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arXiv2009

Dilatation of a one-dimensional nonlinear crack impacted by a periodic elastic wave

The interactions between linear elastic waves and a nonlinear crack with finite compressibility are studied in the one-dimensional context. Numerical studies on a hyperbolic model of contact with sinusoidal forcing have shown that the mean values of the scattered elastic displacements are discontinuous across the crack. The mean dilatation of the crack also increases with the amplitude of the forcing levels. The aim of the present theoretical study is to analyse these nonlinear processes under a larger range of nonlinear jump conditions. For this purpose, the problem is reduced to a nonlinear differential equation. The dependence of the periodic solution on the forcing amplitude is quantified under sinusoidal forcing conditions. Bounds for the mean, maximum and minimum values of the solution are presented. Lastly, periodic forcing with a null mean value is addressed. In that case, a result about the mean dilatation of the crack is obtained.

physics.class-ph↗

arXiv2009

Symmetric lens with extended depth of focus

The lens surface profile is derived based on the instantaneous focal length versus the lens radius data. The lens design based on instantaneous focal length versus the lens radius data has many useful applications in software assisted image focusing technology.

physics.optics↗

arXiv2009

A model for unsteady mixed flows in non uniform closed water pipes and a well-balanced finite volume scheme

We present the derivation of a new unidirectional model for We present the derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipes. We introduce a local reference frame to take into account the local perturbation caused by the changes of section and slope. Then an asymptotic analysis is performed to obtain a model for free surface flows and another one for pressurized flows. By coupling these models through the transition points by the use of a common set of variables and a suitable pressure law, we obtain a simple formulation called PFS-model close to the shallow water equations with source terms. It takes into account the changes of section and the slope variation in a continuous way through transition points. Transition point between the two types of flows is treated as a free boundary associated to a discontinuity of the gradient of pressure. The numerical simulation is performed by making use of a Roe-like finite volume scheme that we adapted to take into account geometrical source terms in the convection matrix. Finally some numerical tests are presented.

math.AP↗

arXiv2009

A simple model for Carnot heat engines

We present a (random) mechanical model consisting of two lottery-like reservoirs at altitude $E_h$ and $E_l<E_h$, respectively, in the earth's gravitational field. Both reservoirs consist of $N$ possible ball locations. The upper reservoir contains initially $n_h\le N$ weight-1 balls and the lower reservoir contains initially $n_l\le N$ weight-1 balls. Empty locations are treated as weight-0 balls. These reservoirs are being shaken up so that all possible ball configurations are equally likely to occur. A cycle consists of exchanging a ball randomly picked from the higher reservoir and a ball randomly picked from the lower reservoir. It is straightforward to show that the efficiency, defined as the ratio of the average work produced to the average energy lost by the higher reservoir is $η=1-E_l/E_h$. We then relate this system to a heat engine. This thermal interpretation is applicable only when the number of balls is large. We define the entropy as the logarithm of the number of ball configurations in a reservoir, namely $S(n)=\ln[N!/n!(N-n)!]$, with subscripts $h,l$ appended to $S$ and to $n$. When $n_l$ does not differ much from $n_h$, the system efficiency quoted above is found to coincide with the maximum efficiency $η=1-T_l/T_h$, where the $T$ are absolute temperatures defined from the above expression of $S$. Fluctuations are evaluated in Appendix A, and the history of the Carnot discovery (1824) is recalled in Appendix B. Only elementary physical and mathematical concepts are employed.

cond-mat.stat-mech↗

arXiv2009

Electrodynamics in a Filled Minkowski Spacetime with Application to Classical Continuum Electrodynamics

Minkowski spacetime is a convenient setting for the study of the relativistic dynamics of particles and fields in the vacuum. In order to study events that occur in a dielectric or other linear medium, we adopt the familiar continuum assumption of a linear, isotropic, homogeneous, transparent medium of refractive index n filling all space and seek the principle of relativity that applies in the filled spacetime. Applying the Einstein postulates with c/n as the speed of light, we show how the effective signal velocity results in a scaling of the proper time by the refractive index and examine the consequences for D'Alembert's principle, the Lagrange equations, and the canonical momentum field. The principles of dynamics in the filled spacetime are then applied to the electromagnetic Lagrangian and we derive equations of motion that are invariant with respect to a material Lorentz transformation. The new representation of the dynamics of macroscopic fields is shown to be consistent with the equal-time commutation relation for quantized macroscopic fields, quantum--classical correspondence, the principle of superposition, and electromagnetic boundary conditions.

physics.class-ph↗

arXiv2011

Unified Statistical Description of Quasithermodynamic Systems in and out of Equilibrium

