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At least 37 records · Page 2Linked to original sources
arXiv2007

Lattice Boltzmann simulation of electrowetting-on-dielectric in a rough-wall channel

A lattice Boltzmann model was proposed to simulate electrowetting-on-dielectric (EWOD). The insulative vapor and the electrolyte liquid droplet were simulated by the lattice Boltzmann method respectively, and the linear property between cosine of contact angle and the electric field force confirms the reliability of this model. In the simulation of electrolyte flowing in a rough-wall channel under an external electric field, we found that a narrow channel is more sensitive than a broad channel and the flux decreases monotonously as the electric field increase, but may suddenly increase if the electric field is strong enough.

physics.comp-ph↗
arXiv2007

Maxwell equations in Riemannian space-time, geometry effect on material equations in media

The known possibility to consider the (vacuum) Maxwell equations in a curved space-time as Maxwell equations in flat space-time(Mandel'stam L.I., Tamm I.E.) taken in an effective media the properties of which are determined by metrical structure of the curved model is studied. Metrical structure of the curved space-time generates effective constitutive equations for electromagnetic fields, the form of four corresponding symmetrical tensors is found explicitly for general case of an arbitrary Riemannian space - time. Four constitutive tensors are not independent and obey some additional constraints between them. Several simple examples are specified in detail:itis given geometrical modeling of the anisotropic media (magnetic crystals) and the geometrical modeling of a uniform media in moving reference frame in the Minkowsky electrodynamics -- the latter is realized trough the use of a non-diagonal metrical tensor determined by 4-vector velocity of the moving uniform media. Also the effective material equations generated by geometry of space of constant curvature (Lobachevsky and Riemann models) are determined.

physics.class-ph↗
arXiv2007

100 Years of dimensional analysis: New steps toward empirical law deduction

On the verge of the centenary of dimensional analysis (DA), we present a generalisation of the theory and a methodology for the discovery of empirical laws from observational data. It is well known that DA: a) reduces the number of free parameters, b) guarantees scale invariance through dimensional homogeneity and c) extracts functional information encoded in the dimensionless grouping of variables. Less known are the results of Rudolph and co-workers that DA also gives rise to a new pair of transforms - the similarity transform (S) that converts physical dimensional data into dimensionless space and its inverse (S'). Here, we present a new matrix generalisation of the Buckingham Theorem, made possible by recent developments in the theory of inverse non-square matrices, and show how the transform pair arises naturally. We demonstrate that the inverse transform S' is non-unique and how this casts doubt on scaling relations obtained in cases where observational data has not been referred to in order to break the degeneracy inherent in transforming back to dimensional (physical) space. As an example, we show how the underlying functional form of the Planck Radiation Law can be deduced in only a few lines using the matrix method and without appealing to first principles; thus demonstrating the possibility of a priori knowledge discovery; but that subsequent data analysis is still required in order to identify the exact causal law. It is hoped that the proof presented here will give theoreticians confidence to pursue inverse problems in physics using DA.

physics.class-ph↗
arXiv2007

Electrical control of surface-wave propagation at the planar interface of a linear electro-optic materials and an isotropic dielectric material

Surface waves can propagate on the planar interface of a linear electro-optic (EO) material and an isotropic dielectric material, for restricted ranges of the orientation angles of the EO material and the refractive index of the isotropic material. These ranges can be controlled by the application of a dc electric field, and depend on both the magnitude and the direction of the dc field. Thus, surface-wave propagation can be electrically controlled by exploiting the Pockels effect.

physics.optics↗
arXiv2011

Fractional Stability

A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate stability with respect to motion changes at fractional changes of variables. Note that dynamical systems, which are unstable "in sense of Lyapunov", can be stable with respect to fractional variations.

physics.class-ph↗
arXiv2009

In-situ observation of a soap film catenoid - a simple educational physics experiment

The solution to the Euler-Lagrange equation is an extremal functional.To understand that the functional is stationary at local extrema (maxima or minima), we propose a physics experiment that involves using soap film to form a catenoid. A catenoid is a surface that is formed between two coaxial circular rings and is classified mathematically as a minimal surface.Using soap film, we create catenoids between two rings and characterize the catenoid in-situ while varying distance between rings. The shape of the soap film is very interesting and can be explained using dynamic mechanics. By observing catenoid, physics students can observe local extrema phenomena. We stress that in-situ observation of soap film catenoids is an appropriate physics experiment that combines theory and experimentation.

physics.class-ph↗
arXiv2008

On the existence of Hamiltonians for non-holonomic systems

We consider the question of existence of Hamiltonians for autonomous non-holonomic mechanical systems in this paper. The approach is elementary in the sense that the existence of a Hamiltonian for a given non-holonomic system is considered to be equivalent to the existence of a non-degenerate Lagrangian for the system in question. The possible existence of such a Lagrangian is related to the inverse problem of constructing a Lagrangian from the appropriate equations of motion. A simple example in three dimensions with one non-holonomic constraint is analysed in detail, and it is shown that in this case there is no Lagrangian reproducing the equations of motion in three dimensions. Thus the system does not admit a variational formulation in three dimensions. However, the system in question is equivalent to a two-dimensional system which admits a variational formulation. Two distinct Lagrangians and their corresponding Hamiltonians are constructed explicitly for this two-dimensional system

physics.class-ph↗
arXiv2007

The number of dimensional fundamental constants

We revisit, qualify, and objectively resolve the seemingly controversial question about what is the number of dimensional fundamental constants in Nature. For this purpose, we only assume that all we can directly measure are space and time intervals, and that this is enough to evaluate any physical observable. We conclude that the number of dimensional fundamental constants is two. We emphasize that this is an objective result rather than a "philosophical opinion", and we let it clear how it could be refuted in order to prove us wrong. Our conclusion coincides with Veneziano's string-theoretical one but our arguments are not based on any particular theory. As a result, this implies that one of the three usually considered fundamental constants "G", "c" or "h" can be eliminated and we show explicitly how this can be accomplished.

physics.class-ph↗
arXiv2012

Can the tidal quality factors of terrestrial planets and moons scale as positive powers of the tidal frequency?

