A Global Approach with Cutoff Exponential Function, Mathematically Well Defined at the Outset, for Calculating the Casimir Energy: The Example of Scalar Field
A global approach with cutoff exponential functions is used to obtain the Casimir energy of a massless scalar field in the presence of a spherical shell. The proposed method, mathematically well defined at the outset, makes use of two regulators, one of them to make the sum of the orders
of Bessel functions finite and the other to regularize the integral involving the zeros of Bessel function. This procedure ensures a consistent mathematical handling in the calculations of the Casimir energy and allows a major comprehension on the regularization process when nontrivial symmetries are under consideration. In particular, we determine the Casimir energy of a scalar field, showing all kinds of divergences. We consider separately the contributions of the inner and outer regions of a spherical shell and show that the results obtained are in agreement with those known in the literature, and this gives a confirmation for the consistence of the proposed approach. The choice of the scalar field was due to its simplicity in terms of physical quantity spin.
Publication Name: Advances in High Energy Physics.
Author: M.S.R. Miltão and Franz A. Farias.
Lecture 3: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
Lecture 6: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
Superconductivity and Spin Density Wave (SDW) in NaFe1-xCoxAsEditor IJCATR
A model is presented utilizing a Hamiltonian with equal spin singlet and triplet pairings based on quantum field theory and
green function formalism, to show the correlation between the superconducting and spin density wave (SDW) order parameters. The
model exhibits a distinct possibility of the coexistence of superconductivity and long-range magnetic phase, which are two usually
incompatible cooperative phenomena. The work is motivated by the recent experimental evidences on high-TC superconductivity in
the FeAs-based superconductors. The theoretical results are then applied to show the coexistence of superconductivity and spin density
wave (SDW) in NaFe1-xCoxAs.
Lecture 4: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
Lecture 3: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
Lecture 6: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
Superconductivity and Spin Density Wave (SDW) in NaFe1-xCoxAsEditor IJCATR
A model is presented utilizing a Hamiltonian with equal spin singlet and triplet pairings based on quantum field theory and
green function formalism, to show the correlation between the superconducting and spin density wave (SDW) order parameters. The
model exhibits a distinct possibility of the coexistence of superconductivity and long-range magnetic phase, which are two usually
incompatible cooperative phenomena. The work is motivated by the recent experimental evidences on high-TC superconductivity in
the FeAs-based superconductors. The theoretical results are then applied to show the coexistence of superconductivity and spin density
wave (SDW) in NaFe1-xCoxAs.
Lecture 4: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
Lecture 2: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
I am Ben R. I am a Statistics Assignment Expert at statisticshomeworkhelper.com. I hold a Ph.D. in Statistics, from University of Denver, USA. I have been helping students with their homework for the past 5 years. I solve assignments related to Statistics.
Visit statisticshomeworkhelper.com or email info@statisticshomeworkhelper.com.
You can also call on +1 678 648 4277 for any assistance with Statistics Assignment.
Energy Grid Theorem.
«For a stable electrical network without sources and energy storage the value of its streams coincide with the solution of optimization task of energy streams across the network with minimal losses».
Lecture 1: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.
I am Baddie K. I am a Magnetic Materials Assignment Expert at eduassignmenthelp.com. I hold a Masters's Degree in Electro-Magnetics, from The University of Malaya, Malaysia. I have been helping students with their assignments for the past 12 years. I solve assignments related to Magnetic Materials.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com. You can also call on +1 678 648 4277 for any assistance with Magnetic Materials Assignments.
I am Joshua M. I am a Statistical Physics Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics from, Michigan State University, UK
I have been helping students with their homework for the past 5 years. I solve assignments related to Statistics.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Statistical Physics Assignments .
Artigo que descreve o trabalho feito com o Chandra nos aglomerados de galáxias de Perseus e Virgo sobre a descoberta de uma turbulência cósmica que impede a formação de novas estrelas.
Lecture 5: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
Casimir energy for a double spherical shell: A global mode sum approachMiltão Ribeiro
In this work we study the configuration of two perfectly conducting spherical shells. This is a problem of basic importance to make possible development of experimental apparatuses that they make possible to measure the spherical Casimir effect, an open subject. We apply the mode sum method via cutoff exponential function regularization with two independent parameters: one to regularize the infinite order sum of the Bessel functions; other, to regularize the integral that becomes related, due to the argument theorem, with the infinite zero sum of the Bessel functions. We obtain a general expression of the Casimir energy as a quadrature sum. We investigate two immediate limit cases as a consistency test of the expression obtained: that of a spherical shell and that of two parallel plates. In the approximation of a thin spherical shell we obtain an expression that allows to relate our result with that of the proximity-force approximation, supplying a correction to this result.
Lecture 2: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
I am Ben R. I am a Statistics Assignment Expert at statisticshomeworkhelper.com. I hold a Ph.D. in Statistics, from University of Denver, USA. I have been helping students with their homework for the past 5 years. I solve assignments related to Statistics.
Visit statisticshomeworkhelper.com or email info@statisticshomeworkhelper.com.
You can also call on +1 678 648 4277 for any assistance with Statistics Assignment.
Energy Grid Theorem.
