Physics

Thermodynamically consistent fractional Burgers constitutive models for viscoelastic media, divided into two classes according to model behavior in stress relaxation and creep tests near the initial time instant, are coupled with the equation of motion and strain forming the fractional Burgers wave equations. Cauchy problem is solved for both classes of Burgers models using integral transform method and analytical solution is obtained as a convolution of the solution kernels and initial data. The form of solution kernel is found to be dependent on model parameters, while its support properties implied infinite wave propagation speed for the first class and finite for the second class. Spatial profiles corresponding to the initial Dirac delta displacement with zero initial velocity display features which are not expected in wave propagation behavior.

This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless. Afterwards, approximated expressions that relate the two equations parameters for the case that the fractional order is close to an integer number are presented. Following, a numerical regression is made using power series expansion, and, also from fractional calculus, the fact that both equations cannot be equivalent is concluded. In the end, from the numerical regression data, the analytical approximated expressions that relate the two equations' parameters are refined.

This work derives exact expressions for the voltage and current induced into a two conductors non isolated transmission lines by an incident plane wave. The methodology is to use the transmission line radiating properties to derive scattering matrices and make use of reciprocity to derive the response to the incident wave. The analysis is in the frequency domain and it considers transmission lines of any small electric cross section, incident by a plane wave from any incident direction and any polarisation. The analytic results are validated by successful comparison with ANSYS commercial software simulation results, and compatible with other published results.

Fresnel's equations describe reflection and transmission of electromagnetic waves at an interface between two media. It turns out that these equations can be used in quasistatics and even statics, for example to straightforwardly calculate magnetic forces between a permanent magnet and a bulk medium. This leads to a generalization of the classical image method.

A short historical account of the curves related to the two-dimensional floating bodies of equilibrium and the bicycle problem is given. Bor, Levi, Perline and Tabachnikov found, quite a number had already been described as Elastica by Bernoulli and Euler and as Elastica under Pressure or Buckled Rings by Levy and Halphen. Auerbach already realized that Zindler had described curves for the floating bodies problem. An even larger class of curves solves the bicycle problem. The subsequent sections deal with some supplemental details: Several derivations of the equations for the elastica and elastica under pressure are given. Properties of Zindler curves and some work on the problem of floating bodies of equilibrium by other mathematicians are considered. Special cases of elastica under pressure reduce to algebraic curves, as shown by Greenhill. Since most of the curves considered here are bicycle curves, a few remarks concerning them are added.

An elementary derivation of the Newton "inverse square law" from the three Kepler laws is proposed. Our proof, thought essentially for first-year undergraduates, basically rests on Euclidean geometry. It could then be offered even to high-school students possessing only the first basics of Calculus.

In a complementary article, we exploited algebraic properties of Maxwell's equations and fundamental principles such as electromagnetic reciprocity and passivity, to derive fundamental limits to radiative heat transfer applicable in near- through far-field regimes. The limits depend on the choice of material susceptibilities and bounding surfaces enclosing arbitrarily shaped objects. In this article, we apply these bounds to two different geometric configurations of interest, namely dipolar particles or extended structures of infinite area in the near field of one another, and compare these predictions to prior limits. We find that while near-field radiative heat transfer between dipolar particles can saturate purely geometric "Landauer" limits, bounds on extended structures cannot, instead growing much more slowly with respect to a material response figure of merit, an "inverse resistivity" for metals, due to the deleterious effects of multiple scattering; nanostructuring is unable to overcome these limits, which can be practically reached by planar media at the surface polariton condition.

Near-field radiative heat transfer between bodies at the nanoscale can surpass blackbody limits on thermal radiation by orders of magnitude due to contributions from evanescent electromagnetic fields, which carry no energy to the far-field. Thus far, principles guiding explorations of larger heat transfer beyond planar structures have assumed utility in surface nanostructuring, which can enhance the density of states, and further assumed that such design paradigms can approach Landauer limits, in analogy to conduction. We derive fundamental shape-independent limits to radiative heat transfer, applicable in near- through far-field regimes, that incorporate material and geometric constraints such as intrinsic dissipation and finite object sizes, and show that these preclude reaching the Landauer limits in all but a few restrictive scenarios. Additionally, we show that the interplay of material response and electromagnetic scattering among proximate bodies means that bodies which maximize radiative heat transfer actually maximize scattering rather than absorption. Finally, we compare our new bounds to existing Landauer limits, as well as limits involving bodies maximizing far-field absorption, and show that these lead to overly optimistic predictions. Our results have ramifications for the ultimate performance of thermophotovoltaics and nanoscale cooling, as well as related incandescent and luminescent devices.

The visualisation of objects moving at relativistic speeds has been a popular topic of study since Special Relativity's inception. While the standard exposition of the theory describes certain shape-changing effects, such as the Lorentz-contraction, it makes no mention of how an extended object would appear in a snapshot or how apparent distortions could be used for measurement. Previous work on the subject has derived the apparent form of an object, often making mention of George Gamow's relativistic cyclist thought experiment. Here, a rigorous re-analysis of the cyclist, this time in 3-dimensions, is undertaken for a binocular observer, accounting for both the distortion in apparent position and the relativistic colour and intensity shifts undergone by a fast moving object. A methodology for analysing binocular relativistic data is then introduced, allowing the fitting of experimental readings of an object's apparent position to determine the distance to the object and its velocity. This method is then applied to the simulation of Gamow's cyclist, producing self-consistent results.

In the past hundred years, chaos has always been a mystery to human beings, including the butterfly effect discovered in 1963 and the dissipative structure theory which won the chemistry Nobel Prize in 1977. So far, there is no quantitative mathematical-physical method to solve and analyze these problems. In this paper, the idea of using field theory to study nonlinear systems is put forward, and the concept of generalized potential is established mathematically. The physical essence of generalized potential promoting the development of nonlinear field is extended and the spatiotemporal evolution law of generalized potential is clarified. Then the spatiotemporal evolution law of conservative system and pure dissipative system is clarified. Acceleration field, conservative vector field and dissipation vector field are established to evaluate the degree of conservation and dissipation of physical field. Finally, the development route of new field research and the precondition of promoting engineering application in the future are discussed.