behavior at the future event horizon, the ingoing waves hit the future event horizon in finite coordinate time as the radial coordinate approaches negative infinity.

GSA-BBO HYBRIDIZATION ALGORITHM

IT IS ABOUT FUSION OF TWO NATURE INSPIRED OPTIMIZATION ALGORITHM(S).THE FIRST ONE IS GRAVITATIONAL SEARCH ALGORITHM(GSA) BASED ON NEWTONS UNIVERSAL LAW OF GRAVITATION AND OTHER ONE i.e; BIOGEOGRAPHY BASED OPTIMIZATION(BBO) BASED ON BIOGEOGRAPGY (THE STUDY OF SPECIES IN A PARTICULAR HABITAT).

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.

Application of vector integration

This document discusses the application of vector integration in various domains. It begins by defining vector calculus concepts like del, gradient, curl, and divergence. It then presents several theorems of vector integration. Next, it explains how vector integration can be used to find the rate of change of fluid mass and analyze fluid circulation, vorticity, and the Bjerknes Circulation Theorem regarding sea breezes. It also discusses using vector calculus concepts in electricity and magnetism.

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.

Trends in daily rainfall erosivity in relation with NAO, MO and WeMO for Spai...

The document discusses trends in daily rainfall erosivity in northeastern Spain from 1955 to 2006 and its relationship to atmospheric teleconnection patterns. It finds increasing rainfall erosivity at annual and seasonal scales over this time period. At the daily scale, there was an increase in high erosivity events and a decrease in low erosivity events. These trends are likely related to changes in atmospheric circulation patterns like the North Atlantic Oscillation, Mediterranean Oscillation, and Western Mediterranean Oscillation, which influence rainfall characteristics and erosivity. The phases of these teleconnection patterns impact average daily erosivity.

Wd equation

This document summarizes Juan M Guerra's presentation on the Weyl-Dirac equation in condensed matter physics and graphene. It discusses Dirac's original equation, the Dirac and Weyl Lagrangians, the massless Weyl equation and its two uncoupled components. It also covers Weyl's gauge theory formulation, the Klein paradox of chiral tunneling, applications to graphene and nanotubes where electrons behave as Dirac particles, and ongoing research on electric transport in graphene nanostructures.

ABOUT MODELLING OF THE GRAVITATIONAL FIELDS

Within the framework of the general theory of relativity (GR) the modeling of the central symmetrical
gravitational field is considered. The mapping of the geodesic motion of the Lemetr and Tolman basis on
their motion in the Minkowski space on the world lines is determined. The expression for the field intensity
and energy where these bases move is obtained. The advantage coordinate system is found, the coordinates
and the time of the system coincide with the Galilean coordinates and the time in the Minkowski space.

Chapter 1: Physical Quantities Unit, And Vectors

This document provides an overview of foundation and materials science studies, including physics and mathematics. It covers topics such as physical quantities and units, scalars and vectors, and multiplication of vectors. Specifically, it defines basic and derived physical quantities and their SI units. It also describes vector addition and subtraction graphically using parallelograms and triangles. Vector components are resolved into x- and y-axes and unit vectors. Scalar (dot) and vector (cross) products are defined, with scalar products providing the parallel component between two vectors and vector products determining the perpendicular component. Formulas for various physical quantities like work and momentum are also presented.

Parabolic Restricted Three Body Problem

Parabolic Restricted Three Body Problem

The Shifting Seasonal Mean Autoregressive Model and Seasonality in the Centra...

The Shifting Seasonal Mean Autoregressive Model and Seasonality in the Centra...

Tachyon inflation in DBI and RSII context

Tachyon inflation in DBI and RSII context

Ground Response Analysis - Geotechnical Earthquake engineering

Ground Response Analysis - Geotechnical Earthquake engineering

Dragoljub Dimitrijević "Tachyon Inflation in the RSII Framework"

Dragoljub Dimitrijević "Tachyon Inflation in the RSII Framework"

Introduction to second gradient theory of elasticity - Arjun Narayanan

Introduction to second gradient theory of elasticity - Arjun Narayanan

Kgeppt spvm 0_try1

Kgeppt spvm 0_try1

CLIM: Transition Workshop - Overview and New Modeling Directions - Dorit Hamm...

CLIM: Transition Workshop - Overview and New Modeling Directions - Dorit Hamm...