«For a stable electrical network without sources and energy storage the value of its streams coincide with the solution of optimization task of energy streams across the network with minimal losses».
Lecture 1: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
All of material inside is un-licence, kindly use it for educational only but please do not to commercialize it.
Based on 'ilman nafi'an, hopefully this file beneficially for you.
Thank you.
I am Baddie K. I am a Magnetic Materials Assignment Expert at eduassignmenthelp.com. I hold a Masters's Degree in Electro-Magnetics, from The University of Malaya, Malaysia. I have been helping students with their assignments for the past 12 years. I solve assignments related to Magnetic Materials.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com. You can also call on +1 678 648 4277 for any assistance with Magnetic Materials Assignments.
I am Joshua M. I am a Statistical Physics Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics from, Michigan State University, UK
I have been helping students with their homework for the past 5 years. I solve assignments related to Statistics.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Statistical Physics Assignments .
Artigo que descreve o trabalho feito com o Chandra nos aglomerados de galáxias de Perseus e Virgo sobre a descoberta de uma turbulência cósmica que impede a formação de novas estrelas.
Lecture 5: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
Similar to A Global Approach with Cutoff Exponential Function, Mathematically Well Defined at the Outset, for Calculating the Casimir Energy: The Example of Scalar Field
Casimir energy for a double spherical shell: A global mode sum approachMiltão Ribeiro
In this work we study the configuration of two perfectly conducting spherical shells. This is a problem of basic importance to make possible development of experimental apparatuses that they make possible to measure the spherical Casimir effect, an open subject. We apply the mode sum method via cutoff exponential function regularization with two independent parameters: one to regularize the infinite order sum of the Bessel functions; other, to regularize the integral that becomes related, due to the argument theorem, with the infinite zero sum of the Bessel functions. We obtain a general expression of the Casimir energy as a quadrature sum. We investigate two immediate limit cases as a consistency test of the expression obtained: that of a spherical shell and that of two parallel plates. In the approximation of a thin spherical shell we obtain an expression that allows to relate our result with that of the proximity-force approximation, supplying a correction to this result.
Ill-posedness formulation of the emission source localization in the radio- d...Ahmed Ammar Rebai PhD
To contact the authors : tarek.salhi@gmail.com and ahmed.rebai2@gmail.com
In the field of radio detection in astroparticle physics, many studies have shown the strong dependence of the solution of the radio-transient sources localization problem (the radio-shower time of arrival on antennas) such solutions are purely numerical artifacts. Based on a detailed analysis of some already published results of radio-detection experiments like : CODALEMA 3 in France, AERA in Argentina and TREND in China, we demonstrate the ill-posed character of this problem in the sens of Hadamard. Two approaches have been used as the existence of solutions degeneration and the bad conditioning of the mathematical formulation problem. A comparison between experimental results and simulations have been made, to highlight the mathematical studies. Many properties of the non-linear least square function are discussed such as the configuration of the set of solutions and the bias.
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.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Relativistic Mean Field Study of SM Isotopes with FTBCS Approach ijrap
A theoretical study of the thermal pairing correlation as a function of temperature is performed for eveneven
148-154Sm isotopes using Finite Temperature Bardeen-Cooper-Schrieffer (FTBCS) approach within the
Relativistic Mean Field (RMF) model. Numerical results obtained at T=0 are found to be consistent with
the available experimental values. Further, results show the thermal dependency of various nuclear
parameters like gap parameter, pairing energy, binding energy, deformation and density. At T≠0.0 MeV,
the destruction of Cooper pairs and the pairing phase transition as well as shape transition is observed in
148-154Sm nuclei at critical temperature Tc≠0.
RELATIVISTIC MEAN FIELD STUDY OF SM ISOTOPES WITH FTBCS APPROACHijrap
A theoretical study of the thermal pairing correlation as a function of temperature is performed for eveneven
148-154Sm isotopes using Finite Temperature Bardeen-Cooper-Schrieffer (FTBCS) approach within the
Relativistic Mean Field (RMF) model. Numerical results obtained at T=0 are found to be consistent with
the available experimental values. Further, results show the thermal dependency of various nuclear
parameters like gap parameter, pairing energy, binding energy, deformation and density. At T≠0.0 MeV,
the destruction of Cooper pairs and the pairing phase transition as well as shape transition is observed in
148-154Sm nuclei at critical temperature Tc≠0.
Quantum-Gravity Thermodynamics, Incorporating the Theory of Exactly Soluble Active Stochastic Processes, with Applications
by Daley, K.
