Dynamics of fluctuations below a stationary bifurcation to electroconvection in the planar nematic liquid crystal N4

We fitted C(k,tau,epsilon) proportional to exp([-sigma(k,epsilon)tau] to time-correlation functions C(k,tau,epsilon) of structure factors S(k,t,epsilon) of shadowgraph images of fluctuations below a supercritical bifurcation at V(0)=V(c) to electroconvection of a planar nematic liquid crystal in the presence of a voltage V=sqrt[2]V(0)cos((2pift) [k=(p,q) is the wave vector and epsilon identical with V(2)(0)/V(2)(c)-1]. There were stationary oblique (normal) rolls at small (large) f. Fits of a modified Swift-Hohenberg form to sigma(k,epsilon) gave f-dependent critical behavior for the minimum decay rates sigma(0)(epsilon) and the correlation lengths xi(p,q)(epsilon).     

Deviations from the Poisson behavior of equilibrium fluctuations in a closed system

A molecular dynamics simulation of dimer formation in an adiabatic, hardcore, square-well, dilute two-dimensional gas yields a non-Poissonian dimer number distribution. Its ratio of variance to mean deviates from unity in a manner recently predicted theoretically.     

Large-density fluctuations for the one-dimensional supercritical contact process

We consider the one-dimensional supercritical contact process. LetT _v be the first time the process reaches a densityq larger than the equilibrium one in the region [1N]. We prove that, starting from equilibrium,T _N /E(T _N ) converges to an exponential random time of mean one. In this way we extend previous results of Lebowitz and Schonmann.     

Appearance potential spectra of barium. Deviations from simple theory

The appearance potential spectra of barium have been recorded for different core levels. Effects are observed which are not predicted by the model involving self-convolution of the density of states.     

Deviations from the Matthiessen rule

Deviations from the Matthiessen rule due to weak anisotropy of the Fermi surface of monovalent cubic metals containing different point defects are investigated. They are found to be smaller than about 2% of the total resistivity for Fermi surfaces not touching the Brillouin-zone boundary. The dependence of deviations from the Matthiessen rule on the point defect concentration is discussed for metals containing point defects and screw dislocations and compared with experiments.     

Magnetization of amorphous alloys — Deviations from spin wave theory at low temperatures

Spin resonance measurements have been used to obtain the temperature dependence of the magnetization in (Fe_xNi_1?x)₇₅P₁₆B₆A?₃ alloys for 4 ? T ? 300K. With x = 0.5, spin wave theory is adequate to account for the observations. For x = 0.4 and 0.3 marked deviations from $\text{T}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ behavior are noted below ～ 70K and we propose a simple model to account for these deviations.     

Analytic scattering theory for many-body systems below the smallest three-body threshold

We consider the Schrödinger operatorH=H ₀+V of a many-body system, whereV is a sum of dilation-analytic, short range (not necessarily local) two-body interactions, together with the associated self-adjoint analytic familyH(z), |Argz|<a, of complex-dilated operators. For eachz we construct the local wave operators and the S-matrix below the smallest 3-body threshold, using abstract stationary scattering theory and the Weinberg-van Winter equation. The diagonal element of the inverse S-matrix describing scattering within the channel in the lowest energy range is proved to be the boundary value of a meromorphic functionL (z)(z), –az<0, whereL (z) is the S-matrix forH(z) on the corresponding cut. Generally, the poles ofL (z) are resolvent resonances, but a resolvent resonance may not be a pole ofL (z), if it is embedded as an eigenvalue in the continuum ofH(z ₀) for a suitablez ₀.     

On the fold-Hopf bifurcation for continuous piecewise linear differential systems with symmetry

In this paper a partial unfolding for an analog to the fold-Hopf bifurcation in three-dimensional symmetric piecewise linear differential systems is obtained. A particular biparametric family of such systems is studied starting from a very degenerate configuration of nonhyperbolic periodic orbits and looking for the possible bifurcation of limit cycles. It is proved that four limit cycles can coexist after perturbation of the original configuration, and other two limit cycles are conjectured. It is shown that the described bifurcation scenario appears for appropriate values of parameters in the celebrated Chua's oscillator.     

Self-consistent perturbation theory for dynamics of valence fluctuations

Dynamical as well as equilibrium properties of model Ce systems are investigated in both the intermediate-valence and nearly integral-valence (Kondo) regimes at finite temperatures. With self-consistent account of hybridization effects between the conduction bands and the highly correlated 4f states, the 4f-electron density of states _4f () and the dynamical magnetic susceptibility () are derived. Equilibrium properties such as the static magnetic susceptibility and the averaged 4f-electron number are also computed within the same approximation scheme that neglects intersite interactions between different Ce ions. In the intermediate-valence regime the calculated line-shape of Im ()/ is close to the Lorentzian at high temperatures, but at low temperatures there appears an inelastic peak. In the Kondo regime it is shown that a sharp peak in _4f () develops at the Fermi level as the temperature decreases. The line-shape of Im ()/ is shown to be close to the Lorentzian at all temperatures. The half-width is considerably enhanced over the Korringa value expected for the local-moment system. The temperature dependence of the half-width agrees qualitatively with experimental results in Kondo compounds such as CeB₆, CeCu₂Si₂ and CeAl₃.     

Allowance for wideband parameter fluctuations in linear inertial networks

A method is developed for analysis of linear inertial networks that undergo parameter fluctuations over a wide detuning range (up to the carrier frequency). Frequency fluctuations caused by reactive-parameter perturbations in LC and tapped-capacitor oscillators are determined as an illustration.Nizhny Novgorod State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 36, No. 10, pp. 936–941, October, 1993.     