Soil Dynamics - Local Site Effects - Ground response - Geotechnical Earthquak...

Soil Dynamics - Local Site Effects - Ground response - Geotechnical Earthquak...

Comments_on_Paper_Shuey_1985

Comments_on_Paper_Shuey_1985

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

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

Outgoing ingoingkleingordon spvmforminit1 - copy - copy

Outgoing ingoingkleingordon spvmforminit1 - copy - copy

GSA-BBO HYBRIDIZATION ALGORITHM

GSA-BBO HYBRIDIZATION ALGORITHM

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

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

Application of vector integration

Application of vector integration

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

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

Trends in daily rainfall erosivity in relation with NAO, MO and WeMO for Spai...

Trends in daily rainfall erosivity in relation with NAO, MO and WeMO for Spai...

Wd equation

Wd equation

ABOUT MODELLING OF THE GRAVITATIONAL FIELDS

ABOUT MODELLING OF THE GRAVITATIONAL FIELDS

Chapter 1: Physical Quantities Unit, And Vectors

Chapter 1: Physical Quantities Unit, And Vectors

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.

Numerical Calculation of the Hubble Hierarchy Parameters and the Observationa...

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.

The Dark Side of the Universe

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

Biermann - Quarks and the Cosmos

This document summarizes Michael S. Turner's 2009 Biermann Lectures on "Quarks and the Cosmos". The lectures covered three topics: I) Cosmic Acceleration and Dark Energy, II) Inflation and Beyond, and III) Future Opportunities and Challenges. Key ideas discussed include the connections between fundamental physics (quarks) and the large-scale structure of the universe, the evidence supporting inflation as the mechanism that seeded structure formation in the early universe, and ongoing efforts to test inflation through precision cosmology experiments seeking to detect gravitational waves in the cosmic microwave background.

Ms 1341-p touze-final

The document discusses refraction modeling and experiments to better understand refraction effects. Key points:
- Experiments using reciprocal simultaneous observations found refraction coefficients (k values) close to zero rather than the typical 0.13 value, indicating refraction is more complex.
- Adjusting a monitoring network found the optimal k value was -2.12 rather than the assumed 0.13, and a stochastic model accounting for zenith angle noise improved results.
- An experiment measuring a triangle closer to a wall found increasing angular errors correlated with decreasing distance from the wall, supporting an asymmetrical refraction model.
- A proposed generalized 3D refraction model accounts for gradient direction, station orientation, and as