Published in IJTP in 2009. http://adsabs.harvard.edu/abs/2009IJTP..tmp...67D
Finite Volume Method For Predicting Radiant Heat TransferRajibul Alam
Mid semester presentation at IIT Kharagpur, Department Of Aerospace Engineering
Similar to A Global Approach with Cutoff Exponential Function, Mathematically Well Defined at the Outset, for Calculating the Casimir Energy: The Example of Scalar Field (20)
Temperatura do Universo: uma proposta de conteúdo para estudantes do nível fu...Miltão Ribeiro
Temos conhecimento, através das atuais pesquisas na área de Ensino de Física, que não é necessário os docentes se concentrarem em memorizações de fórmulas durante suas aulas, eles devem interagir com seus estudantes de forma criativa, com experimentações, melhores recursos metodológicos e boas estratégias avaliativas, a fim de garantir o possível aprendizado do aluno, fazendo-o associar os assuntos dados em sala de aula com o seu cotidiano. Os mapas conceituais, por exemplo, podem ajudar tanto o docente como o estudante a organizar melhor os conteúdos abordados e facilitar na aprendizagem. Conciliando os mapas com conceitos e curiosidades de Astronomia (especificamente a Temperatura do Universo, que engloba quase todos os conteúdos da Física) pode ser uma forma criativa de atrair os estudantes para as aulas de Física, tornando-as mais interessante. Apesar da complexidade dos assuntos de Astronomia, eles podem ser apresentados para uma turma de nível fundamental com uma linguagem mais apropriada e de forma conceitual. O importante é mostrar analogias/comparações com o cotidiano. Para tanto, nesse trabalho foi criado um esquema conceitual, que serviu como ponta-pé inicial para a construção de mapas conceituais para o ensino fundamental, sendo estes construídos com o auxílio de desenhos e figuras, para despertar o interesse do público alvo pela disciplina. Após todas as construções e re-análises, os mapas foram aplicados em duas escolas do município de Feira de Santana -Bahia, Brasil, possibilitando com que os estudantes da 9º ano, que estavam tendo o primeiro contato com assuntos dessa disciplina, pudessem também construir seus próprios mapas de acordo com os conteúdos abordados pelo docente. Assim, esses estudantes puderam buscar nos mapas conceituais uma forma interativa de produzir conhecimentos.
Publication Name: Experiências em Ensino de Ciências.
Author: Tamila Marques Silveira, M. S. R. Miltão.
Model for Analysis of Biaxial and Triaxial Stresses by X-ray Diffraction Assu...Miltão Ribeiro
In this work we aim to develop expressions for the calculation of biaxial and triaxial stresses in polycrystalline anisotropic materials, and to determine their elastic constants using the theory of elasticity for continuum isochoric deformations; thus, we also derive a model to determine residual stress. The constitutive relation between strain and stress in these models must be assumed to be orthotropic, obeying the generalized Hooke’s law. One technique that can be applied with our models is that of X-ray diffraction, because the experimental conditions are similar to the assumptions in the models, that is, it measures small deformations compared with the sample sizes and the magnitude of the tensions involved, and is insufficient to change the volume (isochoric deformation). Therefore, from the equations obtained, it is possible to use the sin^{2}\psi technique for materials with texture or anisotropy by first characterizing the texture through the pole figures to determine possible angles \psi that can be used in the equation, and then determining the deformation for each diffraction peak with the angles \psi obtained from the pole figures.
Publication Name: Japanese Journal of Applied Physics.
Author: Edson M. Santos, Marcos T. D. Orlando, M.S.R. Miltão, Luis G. Martinez, Álvaro S. Alves, and Carlos A. Passos.
Uma Proposta de Estudo Filosófico do Ser Social do Movimento AmbientalMiltão Ribeiro
A lógica da compreensão sócio-ambiental requer o diálogo entre os diferentes campos do saber e uma visão sistêmica deles, pois acreditamos que o problema socioambiental se reflete, em diferentes nuances, em todos os fenômenos. Este trabalho visa trazer ao debate a possibilidade de formação de sujeitos sociais do movimento ambiental em bases filosóficas, apresentando as necessidades objetivas de natureza coletiva que definem esse ser social. Inicialmente, apresentaremos os pressupostos filosóficos, ontológico e epistemológico, do conhecimento humano. Depois, apresentaremos a relação entre a questão socioambiental e a filosofia, bem como as necessidades objetivas de natureza coletiva. Estabeleceremos a necessidade de uma visão de conhecimento que seja cosmológica/holística/histórica/construtivista/dialógica para ter em conta as questões epistemológicas e ontológicas do conhecimento humano, e compreendermos a identidade social do movimento ambiental. Com isso concluímos pela necessidade de uma Educação Ambiental filosófico-crítica que contribua para a formação do ser social desse movimento.
Publication Name: Anais da 35ª Reunião Anual da ANPED.
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Ciências Físicas e Popularização da Astronomia na Chapada Diamantina – Bahia....Miltão Ribeiro
O Departamento de Física da UEFS desenvolve um programa de popularização de Ciências, com ênfase em várias áreas das Ciências Físicas, particularmente em Astronomia, na região da Chapada Diamantina Bahia. O trabalho tem como objetivo a apresentação, na forma de palestras, minicursos e realizações experimentais, de conceitos e teorias das Ciências Físicas e, em particular, de suas relações com o cotidiano. Neste artigo descrevemos as atividades realizadas até o momento bem como faremos algumas considerações sobre alguns desdobramentos delas.
Publication Name: Revista Ciência em Extensão.
Author: M. S. R. Miltão, R. K. Madejsky, A. V. Andrade-Neto, P. C. Araújo, J. B. Santos.
