An Isoperimetric Inequality for Fundamental Tones of Free Plates

We establish an isoperimetric inequality for the fundamental tone (first nonzero eigenvalue) of the free plate of a given area, proving the ball is maximal. Given τ > 0, the free plate eigenvalues ω and eigenfunctions u are determined by the equation ΔΔu − τΔu = ωu together with certain natural boundary conditions. The boundary conditions are complicated but arise naturally from the plate Rayleigh quotient, which contains a Hessian squared term |D ² u|².     

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002     

Essentially different distributions of current in the inverse problem for the Grad-Shafranov equation

The paper answers a question debated by physicists for many years. It is proved that, for almost equal gradients of the magnetic flux u at its zero-level curve ∂ω, which is the piecewise smooth boundary of a simply-connected domain ω ⋐ ℝ², the inverse problem for the Grad-Shafranov equation of plasma equilibrium in a tokamak (in the cylindrical approximation) admits essentially different profiles of distributions f _u : ω ∋ (x, y) ↦ f(u(x, y)) = u _xx (x, y) + u _yy (x, y) ⩾ 0 in the class of third-order polynomials f(u) = Σ _m=0³ a _m u ^m .     

A Generic C1 Expanding Map¶has a Singular S–R–B Measure

We show that for a generic C¹ expanding map T of the unit circle, there is a unique equilibrium state for − log T′ that is an S–R–B measure for T, and whose statistical basin of attraction has Lebesgue measure 1. We also present some results related to the question of whether a generic C¹ expanding map preserves a σ-finite measure, absolutely continuous with respect to Lebesgue measure. Received: 8 December 2000 / Accepted: 27 March 2001     

Nuclear matter properties in relativistic mean-field model with σ- ω coupling

The σ-ω coupling is introduced phenomenologically in the linear σ-ω model to study the nuclear matter properties. It is shown that not only the effective nucleon mass M^* but also the effective σ meson mass m _σ ^* and the effective ω meson mass m _ω ^* are nucleon-density-dependent. When the model parameters are fitted to the nuclear saturation point, with the nuclear radius constant r ₀ = 1.14 fm and volume energy a ₁ = 16.0 MeV, as well as to the effective nucleon mass M ^* = 0.85M, the model yields m _σ ^* = 1.09m _σ and m _ω ^* = 0.90m _ω at the saturation point, and the nuclear incompressibility K ₀ = 501 MeV. The lowest value of K₀ given by this model by adjusting the model parameters is around 227 MeV. Received: 23 March 2001 / Accepted: 8 June 2001     

Inverse problem for the Grad-Shafranov equation with affine right-hand side

For a given domain ω ⋐ ℝ² with boundary γ = ∂ω, we study the cardinality of the set $ \mathfrak{A}_\eta \left( \Phi \right) $ \mathfrak{A}_\eta \left( \Phi \right) of pairs of numbers (a, b) for which there is a function u = u _(a,b): ω → ℝ such that ∇² u(x) = au(x) + b ⩾ 0 for x ∈ ω, u| _γ = 0, and ||∇u(s)| − Φ(s) ⩽ η for s ∈ γ. Here η ⩾ 0 stands for a very small number, Φ(s) = |∇(s)| / ∫ _γ |∇v| d γ, and v is the solution of the problem ∇² v = a ₀ v + 1 ⩾ 0 on ω with v| _γ = 0, where a ₀ is a given number. The fundamental difference between the case η = 0 and the physically meaningful case η > 0 is proved. Namely, for η = 0, the set $ \mathfrak{A}_\eta \left( \Phi \right) $ \mathfrak{A}_\eta \left( \Phi \right) contains only one element (a, b) for a broad class of domains ω, and a = a ₀. On the contrary, for an arbitrarily small η > 0, there is a sequence of pairs (a _j , b _j ) ∈ $ \mathfrak{A}_\eta \left( \Phi \right) $ \mathfrak{A}_\eta \left( \Phi \right) and the corresponding functions u _j such that ‖f _u ^j+1‖ − ‖f _u ^j ‖ > 1, where ‖f _u ^j = max _x∈ω |f _u ^j (x)| and f _u ^j (x) = a _j u _j (x) + b _j . Here the mappings f _u ^j : ω → ℝ necessarily tend as j → ∞ to the δ-function concentrated on γ.     