Quantum gravity phenomenology: Minimal length

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- 1. OBSERVATIONAL PARAMETERS OF INFLATION IN HOLOGRAPHIC COSMOLOGY MILAN MILOŠEVIĆ Faculty of Sciences And Mathematics University of Niš, Serbia & SEENET-MTP Centre Workshop on Quantum Fields and Nonlinear Phenomena 27 September 2020 in collaboration with: N. Bilić (Zagreb), G.S. Djordjević, D.D. Dimitrijević and M. Stojanović (Niš) This work has been supported by the Serbian Ministry for Education, Science and Technological Development under the project No. 176021 and contract No. 451-03-68/2020-14/200124, as well as the ICTP - SEENET-MTP project NT-03 Cosmology-Classical and Quantum Challenges
- 2. INTRODUCTION • The inflation theory proposes a period of extremely rapid (exponential) expansion of the universe during the an early stage of evolution of the universe. • The inflation theory predicts that during inflation (it takes about 10−34 𝑠) radius of the universe increased, at least 𝑒60 ≈ 1026 times. • Although inflationary cosmology has successfully complemented the Standard Model, the process of inflation, in particular its origin, is still largely unknown. • Recent years brought us a lot of evidence from WMAP and Planck observations of the CMB • The most important way to test inflationary cosmological models is to compare the computed and measured values of the observational parameters. Figure: Baumann, D. TASI Lectures on Inflation. (2009), arXiv:0907.5424 [hep-th]
- 3. BRANEWORLD COSMOLOGY • Braneworld universe is based on the scenario in which matter is confined on a brane moving in the higher dimensional bulk with only gravity allowed to propagate in the bulk. • One of the simplest models - Randall-Sundrum (RS) • 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, the 2nd brane is pushed to infinity 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. N. Bilic, G.B. Tupper, AdS braneworld with backreaction, Cent. Eur. J. Phys. 12 (2014) 147–159.
- 4. HOLOGRAPHIC BRANEWORLD • Holographic braneworld - a cosmology based on the effective four-dimensional Einstein equations on the holographic boundary in the framework of anti de Sitter/conformal field theory (AdS/CFT) correspondence. • The model is based on a holographic braneworld scenario with an effective tachyon field on a D3-brane located at the holographic boundary of an asymptotic AdS5 bulk. • The cosmology is governed by matter on the brane in addition to the boundary CFT time Conformal boundary at z=0 space z xRSII brane at z=zbr N. Bilić, Randall-Sundrum vs Holographic Cosmology, IRB (2015)
- 5. HOLOGRAPHIC TACHYON COSMOLOGY • The holographic braneworld is a spatially flat FRW universe with line element ൯𝑑𝑠2 = 𝑔 𝜇𝜈 𝑑𝑥 𝜇 𝑑𝑥 𝜈 = 𝑑𝑡2 − 𝑎2(𝑡)(𝑑𝑟2 + 𝑟2 𝑑𝛺2 • The holographic Friedmann equations • Where the scale 𝓁 can be identified with the AdS curvature radius and we introduced a dimensionless expansion rate ℎ ≡ 𝓁𝐻 and the fundamental dimensionless coupling ℎ2 − 𝓁2 4 ℎ4 = 𝜅2 3 𝓁4 𝜌 ሶℎ 1 − 𝓁2 2 ℎ2 = − 𝜅2 3 𝓁3(𝑝 + 𝜌) Standard cosmology: ℎ2 = 𝜅2 3 𝜌 ሶℎ = − 𝜅2 2 (𝑝 + 𝜌) 𝜅2 = 8𝜋𝐺 𝑁 𝓁2 Bilić, N., Dimitrijević, D. D., Djordjevic, G. S., Milošević, M. & Stojanović, M. Tachyon inflation in the holographic braneworld. Journal of Cosmology and Astroparticle Physics 2019, 034–034 (2019).
