Physics

Another counter-example to Dirac's Conjecture is presented, which resembles the Cawley model but is so modified as to include second class constraints. The arbitrary function in the general solution to the defining equations of momenta satisfies a non-linear differential equation. Dirac's conjecture is examined for some solutions to the equation.

We present a comparison of the dispersion relations derived for anti-plane surface waves using the two distinct approaches of the surface elasticity vis-a-vis the lattice dynamics. We consider an elastic half-space with surface stresses described within the Gurtin-Murdoch model, and present a formulation of its discrete counterpart that is a square lattice half-plane with surface row of particles having mass and elastic bonds different from the ones in the bulk. As both models possess anti-plane surface waves we discuss similarities between the continuum and discrete viewpoint. In particular, in the context of the behaviour of phase velocity, we discuss the possible characterization of the surface shear modulus through the parameters involved in lattice formulation.

We first demonstrate how our general intuition of pseudoforces has to navigate around several pitfalls in rotating frames. And then, we proceed to develop an intuitive understanding of the different components of the pseudoforces in most general accelerating (rotating and translating) frames: we show that it is not just a sum of the contributions coming from translation and rotation separately, but there is yet another component that is a more complicated combination of the two. Finally, we demonstrate using a simple example, how these dynamical equations can be used in such frames.

Using the model based on the Regge-like laws, new analytical formulas are obtained for the moment of inertia, the rotation frequency, and the radius of astronomical non-exotic objects (planets, stars, galaxies, and clusters of galaxies). The rotation frequency and moment of inertia of neutron star and the observable Universe are estimated. The estimates of the average numbers of stars and galaxies in the observable Universe are given. The Darwin instability effect in the binary systems (di-planets, di-stars, and di-galaxies) is also analyzed.

We present a method for assigning probabilities to the solutions of initial value problems that have a Lipschitz singularity. To illustrate the method, we focus on the following toy-example: r ¨ = r α , r(t=0)=0 , and r ˙ ∣ r(t=0) =0 , where the dots indicate derivatives to time and α∈]0,1[ . This example has a physical interpretation as a mass in a uniform gravitational field on a dome of particular shape; the case with α=1/2 is known as Norton's dome. Our approach is based on (1) finite difference equations, which are deterministic, (2) a uniform prior on the phase space, and (3) non-standard analysis, which involves infinitesimals and which is conceptually close to numerical methods from physical praxis. This allows us to assign probabilities to the solutions of the initial value problem in the original, indeterministic model.

We briefly show how classical mechanics can be rederived and better understood as a consequence of three assumptions: infinitesimal reducibility, deterministic and reversible evolution, and kinematic equivalence. This work is an overview of some of the results of Assumptions of Physics, a project that aims to identify a handful of physical principles from which the basic laws can be rigorously derived (see this https URL ).

We estimate the expected magnitudes of the Schumann resonance fields immediately after the Chicxulub impact and show that they exceed their present-day values by about 5× 10 4 times. Long-term distortion of the Schumann resonance parameters is also expected due to the enviromental impact of the Chicxulub event. If Schumann resonances play a regulatory biological role, as some studies indicate, it is possible that the excitation and distortion of Schumann resonances as a result of the asteroid/comet impact was a possible stress factor, which, among other stress factors associated with the impact, contributed to the demise of dinosaurs.

An asymptotic analysis of the energy functional of a fiber-reinforced composite beam with a periodic microstructure in its cross section is performed. From this analysis the asymptotically exact energy as well as the 1-D beam theory of first order is derived. The effective stiffnesses of the beam are calculated in the most general case from the numerical solution of the cell and homogenized cross-sectional problems.

The effect of a perfectly conducting planar boundary on the average linear momentum (LM), angular (momentum (AM), and power of a time-harmonic statistically isotropic random field is analyzed. These averages are purely imaginary and their magnitude decreases in a damped oscillatory manner with distance from the boundary. At discrete quasi-periodic distances and frequencies, the average LM and AM attain their free-space value. Implications for the optimal placement or tuning of power and field sensors are analyzed. Conservation of the flux of the mean LM and AM with respect to the difference of the average electric and magnetic energies and the radiation stresses via the Maxwell stress dyadic is demonstrated. The second-order spatial derivatives of differential radiation stress can be directly linked to the electromagnetic energy imbalance. Analytical results are supported by Monte Carlo simulation results. As an application, performance based estimates for the working volume of a reverberation chamber are obtained. In the context of multiphysics compatibility, mechanical self-stirred reverberation is proposed as an exploitation of electromagnetic stress.

Using a dipole interaction model, we derive generalized sheet transition conditions (GSTCs) for electromagnetic fields at the surface of a metascreen consisting of an array of arbitrarily shaped apertures in a perfectly conducting screen of nonzero thickness. The simple analytical formulas obtained are validated through comparison with full-wave numerical simulations.