Transport and dielectric properties of thin polycrystalline CoO films

Transport and dielectric properties of polycrystalline CoO films were studied as functions of the applied field, frequency and temperature. TheI–V plots showed that the Poole-Frenkel field emission mechanism is responsible for conduction at fields>10⁵ V/cm. The ac conductivity σ(ω), the imaginary part of the dielectric constantε ₂, and tan δ plots as functions of frequency revealed three dispersion regions. The σ(ω) andε ₂ frequency dependence indicates a non-adiabatic hopping of charge carriers at low frequencies and adiabatic hopping at high frequencies. The activation energy of a dielectric oscillator is 0.15 eV. Work supported by the Office of Naval Research.     

Influence of the reagent vibration on the stereo-dynamics of the reactions D- + H2 and H- + D2

Employing the quasi-classical trajectory method and the potential energy surface of Panda and Sathyamurhy [Panda A N and Sathyamurthy N 2004 J. Chem. Phys. 121 9343], the effect of the reagent vibration on vector correlation of the ion-molecule reactions D^- + H₂ and H^- + D₂ is studied at a collision energy of 35.7 kcal/mol. Four generalized polarization-dependent differential cross sections (2π/σ)(dσ₀₀/dω_t),(2π/σ)(dσ₂₀/dω_t),(2π/σ)(dσ₂₂/dω_t), and (2π/σ)(dσ₂₀/dω_t) are presented in the centre-of-mass reference frame, separately. At the same time, the effects on the product angular distributions P(θ_r), P(φ_r) and P(θ_r,φ_r) of the title reactions are also analysed. The calculated results show that the scattering tendencies of the product HD, the alignment and the orientation of j' sensitively depend on reagent molecule vibration.     

Central Limit Theorem¶for Stochastic Hamilton–Jacobi Equations

We study the asymptotic behavior of , where u solves the Hamilton–Jacobi equation u _t +H(x,u _x ) ≡ 0 with H a stationary ergodic process in the x-variable. It was shown in Rezakhanlou–Tarver [RT] that u ^ɛ converges to a deterministic function provided H(x,p) is convex in p and the convex conjugate of H in the p-variable satisfies certain growth conditions. In this article we establish a central limit theorem for the convergence by showing that for a class of examples, u ^ɛ(x,t) can be (stochastically) represented as , where Z(x,t) is a suitable random field. In particular we establish a central limit theorem when the dimension is one and , where ω is a random function that enjoys some mild regularity. Received: 15 February 1999 / Accepted: 14 December 1999     

Density perturbation of unparticle dark matter in the flat Universe

The unparticle has been suggested as a candidate of dark matter. We investigated the growth rate of the density perturbation for unparticle dark matter in the flat Universe. First, we consider the model in which the unparticle is the sole dark matter and find that the growth factor can be approximated well by f=(1+3ω _u )Ω _u ^γ , where ω _u is the equation of state of unparticle. Our results show that the presence of ω _u modifies the behavior of the growth factor f. For the second model where the unparticle co-exists with cold dark matter, the growth factor has a new approximation f=(1+3ω _u )Ω _u ^γ +α Ω _m and α is a function of ω _u . Thus the growth factor of the unparticle is quite different from that of the usual dark matter. This information can help us know more about unparticle and the early evolution of the Universe.     

Determination of nonlinear σ-ω-ρ model parameters in the relativistic mean-field theory by nuclear-matter properties

The parameters of the σ-ω-ρ model in the relativistic mean-field theory with nonlinear σ-meson self-interaction are determined by nuclear-matter properties, which are taken as those extracted by fits to data based on nonrelativistic nuclear models. The values of the relevant parameters are C _σ ²∼ 94, C _ω ²∼ 32, C _ρ ²∼ 26, b∼ - 0.09, c∼ 1, and the σ-meson mass m _σ∼ 370 MeV, while the value of the calculated nuclear- surface thickness is t∼ 1.4 fm. The field system is shown to be stable, since the σ-meson self-interaction energy is a lower bound in this whole parameter region with positive c. On the other hand, the effective nucleon mass M^* is larger than 0.73M, if the symmetry incompressibility K_s is assumed to be negative and the nuclear-matter incompressibility K₀ is kept less than 300 MeV. Received: 27 June 2001 / Accepted: 5 October 2001     