Algumas Considerações sobre a Formação em Física dos Sujeitos das EFAs, consi...Miltão Ribeiro
We investigated the Physical Sciences in the Agricultural Families Schools considering the Pedagogy of the Alternation. In this sense, we take into account the lessons of Ethnophysics that seeks to comprehend, from the own social groups, their world view to be presented the physical academic knowledge. We use field trips, staying in school for three days to start the research process. The results show that the philosophical underpinnings of the PA are not well settled and the transdisciplinarity still not processed properly.
Publication Name: Caderno Multidisciplinar da RESAB.
Author: Carla Suely Correia Santana, M.S.R. Miltão.
Rolamento e atrito de rolamento ou por que um corpo que rola páraMiltão Ribeiro
The dynamics of the rolling motion of an object on a horizontal plane is studied. We use the laws of Newton to analyze the rolling of a rigid body and of a deformable body. The analytical solutions and their discussions in various physical situations are presented. The results allow us to understand the physical basis of why the rolling motion of a body stops after a certain time interval. Also, these results should help undergraduate physics students to investigate this type of motion.
Publication Name: Revista Brasileira de Ensino de Física.
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Reconstruction of magnetic source images using the Wiener filter and a multic...Miltão Ribeiro
A system for imaging magnetic surfaces using a magnetoresistive sensor array is developed. The experimental setup is composed of a linear array of 12 sensors uniformly spaced, with sensitivity of 150 pT∗Hz^{−1/2} at 1 Hz, and it is able to scan an area of (16 × 18) cm^{2} from a separation of 0.8 cm of the sources with a resolution of 0.3 cm. Moreover, the point spread function of the multi-sensor system is also studied, in order to characterize its transference function and to improve the quality in the restoration of images. Furthermore, the images are generated by mapping the response of the sensors due to the presence of phantoms constructed of iron oxide, which are magnetized by a pulse
of 80 mT. The magnetized phantoms are linearly scanned through the sensor array and the remanent magnetic field is acquired and displayed in gray levels using a PC. The images of the magnetic sources are reconstructed using two-dimensional generalized parametric Wiener filtering. Our results exhibit a very good capability to determine the spatial distribution of magnetic field sources, which produce magnetic fields of low intensity.
Publication Name: Review of Scientific Instruments.
Author: J. A. Leyva-Cruz, E. S. Ferreira, M. S. R. Miltão, A. V. Andrade-Neto, A. S. Alves, J. C. Estrada, and M. E. Cano.
Philosophical-Critical Environmental Education: a proposal in a search for a ...Miltão Ribeiro
This paper aims to develop a study on environmental education from philosophical and practical bases. Philosophical considerations being established after critical analysis of some philosophical schools who have taken the environment or the Individuals as a matter of primary concern; practical considerations arising from our experience in the university environmental movement. Thus, we intend to express our thinking towards the discussion about critical Environmental Education in a philosophical perspective called philosophical-critical Environmental Education, which aims to seek a harmony, a balance between subject and object, from a philosophical view-point, and as a consequence, between society and environment, from a socio-political perspective, in addressing the socio-environmental issue.
Publication Name: Journal of Social Sciences (COES&RJ-JSS).
Author: M. S. R. Miltão
O Ensino de Física e a Educação do Campo: uma relação que precisa ser efetivadaMiltão Ribeiro
Nesse capítulo objetivamos discutir como o Ensino de Física pode contribuir nas pesquisas em Educação do Campo. Mostramos que a Educação do Campo tem uma concepção diferenciada da Educação Rural, na medida em que advém de ações desenvolvidas pelos movimentos populares defensores da reforma agrária e de uma defesa de educação que leve em consideração o contexto dos camponeses.
Publication Name: Ensino de Física: reflexões, abordagens & práticas, Edition: 1ª, Chapter: 11, pp.167-196.
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Global approach with cut-off exponential function to spherical Casimir effectMiltão Ribeiro
We presented a method to calculate the spherical electromagnetic Casimir effect through the use of a regularization via the cut-off exponential function in a non ambiguous way from the start. We propose the use of two cut-off parameters: one to regularize the sum of orders of the Bessel function, and the other to regularize the integral related to Bessel function zeros. Both the interior and exterior contributions calculated have revealed all cut-off parameters dependency and give the results previously obtained in literature.
Salas, V. (2024) "John of St. Thomas (Poinsot) on the Science of Sacred Theol...Studia Poinsotiana
I Introduction
II Subalternation and Theology
III Theology and Dogmatic Declarations
IV The Mixed Principles of Theology
V Virtual Revelation: The Unity of Theology
VI Theology as a Natural Science
VII Theology’s Certitude
VIII Conclusion
Notes
Bibliography
All the contents are fully attributable to the author, Doctor Victor Salas. Should you wish to get this text republished, get in touch with the author or the editorial committee of the Studia Poinsotiana. Insofar as possible, we will be happy to broker your contact.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
DERIVATION OF MODIFIED BERNOULLI EQUATION WITH VISCOUS EFFECTS AND TERMINAL V...Wasswaderrick3
In this book, we use conservation of energy techniques on a fluid element to derive the Modified Bernoulli equation of flow with viscous or friction effects. We derive the general equation of flow/ velocity and then from this we derive the Pouiselle flow equation, the transition flow equation and the turbulent flow equation. In the situations where there are no viscous effects , the equation reduces to the Bernoulli equation. From experimental results, we are able to include other terms in the Bernoulli equation. We also look at cases where pressure gradients exist. We use the Modified Bernoulli equation to derive equations of flow rate for pipes of different cross sectional areas connected together. We also extend our techniques of energy conservation to a sphere falling in a viscous medium under the effect of gravity. We demonstrate Stokes equation of terminal velocity and turbulent flow equation. We look at a way of calculating the time taken for a body to fall in a viscous medium. We also look at the general equation of terminal velocity.
