Physics

We investigate generic heat engines and refrigerators operating between two heat reservoirs, for the condition when their efficiencies are equal to each other. It is shown that the corresponding value of efficiency is given as the inverse of the generalized golden mean, ϕ p , where the parameter p depends on the degree of irreversibility of both engine and refrigerator. The reversible case ( p=1 ) yields the efficiency in terms of the standard golden mean. We also extend the analysis to a three-heat-resrervoir setup.

In recent years the chain fountain became prominent for its counter-intuitive fascinating physical behavior. Most widely known is the experiment in which a long chain leaves an elevated beaker like a fountain and falls to the ground under the influence of gravity. The observed chain fountain was precisely described and predicted by an inverted catenary in several publications. The underlying assumptions are a stationary fountain and the knowledge of the boundary conditions, the ground and beaker reaction forces. In contrast to determining the steady-state chain fountain shape, it turns out that the main difficulty lies in predicting the reaction forces. A consistent and complete physical explanation model is currently not available. In order to give a reasonable explanation for the reaction forces an illustrative mechanical system for generating steady-state chain fountain is proposed in this work. The model allows to generate all physical possible chain fountains by adjusting a pulley arrangement. The simplifications incorporated make the phenomenon accessible to undergraduate students.

The tennis racket effect is a geometric phenomenon which occurs in a free rotation of a three-dimensional rigid body. In a complex phase space, we show that this effect originates from a pole of a Riemann surface and can be viewed as a result of the Picard-Lefschetz formula. We prove that a perfect twist of the racket is achieved in the limit of an ideal asymmetric object. We give upper and lower bounds to the twist defect for any rigid body, which reveals the robustness of the effect. A similar approach describes the Dzhanibekov effect in which a wing nut, spinning around its central axis, suddenly makes a half-turn flip around a perpendicular axis and the Monster flip, an almost impossible skate board trick.

In elastic wave systems, combining the powerful concepts of resonance and spatial grading within structured surface arrays enable resonant metasurfaces to exhibit broadband wave focusing, mode conversion from surface (Rayleigh) waves to bulk (shear) waves, and spatial frequency selection. Devices built around these concepts allow for precise control of surface waves, often with structures that are subwavelength, and utilise rainbow trapping that separates the signal spatially by frequency. Rainbow trapping yields large amplifications of displacement at the resonator positions where each frequency component accumulates. We investigate whether this amplification, and the associated control, can be used to create energy harvesting devices; the potential advantages and disadvantages of using graded resonant devices as energy harvesters is considered. We concentrate upon elastic plate models for which the A0 mode dominates, and take advantage of the large displacement amplitudes in graded resonant arrays of rods, to design innovative metasurfaces that focus waves for enhanced piezoelectric sensing and energy harvesting. Numerical simulation allows us to identify the advantages of such graded metasurface devices and quantify its efficiency, we also develop accurate models of the phenomena and extend our analysis to that of an elastic half-space and Rayleigh surface waves.

The various mathematical models developed in the past to interpret the behavior of natural and manmade materials were based on observations and experiments made at that time. Classical laws (such as Newton's for gravity, Hooke's for elasticity, Navier-Stokes for fluidity, Fick's/Fourier's for diffusion/heat transfer, Coulomb's for electricity, as well as Maxwell's for electromagnetism and Einstein's for relativity) formed the basis of current technology and shaping of our civilization. The discovery of new phenomena with the aid of recently developed experimental probes have led to various modifications of these laws across disciplines and the scale spectrum: from subatomic and elementary particle physics to cosmology and from atomistic and nano/micro to macro/giga scales. The emergence of nanotechnology and the further advancement of space technology are ultimately connected with the design of novel tools for observation and measurements, as well as the development of new methods and approaches for quantification and understanding. The paper first reviews the author's previously developed weakly nonlocal or gradient models for elasticity, diffusion and plasticity within a unifying internal length gradient (ILG) framework. It then proposes a similar extension for fluids and Maxwell's equations of electromagnetism. Finally, it ventures a gradient modification of Newton's law of gravity and examines its implications to some problems of elementary particle physics, also relevant to cosmology. Along similar lines, it suggests an analogous extension of London's quantum mechanical potential to include both an "attractive" and a "repulsive" branch. It concludes with some comments on a fractional generalization of the ILG framework.

Electrostatic Green functions for grounded equipotential circular and elliptical rings, and grounded hyperspheres in n-dimension electrostatics, are constructed using Sommerfeld's method. These electrostatic systems are treated geometrically as different radial p-norm wormhole metrics that are deformed to be the Manhattan norm, namely "squashed wormholes". Differential geometry techniques are discussed to show how Riemannian geometry plays a rule in Sommerfeld's method. A comparison is made in terms of strength and position of the image charges for Sommerfeld's method with those for the more conventional Kelvin's method. Both methods are shown to be mathematically equivalent in terms of the corresponding Green functions. However, the two methods provide different physics perspectives, especially when studying different limits of those electrostatic systems. Further studies of ellipsoidal cases are suggested.

In this paper, we investigate the so-called Bopp-Podolsky electrodynamics. The Bopp-Podolsky electrodynamics is a prototypical gradient field theory with weak nonlocality in space and time. The Bopp-Podolsky electrodynamics is a Lorentz and gauge invariant generalization of the Maxwell electrodynamics. We derive the retarded Green functions, first derivatives of the retarded Green functions, retarded potentials, retarded electromagnetic field strengths, generalized Lienard-Wiechert potentials and the corresponding electromagnetic field strengths in the framework of the Bopp-Podolsky electrodynamics for three, two and one spatial dimensions. We investigate the behaviour of these electromagnetic fields in the neighbourhood of the light cone. In the Bopp-Podolsky electrodynamics, the retarded Green functions and their first derivatives show fast decreasing oscillations inside the forward light cone.

We illustrate properties of guided waves in terms of a superposition of body waves. In particular, we consider the Love and SH waves. Body-wave propagation at postcritical angles--required for a total reflection--results in the speed of the Love wave being between the speeds of the SH waves in the layer and in the halfspace. A finite wavelength of the SH waves--required for constructive interference--results in a limited number of modes of the Love wave. Each mode exhibits a discrete frequency and propagation speed; the fundamental mode has the lowest frequency and the highest speed.

We present the basic formulation of Hamilton dynamics in complex phase space. We extend the Hamilton's function by including the imaginary part and find out the corresponding Hamilton's canonical equation of motion. Example of simple harmonic motion are considered and the corresponding trajectory are plotted on real and complex phase space.

It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we show that thermodynamics (or, more precisely, a thermodynamically-like description) can be constructed even for deterministic Hamiltonian systems, for example, systems with only one degree of freedom. We show that for such systems it is possible to introduce analogs of thermal energy, temperature, entropy, Helmholtz free energy, etc., which are related to each other by the usual thermodynamic relations. For the considered Hamiltonian systems, the first and second laws of thermodynamics are rigorously derived, which have the same form as in ordinary (molecular) thermodynamics. It is shown that for Hamiltonian systems it is possible to introduce the concepts of a thermodynamic state, a thermodynamic process, and thermodynamic cycles, in particular, the Carnot cycle, which are described by the same relations as their usual thermodynamic analogs.