We propose the method of statistical description of broad class of dynamic systems (DS) whose equations of motion are determined by two state depending functions: 1) "energy" - the quantity which conserves in time and 2) "entropy" - the quantity which does not decrease in time. It is demonstrated that the behavior of such systems in the equilibrium state reduces to the thermodynamic lows in particular the Le Chatelier principle is satisfed and so on. Taking into account the interaction system of interest with ergometer - the device which continuously measures its energy one can possible to find the system distribution function in arbitrary non-equilibrium stationary state (NESS). Some general relations for mean values of certain quantities in NESS which can be compared with experimental data are obtained.

physics.class-ph↗

arXiv2008

Entropy oscillations

The opportunity of occurrence of entropy oscillations around of a stationary state in linear and nonlinear processes is theoretically shown. The new mechanism of global tendencies appearance is described.

physics.gen-ph↗

arXiv2009

Scaling factors for ab initio vibrational frequencies: comparison of uncertainty models for quantified prediction

Bayesian Model Calibration is used to revisit the problem of scaling factor calibration for semi-empirical correction of ab initio calculations. A particular attention is devoted to uncertainty evaluation for scaling factors, and to their effect on prediction of observables involving scaled properties. We argue that linear models used for calibration of scaling factors are generally not statistically valid, in the sense that they are not able to fit calibration data within their uncertainty limits. Uncertainty evaluation and uncertainty propagation by statistical methods from such invalid models are doomed to failure. To relieve this problem, a stochastic function is included in the model to account for model inadequacy, according to the Bayesian Model Calibration approach. In this framework, we demonstrate that standard calibration summary statistics, as optimal scaling factor and root mean square, can be safely used for uncertainty propagation only when large calibration sets of precise data are used. For small datasets containing a few dozens of data, a more accurate formula is provided which involves scaling factor calibration uncertainty. For measurement uncertainties larger than model inadequacy, the problem can be reduced to a weighted least squares analysis. For intermediate cases, no analytical estimators were found, and numerical Bayesian estimation of parameters has to be used.

physics.data-an↗

arXiv2009

Electrodynamics in Iron and Steel

In order to calculate the reflected EM fields at low amplitudes in iron and steel, more must be understood about the nature of long wavelength excitations in these metals. A bulk piece of iron is a very complex material with microstructure, a split band structure, magnetic domains and crystallographic textures that affect domain orientation. Probing iron and other bulk ferromagnetic materials with weak reflected and transmitted inductive low frequency fields is an easy operation to perform but the responses are difficult to interpret because of the complexity and variety of the structures affected by the fields. First starting with a simple single coil induction measurement and classical EM calculation to show the error is grossly under estimating the measured response. Extending this experiment to measuring the transmission of the induced fields allows the extraction of three dispersion curves which define these internal fields. One dispersion curve yielded an exceedingly small effective mass of 1.8 10^{-39}kg (1.3 10^{-9} m_e) for those spin waves. There is a second distinct dispersion curve more representative of the density function of a zero momentum bound state rather than a propagating wave. The third dispersion curve describes a magneto-elastic coupling to a very long wave length propagating mode. These experiments taken together display the characteristics of a high temperature Bose-Einstein like condensation that can be initiated by pumping two different states. A weak time dependent field drives the formation of coupled J=0 spin wave pairs with the reduced effective mass reflecting the increased size of the coherent state. These field can dominate induction measurements well past the Curie temperature.

physics.gen-ph↗

arXiv2009

Understanding the special theory of relativity

This paper constitutes a background to the paper 'Quantum mechanics as "space-time statistical mechanics"?', arXiv:quant-ph/0501133, presented previously by the author. But it is also a free-standing and self-contained paper. The purpose of this paper is to give the reader an increased and a deeper understanding of the special theory of relativity, and the spacetime ideas lying behind the above mentioned paper. We will here consider, discuss, define, analyse, and explain things such as, e.g., the constancy of the speed of light, synchronization, simultaneity, absolute simultaneity, absolute space and time, the ether, and spacetime. Albert Einstein's original version of the special theory of relativity is fundamentally an operational theory, free from interpretation. But the old "Lorentzian interpretation" and the standard "spacetime interpretation" of the special theory of relativity will also be considered. This paper also discusses and analyses aspects of the philosophy of science that in my opinion are relevant for an understanding of the special theory of relativity.