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.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
What is greenhouse gasses and how many gasses are there to affect the Earth.moosaasad1975
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.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
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A Global Approach with Cutoff Exponential Function, Mathematically Well Defined at the Outset, for Calculating the Casimir Energy: The Example of Scalar Field
1. Hindawi Publishing Corporation
Advances in High Energy Physics
Volume 2010, Article ID 120964, 13 pages
doi:10.1155/2010/120964
Research Article
A Global Approach with Cutoff Exponential
Function, Mathematically Well Defined at
the Outset, for Calculating the Casimir Energy:
The Example of Scalar Field
M. S. R. Milt˜ao and Franz A. Farias
Departamento de F´ısica-UEFS, 44036-900 Feira de Santana, BA, Brazil
Correspondence should be addressed to M.S.R. Milt˜ao, miltaaao@ig.com.br
Received 9 October 2010; Accepted 6 December 2010
Academic Editor: Ira Rothstein
Copyright q 2010 M.S.R. Milt˜ao and F. A. Farias. This is an open access article distributed under
the Creative Commons Attribution License, which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.
A global approach with cutoff exponential functions is used to obtain the Casimir energy of
a massless scalar field in the presence of a spherical shell. The proposed method, mathematically
well defined at the outset, makes use of two regulators, one of them to make the sum of the orders
of Bessel functions finite and the other to regularize the integral involving the zeros of Bessel
function. This procedure ensures a consistent mathematical handling in the calculations of the
Casimir energy and allows a major comprehension on the regularization process when nontrivial
symmetries are under consideration. In particular, we determine the Casimir energy of a scalar
field, showing all kinds of divergences. We consider separately the contributions of the inner
and outer regions of a spherical shell and show that the results obtained are in agreement with
those known in the literature, and this gives a confirmation for the consistence of the proposed
approach. The choice of the scalar field was due to its simplicity in terms of physical quantity
spin.
1. Introduction
The relevance of the Casimir effect has increased over the decades since the seminal paper
1948 1 by the Dutch Physicist Hendrik Casimir. This effect concerns to the appearance of
an attractive force between two plates when they are placed close to each other. Casimir was
the first to predict and explain the effect as a change in vacuum quantum fluctuations of the
electromagnetic field.
2. 2 Advances in High Energy Physics
Nowadays, the Casimir effect has been applied to a variety of quantum fields and
geometries and it has gained a wider understanding as the effect which comes from the
fluctuations of the zero point energy of a relativistic quantum field due to changes in its base
manifold. This interpretation can be confirmed when we see the large range where the
Casimir effect has been applied: the study of gauge fields with BRS symmetry 2 , in the
Higgs fields 3 , in supersymmetric fields 4 , in supergravity theory 5, 6 , in superstrings
7 , in the Maxwell-Chern-Simons fields 8 , in relativistic strings 9 , in M-theory 10 ,
in cosmology 11 , and in noncommutative spacetimes 12 , among other subjects in the
literature 13, 14 , the review articles 15–17 , and textbooks 18–23 .
In this present work, the meaning of base manifold is that the confinement that
the field is subjected is due to the presence of a sphere, where the boundary conditions
take place. The point we aim to emphasize is that once the calculation of the Casimir
effect involves dealing with infinite quantities, we need to use a regularization procedure
appropriately defined. Many different regularization methods have been proposed and we
can quote some of them: the summation mode method—using the general cutoff function
1 , exponential cutoff function 24, 25 , Green function 26–30 , Green function through
multiple scattering 31 , exponential function and cutoff parameter 32, 33 , zeta function
34–40 , Abel-Plana formula 21, 41 , or point-splitting 42–44 ; the Green function method—
using the point-splitting 45–48 , Schwinger’s source theory 49–51 , or zeta function
52 ; the statistical approach method—using the path integral formalism 53 , or Green
function 54 ; as some examples among others. These methods are distinguished by the
approach used to carry out the calculations of the Casimir energy, and it is clear that
the physical result must be independent from the regulators or the method employed for
them. But the literature has shown that the results found there exhibit a divergence among
them.
In a general way, the methods used to obtain the Casimir effect lie on one of the two
categories: a local procedure or a global one. With a local procedure, we mean one that the
expression for the change of the vacuum energy is explicitly dependent on the variables of the
base manifold, and only in the final step of calculations the integration over these variables
is carried out. On the other hand, in a global one, we start with an expression for the vacuum
energy where there is no space-time variables present as they already were integrated.