Self-consistent perturbation theory for dynamics of valence fluctuations

A perturbation-theoretic scheme is developed for dynamics of valence fluctuations in rare-earth systems with unstable 4f shells. The theory is formulated in close analogy to the standard Green-function method for many-body systems but without use of the linked-cluster theorem. This formulation regards hybridization between 4f and conduction-band states as perturbation and naturally incorporates the strong on-site 4f-electron correlation. Some favorable features are: (i) the approximation scheme automatically satisfies conservation laws required for response functions; (ii) realistic 4f-shell structures with crystalline-electric-field effects can be taken into account; (iii) the theory does not have divergence difficulties over the whole temperature range. In the lowest-order self-consistent approximation, explicit formulae for dynamical susceptibilities and 4f-electron density of states are presented. At high temperatures, the theory reproduces previous results obtained by the Mori method.     

The bifurcation approach to the theory of the first order isotropiv-nematic phase transition

The known results about the first order transition of the isotropic liquid of rod-like molecules into nematic phase are obtained in a simple way in terms of bifurcations of a nonlinear intergal equation solution.     

Self-consistent perturbation theory for dynamics of valence fluctuations

Dynamical properties of valence-fluctuating systems are studied at absolute zero of temperature. The self-consistent perturbation theory developed for rare-earth impurity systems is used with some refinement. The theory takes account of the orthogonality catastrophe caused by hybridization of 4f and conduction electrons. Extensive numerical results are reported for the 4f-electron density of states _4f () and the dynamical magnetic susceptibility (). The results cover both the intermediate-valence and nearly integral-valence regimes of a model Ce impurity system. The present theory gives reasonable overall feature of dynamics including a sharp peak in _4f (0) in the Kondo regime. However, the low-frequency limit of dynamical quantities is not consistent with the Fermi-liquid property. It is shown that interpolation of the present results and those by the Fermi-liquid theory is possible. Hence accurate dynamical information is obtained over a wide excitation-frequency range.     

Self-consistent perturbation theory for dynamics of valence fluctuations

Dynamical property of an intermediate-valence Tm ion in a metallic matrix is investigated by the use of the self-consistent perturbation theory. Both of the fluctuating valence states in Tm have nonzero angular momentum in contrast to Ce and Yb systems. It is shown that the participation of two valence states in the magnetic susceptibility leads to peculiar magnetic properties such as enhanced Korringa-type magnetic relaxation and a systematic deviation from the Curie-Weiss law of the susceptibility. The susceptibility diverges in the zero-temperature limit. The dynamical susceptibility can be fitted by the Lorentzian lineshape very well for a wide frequency and temperature range. The single-particle excitation spectrum is also derived from which the resistivity is calculated. A logarithmic increase of the resistivity with decreasing temperature is found.     

Deviations from hydrodynamics on the nanoscale

This study has examined the decay of an instantaneously imposed heat pulse on an equilibrium model of a dense fluid. The spatial extent of the initial pulse is quite small, of the order of 100 cubic nanometres; the amount of energy added to the system is only 5% of the total system kinetic energy. This small pulse decays quite rapidly, within several picoseconds, but the decay proceeds more slowly than predicted by the hydrodynamic equations. During the first picosecond of the decay, the kinetic energy is not equipartitioned, and a rapid process of energy transfer from kinetic energy to potential energy via interparticle interactions takes place. A new transport theory is developed that includes the ‘pre-hydrodynamic’ stage of evolution of non-equilibrium systems. Formally exact expressions for the local density, velocity, and kinetic energy (temperature) fields are developed in terms of Green's functions that depend on dynamic quantities, such as the mean-square displacement, averaged over the ensemble of initial states. No partial differential equations are involved.     

Charting the landscape of supercritical string theory

Special solutions of string theory in supercritical dimensions can interpolate in time between theories with different numbers of spacetime dimensions and different amounts of world sheet supersymmetry. These solutions connect supercritical string theories to the more familiar string duality web in ten dimensions and provide a precise link between supersymmetric and purely bosonic string theories. Dimension quenching and c duality appear to be natural concepts in string theory, giving rise to large networks of interconnected theories.     

The concentration fluctuations and the mutual diffusion coefficient in the supercritical solution

Molecular dynamics simulations on Lennard-Jones mixture in the supercritical region are performed. The number of the molecules in the unit cell is 23328 and the mole fraction is 0.5. The concentration fluctuations near the critical point are large compared to the ideal mixing. The mutual diffusion coefficient normalized by the self-diffusion coefficient has a small value near the critical density because of the large concentration fluctuation. The heat capacity, partial molar volume and correlation lengths of density and concentration in the supercritical region are compared with those at the normal density.     

Global correlation matrix spectra of the surface temperature of the oceans from random matrix theory to Poisson fluctuations

In this work we use the random matrix theory (RMT) to correctly describe the behavior of spectral statistical properties of the sea surface temperature of oceans. This oceanographic variable plays an important role in the global climate system. The data were obtained from National Oceanic and Atmospheric Administration (NOAA) and delimited for the period 1982 to 2016. The results show that oceanographic systems presented specific β values that can be used to classify each ocean according to its correlation behavior. The nearest-neighbors spacing of correlation matrix for north, central and south of the three oceans get close to a RMT distribution. However, the regions delimited in the Antarctic pole exhibited the distribution of the nearest-neighbors spacing well described by the Poisson model, which shows a statistical change of RMT to Poisson fluctuations.