High resolution X-ray photoelectron spectroscopy on nitrogen molecules

This paper summarizes recent developments for experimental and theoretical studies on core-level photoelectron spectroscopy of N₂. Analysis of experimental spectra reveals that the 1σ_g and 1σ_u core-hole states differ in energy by ~100meV and in equilibrium bond length by ~0.04pm, in agreement with ab initio predictions. The ratio of the 1σ_g and 1σ_u photoionization cross sections measured in the photon energy range up to 1 keV reveals oscillatory structure due to two-center interference, equivalent to Young’s double-slit experiment, as Cohen and Fano predicted. The experimental Auger rates for the transition to the dicationic ground state are found to be different by a factor of two for 1σ_g and 1σ_u hole states and are well reproduced by the ab initio calculations. All these findings support the delocalized picture of the core hole. Discussion is given how many-body processes involved and observations for these processes affect the observation of the localized and/or delocalized core hole.     

ωN final state interactions and ω-meson production from heavy-ion collisions

We calculate the elastic and inelastic ωN→ωN, →πN, →ρN, →ρπN, →ππN, →σN reactions within a boson exchange approximation where the ωρπ coupling constant and form factor are fixed by the reaction πN→ωN in comparison to the experimental data. We find rather large ωN cross sections at low relative momenta of the ω-meson which leads to a substantial broadening of the ω-meson width in nuclear matter. The implications of the ωN final state interactions are studied for ω production in ¹²C +¹²C, ⁴⁰Ca +⁴⁰Ca and ⁵⁸Ni +⁵⁸Ni reactions at about 2 · A GeV within the HSD transport approach; the drastic changes of the transverse mass spectra relative to a general m _T-scaling (for π⁰ and η mesons) might be controlled experimentally by the TAPS Collaboration. Received: 28 April 1999 / Revised version: 7 June 1999     

Speed and shape of large-amplitude solitary waves in ion-beam plasma system

Large-amplitude solitary waves are investigated in ion-beam plasma system. The Sagdeev’s pseudopotential is determined in terms of the ion speedu. It is found that there exists a critical value ofu ₀, the value ofu at (u′)² = 0, beyond which the solitary waves cease to exist. The critical value also depends on σ (the ion temperature) or σ_b (the ion beam temperature). One of the author (PC) is grateful to UGC, India for the financial support under SAP(No F.510/8/DRS/2004(SAP-1)).     

Random Homogenization and Singular Perturbations¶in Perforated Domains

The paper considers the singularly perturbed Dirichlet problem −ɛΔu ^ɛ+u ^ɛ=f in a randomly perforated domain Ω^ɛ, which is obtained from a bounded open set Ω in R ^N after removing many holes of size ɛ ^q . The perforated domain is described in terms of an ergodic dynamical system acting on a probability space. Imposing certain conditions on the domain, the behaviour of u ^ɛ when ɛ→ 0 in Lebesgue spaces L ⁿ (Ω) is studied. Test functions together with the Birkhoff ergodic theorem are the main tools of analysis. The Poisson distribution of holes of size ɛ ^p with the intensity λɛ^{− r} is then considered. The above results apply in some cases; other cases are treated by the Wiener sausage approach. Received: 15 December 1999 / Accepted: 14 April 2000     

Quantum states with continuous spectrum for a general time-dependent oscillator

We investigated quantum states with continuous spectrum for a general time-dependent oscillator using invariant operator and unitary transformation methods together. The form of the transformed invariant operator by a unitary operator is the same as the Hamiltonian of the simple harmonic oscillator:I’ = p²/2 +ω ² q ²/2. The fact thatω ² of the transformed invariant operator is constant enabled us to investigate the system separately for three cases, whereω ² > 0,ω ² < 0, andω ² = 0. The eigenstates of the system are discrete forω ² > 0. On the other hand, forω ² <− 0, the eigenstates are continuous. The time-dependent oscillators whose spectra of the wave function are continuous are not oscillatory. The wave function forω ² < 0 is expressed in terms of the parabolic cylinder function. We applied our theory to the driven harmonic oscillator with strongly pulsating mass.     