In geophysics and seismology, it is a common knowledge that the quality factors Q of the mantle and crust materials scale as the tidal frequency to a positive fractional power (Karato 2007, Efroimsky and Lainey 2007). In astronomy, there exists an equally common belief that such rheological models introduce discontinuities into the equations and thus are unrealistic at low frequencies. We demonstrate that, while such models indeed make the conventional expressions for the tidal torque diverge for vanishing frequencies, the emerging infinities reveal not the impossible nature of one or another rheology, but a subtle flaw in the underlying mathematical model of friction. Flawed is the common misassumption that the tidal force and torque are inversely proportional to the quality factor. In reality, they are proportional to the sine of the tidal phase lag, while the inverse quality factor is commonly identified with the tangent of the lag. The sine and tangent of the lag are close everywhere {\it{except in the vicinity of the zero frequency}}. Reinstating of this detail tames the fake infinities and rehabilitates the "impossible" scaling law (which happens to be the actual law the mantles obey). This preprint is a pilot paper. A more comprehensive treatise on tidal torques is to be published (Efroimsky and Williams 2009).

astro-ph↗
arXiv2008

On the Relationship between Thermodynamics and Special Relativity

Starting from a formulation for the $dS$ element that includes movement, and considering the variation of the entropy Lorentz invariant, we found the relativistic transformations for thermodynamic systems that satisfy the three laws of thermodynamics. Particularly, we found the temperature and pressure transformations, given by $T'=γT$ and $p'=γ^2p$ respectively. Furthermore, we show that this transformations keeps the form of the state equation for an ideal gas in agreement with the relativity principle.

physics.class-ph↗
arXiv2009

Statistical relativistic temperature transformation for ideal gas of bradyons, luxons and tachyons

Starting from a microcanonical statistical approach and special relativity, the relativistic transformations for temperature and pressure for an ideal gas of bradyons, luxons or tachyons is found. These transformations are in agreement with the three laws of thermodynamic and our temperature transformation is the same as Ott's. Besides, it is shown that the thermodynamic $dS$ element is Lorentz-invariant.

physics.gen-ph↗
arXiv2008

Functions of diffraction correction and analytical solutions in nonlinear acoustic measurement

This paper presents an analytical formulation for correcting the diffraction associated to the second harmonic of an acoustic wave, more compact than that usually used. This new formulation, resulting from an approximation of the correction applied to fundamental, makes it possible to obtain simple solutions for the second harmonic of the average acoustic pressure, but sufficiently precise for measuring the parameter of nonlinearity B/A in a finite amplitude method. Comparison with other expressions requiring numerical integration, show the solutions are precise in the nearfield.

physics.class-ph↗
arXiv2008

Nonlocal description of a falling body through the air

In this present work we consider a falling body through the air under the influence of gravity. In particular, we consider the experimental data based upon the free fall of six men in the atmosphere of the earth. In order to describe this process we employ a nonlocal dissipative force. We show that our description, by using an exponential memory kernel, can fit the experimental data as well as that of a local dissipative force.

physics.gen-ph↗
arXiv2008

Hamiltonian structure of the complex Monge-Ampère equation

We discover Hamiltonian structure of the complex Monge-Amp`ere equation when written in a first order two-component form. We present Lagrangian and Hamiltonian functions, a symplectic form and the Hamiltonian operator that determines the Poisson bracket.

physics.class-ph↗
arXiv2008

Modélisation de la propagation dans une structure fermée surdimensionnée

The propagation of an electromagnetic wave in closed structures led to numerous applications ranging from the characterization of materials in resonating cavities to the measurements using pregnant reverberant EMF. We created models to study the existence of electromagnetic waves in large closed structures. There are two ways of excitation in such structures. One of these methods is based on continuous excitation with specific resonant modes, which has a variety of applications. The second method consists of a pulsed excitation similar to the impulse wave radar. This excitation provides other information. The structures studied were closed by perfectly conducting walls and the electromagnetic wave was generated in the structure using dipole antennas. The dimensions (length, width and height) were always much larger than the wavelength.

physics.class-ph↗
arXiv2008

Is the phase of plane waves a frame-independent quantity?

The invariance of the phase of plane waves among inertial frames is investigated in some details. The reason that eventually led the author of a recent EPL letter [EPL \textbf{79}, 1006 (2007)] to a spurious conclusion of the non-invariance of the phase of waves has been identified -- it is the ignorance of the effect of relativistically-induced optical anisotropy in the analysis of the problem. It is argued that the Lorentz-invariant expression for the phase of waves should be taken in the form $Φ=\mathbf{k\cdot r}-\mathbf{k\cdot u}/c$, instead of the widely-used expression $Φ=\mathbf{k\cdot r}-ωt$ which has a limited validity.

physics.optics↗