In the present work, we pretend detailing a global approach 55, 56 for the calculation
of Casimir energy. In this method, mathematically well defined at the outset, we propose
the use of two regulators into the cutoff exponential function, and we demonstrate that this
regularization approach is one appropriate for the calculation of Casimir effect in the case of
nontrivial symmetries, in particular a spherical symmetry.
With the use of scalar field, we can avoid the inherent complications brought by the
vector nature of the electromagnetic field, and due to its simple structure, the scalar field
usually becomes an effective tool to be used in the investigation of field proprieties as in these
examples: in the dynamical Casimir effect 57 , in the Casimir effect at finite temperature
58, 59 , and in the Casimir effect on a presence of a gravitational field 60, 61 , among others
62–64 .
The paper is organized as follows: we detail in Section 2 the method to be used and
why we need two cutoff parameters to obtain an regularized expression for the Casimir
energy, which is the starting point for a consistent mathematical handling. Section 3 exhibits
the calculations for the contributions of the inner and the outer regions of the spherical shell.
We analyze in Section 4 the results and compare them with those ones in the literature and
make some considerations.
3. Advances in High Energy Physics 3
2. The Global Procedure Proposed with Two Parameters
The starting point is the expression for the Casimir energy defined as the difference between
the vacuum energy under a given boundary condition and the reference vacuum energy.
When we consider a scalar field in the presence of a spherical shell, this vacuum energy is
E0
∞
n 1
∞
j 0
j
m −j τ
1
2
ωτ
jn, 2.1
where ωτ
jn are the mode frequencies. They are obtained when the boundary conditions are
imposed on the field. In the absence of boundary conditions, the frequencies take some values
which let us designate as ω
τ ref
jn and these lead to the vacuum reference energy
E ref
∞
n 1
∞
j 0
j
m −j τ
1
2
ω
τ ref
jn , 2.2
so the Casimir energy is E E0 − E ref
. The boundary conditions due to a spherical shell with
radius a are
kajj ka 0, for r a − 0,
Ajkajj ka Bj kanj ka 0, for r a 0.
2.3
The Casimir energy will be calculated by using the mode summation and the argument
theorem also known as argument principle 65–67 . This theorem gives the summation of
zeros and poles of an analytic function as a contour integral. This contour is a curve that
encompasses the interior region of the complex plane which contains the zeros and poles
65–67 . In our case, we are interested in the root functions which match the conditions 2.3 .
So, the following equations are appropriate as root functions
f1
j az azjj az ,
f2
j az cos δj z azjj az tan δj z aznj az ,
2.4
where
z k
ω
c
, δj z zR −
jπ
2
. 2.5
When we apply the argument theorem and carry out some handling, we get
g
n 1
ωτ
jn
c
2πi C
dz z
d
dz
log fτ
j az . 2.6
4. 4 Advances in High Energy Physics
ϕ
Γ1
Γ2
ϕ Cλ
Figure 1: The path of integration in the complex plane.
a
R
R/ξ
R
Figure 2: A sketch of the subtraction process which takes place on the regularization of the Casimir effect
of a spherical shell.
In the above equation, the argument for logarithm must involve the product of all root
functions. The contour to be taken on the calculations is given by 68 according to Figure 1.
The subtraction process renormalization , defined by E, can be schematically
represented as in Figure 2.
The vacuum energy 2.1 which takes into account the boundary conditions can be
used to obtain the reference energy in 2.2 . This is done when we take the limit for the
radius a going to infinity. This procedure is sensible, but it already has been made clear by
Boyer 69, 70 . After all, we obtain for the Casimir energy
E
∞
n 1
∞
j 0
j
m −j
4
τ 1
1
2
ωτ
jn − ω
τ ref
jn
lim
σ → 0, → 0, R → ∞, ξ → 1
c
2πi
∞
j 0
ν exp − ν
C
dz z exp −σz
×
d
dz
log f
1
j az f
2
j az − log f
1 ref
j
R
ξ
z f
2 ref
j
R
ξ
z ,
2.7
5. Advances in High Energy Physics 5
where ν j 1/2. We can see from above that two exponential functions were used, one of
them is the function under the integral sign, exp −σz , σ > 0 , that stems from the argument
theorem and the other is the function exp − ν , > 0 , under summation sign on j ν −
1/2 . Now, group together these two developments, and 2.7 may be rewritten as
E −
c
π
Ê
∞
j 0
ν2
exp − ν
∞ exp −iϕ
0
dz exp −iσνz z
d
dz
log Iν νaz log Kν νaz
− E ref
,
2.8
where the limits for R and ξ have been taken into account. The other limits will be taken in
an appropriate moment after the cancelation of possible remaining divergences.