physics.class-ph↗

arXiv2009

Symmetry Properties of Electromagnetic Field in the Matter

The sets ${Φ({F}^{μν})}, {Φ(\tilde {F}^{μν})}$ of linear functionals on the space $< F,+,\cdot >$ represent themself linear space $< Φ,+,\cdot >$ over the field of \textit{scalars} $P$, which is dual to space $< F,+,\cdot >$, but it is substantial, that given linear space is not self-dual. It has been found, that the partition of linear space $< F,+,\cdot >$ over the field of genuine scalars and pseudoscalars, the vectors in which are sets of contravariant and covariant electromagnetic field tensors and pseudotensors ${{F}^{μν}}$, ${\tilde{F}^{μν}}$, ${{F}_{μν}}$, ${\tilde{F}_{μν}}$, on 4 subspaces takes place. It corresponds to appearance of 4 kinds of electromagnetic field potential 4-vectors $A_μ$, which are transformed according to the representations of general Lorentz group with various symmetry relatively improper rotations. It has been found, that conserving quantity, corresponding to complex fields is complex charge. It is argued, that electromagnetic field in the matter is complex field and that two-parametric group $Γ(α,β) = U_{1}(α) \otimes \mathfrak R(β)$, where $\mathfrak R(β)$ is abelian multiplicative group of real numbers (excluding zero), determines the gauge symmetry of electromagnetic field. It is also argued, that free electromagnetic field is characterized by pure imagine charge.

physics.class-ph↗

arXiv2009

Boosted high harmonics pulse from a double-sided relativistic mirror

An ultra-bright high-intensity X- and gamma-radiation source is proposed. A high-density thin plasma slab, accelerating in the radiation pressure dominant regime by a co-propagating ultra-intense electromagnetic wave, reflects a counter-propagating relativistically strong electromagnetic wave, producing strongly time-compressed and intensified radiation due to the double Doppler effect. The reflected light contains relativistic harmonics generated at the plasma slab, all upshifted with the same factor as the fundamental mode of the incident light.

physics.plasm-ph↗

arXiv2009

Weakly nonlocal non-equilibrium thermodynamics - variational principles and Second Law

A general, uniform, rigorous and constructive thermodynamic approach to weakly nonlocal non-equilibrium thermodynamics is reviewed. A method is given to construct and restrict the evolution equations of physical theories according to the Second Law of thermodynamics and considering weakly nonlocal constitutive state spaces. The evolution equations of internal variables, the classical irreversible thermodynamics and Korteweg fluids are treated.

physics.class-ph↗

arXiv2009

From Maxwell Stresses to Photon-like Objects through Curvature Geometrisation of Physical Interaction

This paper aims to review our recent results on exploring the capabilities of non-quantum field theory as a possible tool for describing single photon-like objects, considered as massless time-stable spatially finite physical entities with compatible translational-rotational dynamical structure. The main idea is to interpret the local physical interaction as available Frobenius curvature. It consists of five chapters and includes 22 sections and subsections.

math-ph↗

arXiv2009

Evanescent gravitational mass

A simple and {\it innocent} modification of Poisson's equation leads to a modified Newtonnian theory of gravitation where a localized and {\it positive} energy density of the gravitational field contributes to its own source. The result is that the total {\it active gravitational mass} of a compact object is the sum of its {\it proper mass} and an {\it evanescent gravitational mass} which is a mass equivalent to the gravitational energy.

physics.class-ph↗

arXiv2009

Spectrum of a fluid-loaded vibrating plate: the multiple resonance phenomenon

It was recently observed in a numerical study on a high order perturbation method under heavy fluid loading that a loaded vibrating plate results, not only in the classical frequency shift of the in vacuo single resonance (in both the real part because of the fluid added mass and the imaginary part because of energy lost by radiation), but also in an increase in the number of the resonance. As a result of the loading, a single in vacuo resonance of the structure is transformed into a multiple resonance. Here we show that this phenomenon is a refinement of the Sanchez's classical result where it was established, using asymptotic analysis, that in the case of a light loading conditions " the scattering frequencies of a fluid loaded elastic structure (ie the resonance frequencies) are nearly the real eigenfrequencies of the elastic body alone and the complex scattering frequencies of the fluid with a rigid solid ". A theoretical explanation of the multiple resonances is given using classical results on theory of entire functions. It is established that every single in vacuo resonance of a simply supported rectangular plate is transformed into an infinite number of resonances under fluid-loading condition.

physics.class-ph↗

arXiv2014

New perspectives on classical electromagnetism

The fallacies associated with the gauge concept in electromagnetism are illustrated. A clearer and more valid formulation of the basics of classical electromagnetism is provided by recognizing existing physical constraints as well as the physical reality of the vector potential.

physics.class-ph↗

arXiv2009

Estimating nonlinearities in twophase flow in porous media

In order to analyze numerically inverse problems several techniques based on linear and nonlinear stability analysis are presented. These techniques are illustrated on the problem of estimating mobilities and capillary pressure in one-dimensional two-phase displacements in porous media that are performed in laboratories. This is an example of the problem of estimating nonlinear coefficients in a system of nonlinear partial differential equations.

math.NA↗