- 6. HOLOGRAPHIC TACHYON COSMOLOGY • Interesting property - solving the first Friedmann equation as a quadratic equation ℎ2 = 2 1 ± 1 − 𝜅2 3 𝓁4 𝜌 • We do not want our modified cosmology to depart too much from the standard cosmology after the inflation era and demand that this equation reduces to the standard Friedmann equation in the low density limit 𝜅2 𝓁4 𝜌 ≪ 1 • This demand will be met only by the (−) sign solution. We discard the (+) sign solution as unphysical.
- 7. HOLOGRAPHIC TACHYON COSMOLOGY • The physical range of the Hubble expansion rate is between ℎmin = 0 and the maximal value ℎmax = 2 • It corresponds to the maximal energy density 𝜌max = Τ3 𝜅2 𝓁4 • Assuming no violation of the weak energy condition 𝑝 + 𝜌 ≥ 0, the expansion rate will be a monotonously decreasing function of time. • The universe starts from 𝑡 = 0 with an initial ℎ𝑖 ≤ ℎ 𝑚𝑎𝑥 with energy density and cosmological scale both finite. • The Big Bang singularity is avoided. Bilić, N., Dimitrijević, D. D., Djordjevic, G. S., Milošević, M. & Stojanović, M. Tachyon inflation in the holographic braneworld. JCAP, 034–034 (2019).
- 8. EQUATIONS OF MOTION • Tachyon matter in the holographic braneworld is described by the DBI Lagrangian and the Hamiltonian ℒ = −𝓁−4 𝑉( Τ𝜃 𝓁) 1 − 𝑔 𝜇𝜈 𝜃,𝜇 𝜃,𝜈 ℋ = 𝓁−4 𝑉 1 + 𝜂2 where 𝜂 = 𝑔 𝜇𝜈 𝜋 𝜇 𝜋 𝜈 𝓁4 𝑉 . • As usual, the conjugate momentum is 𝜋 𝜇 = 𝜕ℒ 𝜕𝜃,𝜇 • The Hamilton equations are 𝜃,𝜇 = 𝜕ℋ 𝜕𝜋 𝜇 𝜋;𝜇 𝜇 = − 𝜕ℋ 𝜕𝜃
- 9. EQUATIONS OF MOTION • The equations of motions ሶ𝜃 = 𝜂 1 + 𝜂2 ሶ𝜂 = − 3ℎ𝜂 𝓁 − 𝑉,𝜃 𝑉 1 + 𝜂2 + 𝜂2 1 + 𝜂2 • As usual, the pressure and energy density are equal to Lagrangian and Hamiltonian 𝑝 ≡ ℒ = −𝓁−4 𝑉 1 − ሶ𝜃2 = − 𝓁−4 𝑉 1 − 𝜂2 𝜌 ≡ ℋ = 𝓁−4 𝑉 1 − ሶ𝜃2 = 𝓁−4 𝑉 1 − 𝜂2
- 10. INITIAL CONDITIONS • Two natural initial conditions a) 𝜂𝑖 = 0 b) ሶ𝜂𝑖 = 0 • The condition: • (a) assures a finite initial ሶℎ, and • (b) provides the solution consistent with the slow-roll regime
- 11. A) 𝜂𝑖 = 0 • 0 < ℎ𝑖 < 2 • From 𝑝 = − 𝓁−4 𝑉 1−𝜂2 and 𝜌 = 𝓁−4 𝑉 1 − 𝜂2 it follows 𝑝𝑖 = −𝜌𝑖 • From ℎ2 − 𝓁2 4 ℎ4 = 𝜅2 3 𝓁4 𝜌 and 𝜌 = 𝓁−4 𝑉 1− ሶ𝜃2 the initial 𝜃𝑖 can be fixed 𝑉 𝜃𝑖 = 3 𝜅2 ℎ𝑖 2 − ℎ𝑖 4 4
- 12. B) ሶ𝜂𝑖 = 0 • From EqM we have 𝜂𝑖 = − 2 𝓁 Τ𝑉,𝜃 𝑉 𝑖 9ℎ 𝑖 2 −4 𝓁 Τ𝑉,𝜃 𝑉 𝑖 2 +3 9ℎ 𝑖 4 −4ℎ 𝑖 2 𝓁 Τ𝑉,𝜃 𝑉 𝑖 2 • From Friedmann equations we obtain 1 − ℎ𝑖 2 2 2 = 1 − 𝜅2 3 𝑉 𝜃𝑖 1 + 𝜂𝑖 2 • Random numbers: ℎ𝑖, 𝜅 and parameters in the potential 𝑉 𝜃 • Numerical solutions: 𝜂𝑖 and 𝜃𝑖 • Not easy to solve, sometimes the real solution doesn’t exist, etc 𝑉 = 𝑉 𝜃 𝑉′𝜃 = 𝑑𝑉(𝜃) 𝑑𝜃
- 13. B) ሶ𝜂𝑖 = 0 • A different way • Random numbers ℎ𝑖, 𝜃𝑖 and parameters in the potential 𝑉 𝜃 𝜅2 = )3𝑉(𝜃𝑖 1 + 𝜂𝑖 2 1 − 1 − ℎ𝑖 2 2 2 and calculate 𝜂𝑖 in the same way as in the previous way.