3. Casimir Effect of a Spherical Shell: The Case of a Scalar Field
We now rewrite 2.8 in a more appropriate way, so that the contributions can be separated
by regions as E EI EO, where
EI −
c
π
Ê 1
2
2
exp −
1
2
∞ exp −iϕ
0
dz z exp −iσ
1
2
z
d
dz
log I1/2
1
2
az
−
c
π
Ê
∞
j 1
ν2
exp − ν
∞ exp −iϕ
0
dz z exp −iσνz
d
dz
log Iν νaz − Eref
I
3.1
is the contribution due to the internal modes and
EO −
c
π
Ê 1
2
2
exp −
1
2
∞ exp −iϕ
0
dz z exp −iσ
1
2
z
d
dz
log K1/2
1
2
az
−
c
π
Ê
∞
j 1
ν2
exp − ν
∞ exp −iϕ
0
dz z exp −iσνz
d
dz
log Kν νaz − Eref
O
3.2
is the contribution due to the external modes. As it can be observed, the above contributions
were written in such a way that the term for j 0 was detached from the summation on j.
This has been done to the effect of making explicit the term on which we will focus attention
as well as taking into account some developments already accomplished 55 .
3.1. Internal Mode
Now, we proceed with the calculations of 3.1 , and the first step is to take the Debye
expansion for the Bessel functions up to order O ν−4
71, 72 . The Debye expansion gives
6. 6 Advances in High Energy Physics
accurate results when we consider large order of ν j 1/2 and larger arguments and that
also makes an analytical treatment possible for the resulting expressions. So, we have
EI EI − E
ref
I , 3.3
where EI EI,0 EI,1 EI,2 EI,3 EI,4 and the terms EI,n are given by
EI,0 −
c
2π
Êexp −
1
2
exp −iϕ
∞
0
dρ exp −iσρ exp −iϕ
× −
1
2
exp −iϕ aρ coth aρ exp −iϕ ,
3.4
EI,1
c
πa
∞
j 1
ν2
∞
0
dρ log II ν, ρ −
4
k 1
U I,k t
νk
, 3.5
EI,2 −
c
π
Ê
4
k 1
∞
j 1
ν2−k
exp − ν
∞ exp −iϕ
0
dz exp −iσνz z
d
dz
U I,k t , 3.6
EI,3
c
2π
Ê
∞
j 1
ν2
exp − ν
∞ exp −iϕ
0
dz exp −iσνz
a2
z2
1 a2z2
, 3.7
EI,4 −
c
π
Ê
∞
j 1
ν3
exp − ν
∞ exp −iϕ
0
dz exp −iσνz 1 a2z2, 3.8
with the definitions 37
II ν, ρ
√
2πν 1 ρ2
1/4
exp −νη Iν νρ , 3.9
U I,1 t
t
8
−
5t3
24
, 3.10
U I,2 t
t2
16
−
3t4
8
5t6
16
, 3.11
U I,3 t
25t3
384
−
531t5
640
221t7
128
−
1105t9
1152
, 3.12
U I,4 t
13t4
128
−
71t6
32
531t8
64
−
339t10
32
565t12
128
. 3.13
The contributions 3.7 and 3.8 compound the zero-order terms of the Debye expansion.
The contribution 3.5 stems from small values of the angular momentum j, and its value
was already determined by 37
EI,1 0.00024
c
πa
. 3.14
7. Advances in High Energy Physics 7
The contributions 3.6 to 3.8 are calculated taking into account the Euler-Maclaurin
formula with remainder 73–75 , and these were calculated by 55
EI,2
c
π
Ê 8099
63839
1
a
7
24
a
σ2
11
192
1
a
log
σ
a
229
40320
1
a
log i
7801
86684
1
a
, 3.15
EI,3
c
π
Ê 52529
267528
1
a
i −
1
3
1
σ
−
3
4
1
σ
−
1
2
1
σ 2
, 3.16
EI,4
c
π
Ê 7375
85696
1
a
−
11
24
a
σ2
2
a3
σ4
−
127
1920
1
a
log
σ
a
− i
2197
21145
1
a
. 3.17
Collecting the terms 3.14 , 3.15 , 3.16 , and 3.17 , we get
EIpartial
0.4095155894
c
πa
c
π
−
1
6
a
σ2
2
a3
σ4
−
17
1920
1
a
log
σ
a
229
40320
1
a
log . 3.18
For 3.4 , corresponding to j 0, we obtain
EI,0
c
π
−
1
24
π2
a
1
2
a
σ2
. 3.19
So, the energy of a scalar field considering a spherical configuration due the internal modes
is
EI EIpartial
EI,0
−
c
πa
0.0017179275
c
π
1
3
a
σ2
2
a3
σ4
−
17
1920
1
a
log
σ
a
229
40320
1
a
log .
3.20
The expression 3.20 shows in an undoubted way the need for a second regularized
exponential function, exp − ν , to make a consistent mathematical handling of the
divergences possible. Both divergences, the logarithm in 3.15 and the polynomial in 3.16 ,
stem from the summation on j. This type of divergence was already observed in 76 , but
only with the procedure established here this discard turns to be completely justified as an
appropriate regularization allows the real part of 3.16 to be taken in an unambiguous way.
