Log-periodic corrections to the Cole–Cole expression in dielectric relaxation

A model of the self-similar process of relaxation is given, and a method of derivation of the kinetic equations for the total polarization based on the ideas of fractional kinetics is suggested. The derived kinetic equations contain integro-differential operators having non-integer order. They lead to the Cole–Cole expression for the complex dielectric permittivity. It is shown rigorously that the power-law exponent α$\alpha$ in the Cole–Cole expression coincides with the dimension of the mixed space-temporal fractal ensemble. If the discrete scale invariance for the temporal-space structure of the dielectric medium considered becomes important, then the expression for the complex dielectric permittivity contains log-periodic corrections (oscillations) and, hence, it generalizes the conventional Cole–Cole expression. The corrections obtained in this model suggest another way of interpretation and analysis of dielectric spectra for different complex materials.     

Applications of a Cole–Hopf transform to the 3D Navier–Stokes equations

The Navier–Stokes equations written in the vector potential can be recast as non-linear Schrödinger equations at imaginary times, i.e. heat equations with a potential term, using the Cole–Hopf transform. On this basis, we study two kinds of Navier–Stokes flows by means of direct numerical simulations. In an experiment on vortex reconnection, it is found that the potential term takes large negative values in regions where intensive reconnection takes place, whereas the signature of the non-linear term is more broadly spread. For decaying turbulence starting from a random initial condition, such a correspondence is also observed in the early stage when the flow is dominated by vorticity layers. At later times, when the flow features several tubular vortices, this correspondence becomes weaker. Finally, a similar set of transformations is presented for the magneto–hydrodynamic equations, which reduces them to a set of heat equations with suitable potential terms, thereby obtaining new criteria for the regularity of their solutions.     

Can the CMB reveal the topology of the universe?

This article summarizes recent progress in the development of tools to study the topology of the universe with the cosmic microwave background. The different signatures of the topology and observational constraints are described. The ability of future experiments to reveal the topological structure of our universe is then discussed. To cite this article: J.P. Uzan, A. Riazuelo, C. R. Physique 4 (2003).     

Dark Energy： Relating the Evolutions of the Universe from the Past to the Future

Using the evolution history of the universe, one can make constraint on the parameter space of dynamic dark energy models. We discuss two different parameterized dark energy models. Our results further restrict the combined constraints obtained from supernova and the first-year Wilkinson-microwave-anisotropy-probe observations. From the allowed parameter space, it is found that our universe will experience an eternal acceleration. We also estimate the bound on the physically relevant regions both in the re-inflationary and inflationary phases.     

On the interpretation of the results of the experimental test of the Askar’yan effect

The effect of the environment on the results of measuring the radio radiation spectrum is considered in the experimental simulation of the cascade shower by a high-energy γ-ray beam in a dense medium. The calculation shows that the character of the measured energy spectrum depends on the location of the receiving antenna with respect to the shower axis.     

Why is the Euclidean Line the Same as the Real Line?

This paper investigates whether the differential structure of space-time follows from accepted laws of physics, or is a mathematical invention. In view of the results of [7], it suffices to consider whether the assumed identity of the Euclidean line E—the line of the geometers of ancient Greece—and the real line R of modern analysis, follows from any known law of nature (i.e., one that can be falsified empirically). Since the totality of empirical data is finite, one is forced to conclude that the completeness of R cannot be falsified empirically—and therefore, according to Popper's criterion, the real line must be an invention, and not a discovery. It then becomes difficult to tell whether Newton's second law of motion (expressed as the differential equation is an invention or a discovery! Finally, some alternatives to the above analysis are briefly analysed.     

Telecommunications—the state of the art

This article is a survey of the technological foundations of telecommunications, including both point-to-point electrical communication wing wires, cables and other guiding media. and radio wave broadcasting to many receivers via terrestrial transmitters or Earth-orbiting space satellites. The characteristics of analogue and digital telecommunication signals, the means available for their transmission and switching me described, together with the organization of local distribution, national and global networks. The various services that can be provided over such networks, including in addition to telephonic communication, audio and video conferencing, data and facsimile transmission and new vied-display data/information access services (Teletext) are outlined. Finally, the sociological implications of these technological and service developments me considered, for example in terms of their impact on urban and rural planning, where people live and work, and on energy economy by reducing the need to travel.     

Study on the optical system for the record of the pulsed acoustic field and the scattering of the cylindrical-like objects buried in underwater sand

11尬roductlon For the vlsuallzatlon and the studies of the physical properties of acoustic ield;the schlierentechnique was the most useful for the co尬Inuous waves[1,2].ReceNwars,the shadowgraphmode was appeared for the recording of＊theing acoustic pulse[3-p].Although the shadowgr地hmode Is used more frequently In experimental fluid dynamics[6],In the irst part of this paper;the response of＊these opticall扯enslty of＊the recorded acoustic pulse related to the acousticpressure gradlem Is st…     

Characteristics of the internal waves and their effects on the sound transmission in the Midst of the Yellow Sea