- 14. THE SLOW-ROLL PARAMETERS • Number of e-folds 𝑁 𝑡 = න 𝑡 𝐶𝑀𝐵 𝑡 𝑒𝑛𝑑 𝐻 𝑡 𝑑𝑡 • Hubble hierarchy (slow-roll) parameters 𝜀𝑖+1 ≡ 𝑑ln|𝜀𝑖| 𝑑𝑁 , 𝑖 ≥ 0, 𝜀0 ≡ 𝐻∗ 𝐻 where 𝐻∗ is the Hubble parameter at some chosen time • The first two 𝜀 parameters 𝜀1 = − ሶ𝐻 𝐻2, 𝜀2 = 2𝜀1 + ሷ𝐻 𝐻 ሶ𝐻 , etc. • The end of inflation 𝜀𝑖(𝜙 𝑒𝑛𝑑) ≈ 1 𝜙 𝑒𝑛𝑑 = 𝜙(𝑡 𝑒𝑛𝑑)
- 15. OBSERVATIONAL PARAMETERS • Three independent observational parameters: amplitude of scalar perturbation 𝐴 𝑠, tensor-to-scalar ratio 𝑟 and scalar spectral index 𝑛 𝑠 𝑟 = 16𝜀1(𝜙𝑖) 𝑛 𝑠 = 1 − 2𝜀1(𝜙𝑖) − 𝜀2(𝜙𝑖) • Satellite Planck (May 2009 – October 2013) • Planck Collaboration • The latest results were published in 2018. At the lowest order in parameters 𝜀1 and 𝜀2 Planck 2018 results. X Constraints on inflation, arXiv:1807.06211 [astro-ph.CO]
- 16. OBSERVATIONAL PARAMETERS 𝑛 𝑠, 𝑟 𝑟 = 16𝜀1 1 + 𝐶𝜀2 + )2(2 − ℎ2 )3(4 − ℎ2 𝑝𝑝,𝑋𝑋 𝑝,𝑋 2 𝜀1 𝑛s = 1 − 2𝜀1 − 𝜀2 − 2 + 8ℎ2 3 4 − ℎ2 2 𝑝𝑝,𝑋𝑋 𝑝,𝑋 2 𝜀1 2 − 3 + 2𝐶 + )2(2 − ℎ2 )3(4 − ℎ2 𝑝𝑝,𝑋𝑋 𝑝,𝑋 2 𝜀1 𝜀2 − 𝐶𝜀2 𝜀3 • For 𝑋 = ሶ𝜃2 and 𝑝 = −𝑉 1 − 𝑋 we have 𝑝𝑝,𝑋𝑋 𝑝,𝑋 2 = −1 Bertini, N. R., Bilic, N. & Rodrigues, D. C. Primordial perturbations and inflation in holographic cosmology. arXiv:2007.02332 [gr-qc]
- 17. POTENTIALS 𝑽 𝜽 = 𝟏 𝒄𝒐𝒔𝒉(𝝎𝜽) 𝑽 𝜽 = (𝟏 + 𝜽)𝒆−𝝎𝜽
- 18. 𝑽 𝜽 = 𝟏 𝒄𝒐𝒔𝒉(𝝎𝜽)
- 19. 𝑽 𝜽 = 𝟏 𝒄𝒐𝒔𝒉(𝝎𝜽) 60 < 𝑁 < 90 0 < 𝜔 < 0.25 0 < 𝜃𝑖 < 20 Colour represents the number of 𝑛 𝑠, 𝑟 points in a hexagon
- 20. 𝑽 𝜽 = 𝟏 𝒄𝒐𝒔𝒉(𝝎𝜽)
- 21. 𝑽 𝜽 = 𝟏 𝒄𝒐𝒔𝒉(𝝎𝜽) - THE BEST FITTING RESULTS
- 23. 𝑽 𝜽 = (𝟏 + 𝜽)𝒆−𝝎𝜽
- 24. 𝑽 𝜽 = (𝟏 + 𝜽)𝒆−𝝎𝜽 60 < 𝑁 < 90 0 < 𝜔 < 0.25 0 < 𝜃𝑖 < 20
- 25. 𝑽 𝜽 = (𝟏 + 𝜽)𝒆−𝝎𝜽
- 26. 𝑽 𝜽 = (𝟏 + 𝜽)𝒆−𝝎𝜽 - THE BEST FITTING RESULTS
- 27. CONCLUSIONS • We discussed a model of tachyon inflation based on a holographic braneworld scenario with a brane located at the boundary of the AdS5 bulk. • We simulated observational parameters of inflation for two potentials 𝑽 𝜽 = 𝟏 𝒄𝒐𝒔𝒉(𝝎𝜽) , 𝑽 𝜽 = (𝟏 + 𝜽)𝒆−𝝎𝜽 • The agreement of our model with the Planck observational data is good, especially for a higher number of e-folds. • Preliminary results are promising and open good opportunity for further analytical research of these potentials. This work has been supported by the Serbian Ministry for Education, Science and Technological Development under the project No. 176021 and contract No. 451-03-68/2020-14/200124, as well as the ICTP - SEENET-MTP project NT-03 Cosmology-Classical and Quantum Challenges
- 28. REFERENCES 1. Bilić, N., Dimitrijević, D. D., Djordjevic, G. S., Milošević, M. & Stojanović, M. Tachyon inflation in the holographic braneworld. Journal of Cosmology and Astroparticle Physics 2019, 034–034 (2019). 2. 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. 3. N.R. Bertini, N. Bilic & D.C. Rodrigues, Primordial perturbations and inflation in holographic cosmology. arXiv:2007.02332 [gr-qc]. 4. N. Bilić, Holographic cosmology and tachyon inflation. International Journal of Modern Physics A 33, 1845004 (2018). 5. N. Bilić, Randall-Sundrum versus holographic cosmology, Phys. Rev. D 93 (2016) 066010 [arXiv:1511.07323]