3.2. External Mode
The contribution of the external modes comes by 3.2 . We proceed with the calculations in
an analogous way to that of the previous subsection. So,
EO EO − E
ref
O , 3.21
8. 8 Advances in High Energy Physics
where EO EO,0 EO,1 EO,2 EO,3 EO,4 and
EO,0 −
c
2π
Êexp −
1
2
exp −iϕ
∞
0
dρ exp −iσρ exp −iϕ −
1
2
− exp −iϕ aρ , 3.22
EO,1
c
πa
∞
j 1
ν2
∞
0
dρ log KO ν, ρ −
4
k 1
U O,k t
νk
, 3.23
E0,2 −
c
π
Ê
4
k 1
∞
j 1
ν2−k
exp − ν
∞ exp −iϕ
0
dz exp −iσνz z
d
dz
U O,k t , 3.24
EO,3
c
2π
Ê
∞
j 1
ν2
exp − ν
∞ exp −iϕ
0
dz exp −iσνz
a2
z2
1 a2z2
, 3.25
EO,4
c
π
Ê
∞
j 1
ν3
exp − ν
∞ exp −iϕ
0
dz exp −iσνz 1 a2z2, 3.26
with the following definitions 37 :
KO ν, ρ
2ν
π
1 ρ2
1/4
exp νη Kν νρ , 3.27
U O,1 t −U I,1 t , 3.28
U O,2 t U I,2 t , 3.29
U O,3 t −U I,3 t , 3.30
U O,4 t U I,4 t , 3.31
where the U O,k are given by 3.10 to 3.13 , respectively. The term 3.28 was numerically
determined by 37
EO,1 −0.00054
c
πa
. 3.32
The other contributions are calculated following the analogous procedure detailed in the
previous subsection:
EO,2
c
π
Ê −
5821
56688
1
a
−
7
24
a
σ2
−
11
192
1
a
log
σ
a
−
229
40320
1
a
log − i
7801
86684
1
a
,
EO,3 EI,3,
EO,4 −EI,4 .
3.33
9. Advances in High Energy Physics 9
After collecting the terms 3.32 and 3.33 , we have
EOpartial
0.01056399145
c
πa
c
π
1
6
a
σ2
− 2
a3
σ4
17
1920
1
a
log
σ
a
−
229
40320
1
a
log . 3.34
The contribution 3.22 , related to j 0, when we repeat the calculation gives
EO,0
c
π
−
1
2
a
σ2
. 3.35
Gathering together 3.34 and 3.35 , we get the total contribution to the energy of a scalar
field of a spherical configuration due the external modes
EO EOpartial
EO,0
c
πa
0.01056399145
c
π
−
1
3
a
σ2
− 2
a3
σ4
17
1920
1
a
log
σ
a
−
229
40320
1
a
log .
3.36
Our next task is to determine the reference energy and take the regularizations as indicated
by 3.3 and 3.21 .
4. The Regularized Results
Calculating the reference energy, we get
E
ref
± ±
R
ξ
f
σ2
, 4.1
where the plus sign refers to EI and the minus sign to EO and
f exp −
2
3 exp − 1 exp − 1
−2
. 4.2
Now, we can gather together the internal 3.20 and external 3.36 contributions,
taking into account 4.1 , to obtain the Casimir effect for a scalar field due to the presence
of a spherical shell with radius a
E a
c
a
0.002815789609. 4.3
This result is free of divergences since we get an exact cancelation for the terms which depend
on the cutoff parameters. Equation 4.3 is in agreement with that obtained by 37 , through
the zeta function method, and with that in 77 , which uses the Green function formalism and
the dimensional analytical extension in this reference the starting point is the expression for
the force .
10. 10 Advances in High Energy Physics
5. Conclusions
Our purpose in this work was to show the form and nature of each divergent term that
appears in the calculation of Casimir energy and demonstrate that the method proposed is
mathematically consistent and that it is in accordance with the results existing in literature.
To this end, we show explicitly, to the scalar field, the characteristic of the divergent
terms calculated in 3.20 , 3.36 , and 4.1 as a function of the geometrical proprieties of
boundary if we rewrite the divergent part of those assuming a dimensionless parameter ε
a 357/155
, with dim L−1
, so
E± ± c
3
π2
V a
1
σ4
−
17
3840π2
S a κ3
log σε
1
3π2
S a κ
1
σ2
−
1
4π2
S
R
ξ
κS
R
ξ
f ε
σ2
,
5.1
where the plus sign refers to the index I while the minus sign refers to the index O, and
κ 1/a is the curvature. In 5.1 , V a is a volume, S a is an area, and σ and are cutoff
parameters. As we can see, the second and fourth terms in 5.1 explain why two regulators
are required to get a well-defined expression for the Casimir energy of the scalar field. This
is the same case when we consider an electromagnetic field see 55 . The result 5.1 is in
agreement with 78 , except for the divergence due to log and due to the relative self-
energy of the spherical shell, f ε /σ2
, that does not appear there.
Our purpose in this work is to confirm that the prescription in 2.7 works well
when we assume non trivial symmetries for the fields. In fact, the approach has succeed
in demonstrating the cancelation of all types of divergences appearing in the expression for
the Casimir energy of the scalar field. Besides, this calculation presented at this work shows
the desired agreement with the results existing in the literature. Furthermore, as it has been
mentioned by the authors in 79–81 , a better understanding of the quantum field theory
undoubtedly involves the necessity to understand these infinities.
Acknowledgment
The authors wish to thank Dr. Ludmila Oliveira H. Cavalcante DEDU-UEFS for valuable
help with English revision.
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