1IntroductionInternalwavesarefoundthroughouttheworld's...an[1-3].Theactivityofinternalwavescausesthechangesofthesoundspeedprofile,andthereforeaffectsthesoundpropagation['].Duringthepastdecades,considerableprogresshasbeenmadeinunderstandinginternaIwavesandtheireffectsonsoundindeepocean.Nowtheresearchcommunityhasshiftedtheemphasistoshallowwaterarea[5~l1].Inthelatesummerof1996,scientistsfromChinaandtheUnitedStatesconductedacombinedacousticsandphysicaloceanographyexperimentintheYellowSea(YS96)…     

Model independent bounds on the modulus of the pion form factor on the unitarity cut below the ωπ threshold

We study the structure of local baryon fields using the method of QCD sum rule. We only consider the single baryon fields and calculate their operator product expansions. We find that the octet baryon fields belonging to the chiral representations $[(\mathbf{3},\bar{\mathbf{3}}) \oplus(\bar{\mathbf{3}}, \mathbf{3})]$ and [(8,1)??(1,8)] and the decuplet baryon fields belonging to the chiral representations [(3,6)??(6,3)] lead to the baryon masses which are consistent with the experimental data of ground baryon masses. We also calculate their decay constants, check our normalizations for baryon fields in Chen et?al. (Phys. Rev.?D 81:054002, 2009) and find that they are well-defined.     

On the polynomial τ-functions for the KP hierarchy and the bispectral property

We show that the -functions obtained from Schur polynomials lead to wave functions w(x ₁, x ₂, ... ; k) that possess the following bispectral property: There exists a differential operator B{k,_k}, independent of x ₁ , such that B{k,_k}w = {x ₁}w, where {x ₁} is independent of k. This extends for the KP hierarchy some earlier results of J. J. Duistermaat and F. A. Grünbaum for the rational solutions of KdV and of P. Wright for certain rational solutions of the generalized KdV equations.     

Variation in the structural state of the α-phase in the Pd-In-H system during the β → α transformation

Increasing the concentration of indium atoms and hydrogen was found in the α-phase of the foil of a Pd-In alloy (with 5.3 and 5.0 at % In) after its electrolytic hydrogenation and 500-h relaxation. It is shown that the structural variations in the foil during the β → α transformation are nonmonotonic.     

A New Approach to the Justification of the Wolkenstein–Ptitsyn Formula for the Parameter of the Vitrification Equation

Technical Physics - An extended interpretation of the Wolkenstein–Ptitsyn formula for temperature band δTg, characterizing a range of transition from liquid to glass, is considered using...     

On the Structure of the B¨acklund Transformations for the Relativistic Lattices

Abstract

The B¨acklund transformations for the relativistic lattices of the Toda type and their discrete analogues can be obtained as the composition of two duality transformations. The condition of invariance under this composition allows to distinguish effectively the integrable cases. Iterations of the B¨acklund transformations can be described in the terms of nonrelativistic lattices of the Toda type. Several multifield generalizations are presented.     

Does the market maker stabilize the market?

The market maker plays an important role in price formation, but his/her behavior and stabilizing impact on the market are relatively unclear, in particular in speculative markets. This paper develops a financial market model that examines the impact on market stability of the market maker, who acts as both a liquidity provider and an active investor in a market consisting of two types of boundedly rational speculative investors—the fundamentalists and trend followers. We show that the market maker does not necessarily stabilize the market when he/she actively manages the inventory to maximize profits, and that rather the market maker’s impact depends on the behavior of the speculators. Numerical simulations show that the model is able to generate outcomes for asset returns and market inventories that are consistent with empirical findings.     

On the Scattering of the Electron off the Hydrogen Atom and the Helium Ion Below and Above the Ionization Threshold: Temkin–Poet Model

We generalize here the splitting approach to the long range (Coulomb) interaction for the three body scattering problem. With this approach, the exterior complex rotation technique can be applied for systems with asymptotic Coulomb interaction. We illustrate the method with calculations of the electron scattering on the hydrogen atom and positive helium ion in the frame of the Temkin–Poet model.     

Do the seagull terms really survive for the electric polarizability of the nucleon?

The seagull terms for the electric polarizability of the nucleon are shown indeed to vanish, if one introduces fluctuations around the Skyrmion configuration, and the origin of the electric polarizability cannot after all be attributed to the seagull terms in the Skyrme model.     

Can the LHC rule out the MSSM?

If supersymmetry (SUSY) exists in nature and is a solution to the hierarchy problem then it should be detectable at the TeV energy scale which the large hadron collider (LHC) is now exploring. One of the main goals of the LHC is the discovery or exclusion of the R-parity conserving minimal supersymmetric standard model (MSSM). So far, the SUSY search results are presented in the context of the constrained MSSM and other specific simplified SUSY models. A model-independent analysis necessarily relies on the trigger-system of the LHC detectors. By using the posterior samples of a 20-parameter MSSM, the phenomenological MSSM, from a fit to indirect collider and cosmological data we find that there is a significant volume in the MSSM parameter space that would escape the standard trigger-systems of the detectors. As such, in the absence of discovery in the current and future LHC runs, it would be difficult if not impossible to exclude the MSSM unless some dedicated and special triggers are commissioned or a Higgs boson with mass as predicted by the supersymmetric models is not found.