Tails in harnesses

We consider space- and time-uniformd-dimensional random processes with linear local interaction, which we call harnesses and which may be used as discrete mathematical models of random interfaces. Their components are rea random variablesa _s ^t , wheres ∈ Z ^d andt=0, 1, 2.,... At every time step two events occur: first, every component turns into a linear combination of itsN neighbors, and second, a symmetric random i.i.d. “noise”v is added to every component. For any σ ∈Z _d ⁺ define Δ_σ a′ _s as follows. If σ=(0,...,0), σ=(0,...,0), Δ_σ a _s ^t =a _s ^t . Then by induction, wheree _i is thed-dimensional vector, whoseith component is one and other components are zeros. Denote |σ| the sum of components of σ. Call a real random variable ϕ symmetric if it is distributed as −ϕ. For any symmetric random variable ϕpower decay or P-decay is defined as the supremum of thoser for which therth absolute moment of ϕ is finite. Convergence a.s., in probability and in law whent→∞ is examined in terms of P-decay(v): Ifd=1, σ=0 ord=2, σ=(0,0), Δ_σ a _s ^t diverges. In all the other cases: If P-decay(v)<(d+2)/(d+|σ|), Δ_σ a _s ^t diverges; if P-decay(v)>(d+2)/(d+|σ|), Δ_σ a _s ^t , converges and P-decay(ν) For any symmetric random variable ϕexponential decay or E-decay is defined as the supremum of thoser for which the expectation of exp(|x|^r) is finite. Let E-decay(v)>0. Whenever Δ_σ a _s ^t converges (that is, ifd>2 or |σ|>0: Ifd>2, E-decay(lima _s ^t )=min(E-decay(v),d+2/2); if |σ|=1, E-decay (lim Δ_σ a _s ^t )=min(E-decay(ν),d+2); if |σ| ⩾, E-decay (lim Δ_σ a _s ^t )=E-decay(ν).     

Perturbations in the rotational structure of the 4<Emphasis Type="Italic">p</Emphasis> complex of H<Subscript>2</Subscript> molecule terms

A statistical analysis of all the available data on the wave numbers of spectral lines related to triplet-triplet electronic-vibrational-rotational (rovibronic) radiation transitions into the H₂ molecule (1sσ2sσ) a ³Σ _g ⁺ electronic state was performed for the first time. This allowed us to check and refine the controversial identification of several spectral lines. Optimum rovibronic term values were found for 15 electronic states, including the (4pσ)f ³Σ _u ⁺, (4pπ)k ³Π _u ⁺, and (4pπ)k ³Π _u ⁻ states studied in this work. The ratios between the oscillator strengths of R- and P-branch lines with common upper levels (branching coefficients) for the f ³Σ _u ⁺ → a ³Σ _g ⁺ and k ³Π _u ⁺ → a ³Σ _g ⁺ systems of H₂ molecule bands were measured for the first time. Substantial deviations of the measured branching coefficients from the corresponding ratios between the Henl-London factors were observed. The deviations monotonically increased as the rotational quantum number N grew, which, in combination with substantial Λ-doubling in the k ³Π _u state, was evidence of an important role played by electronicrotational interaction in the 4pσ³Σ _u ⁺ and 4pπ³Π _u ⁺ adiabatic electronic states. A strong correlation was observed between the N dependences of branching coefficients for transitions from the mutually perturbed f ³Σ _u ⁺ and k ³Π _u ⁺ electronic states. The results of this work show that the measured branching coefficients are a much more sensitive and capacious channel of information about perturbation effects than rovibronic term values.     

Influences on the pseudospin symmetry from the different fields of mesons in deformed nuclei

Influences from different fields of mesons on the pseudospin symmetry are investigated for deformed nuclei. The energy splitting between pseudospin partners are extracted from the relativistic mean field calculations. The results show that the σ-field contribution to the pseudospin energy splitting has nearly the same magnitude as the one obtained by the ω-field, but with opposite signs. The pseudospin energy splittings either for neutron or for protons are almost the same if the σ-field (V _σ ) and the ω-field (V _ω ) change at the same scale. The pseudospin energy splitting depends in the same way as the nucleus binding energy of the cancellation of these two potentials, and is controlled by the same nuclear physics scale as the potential sum V _ω + V _σ In comparison with the σ- and ω-fields, it is seen that the ρ meson field produces a minor influence on the pseudospin symmetry.     

Transport properties of hexanoyl chitosan-based gel electrolyte

Films of hexanoyl chitosan-based polymer electrolyte were prepared by the technique of solution casting. The effect of plasticizer on the transport properties of hexanoyl chitosan:lithium trifluoromethanesulfonate (LiCF₃SO₃) electrolytes have been investigated. The plasticizer used was ethylene carbonate (EC). The highest room temperature conductivity achieved in the EC-plasticized hexanoyl chitosan-based electrolytes is 2.75×10⁻⁵ S cm⁻¹. The Rice and Roth model was used to explain the variations in the dc conductivity observed. The exponent, s, in Jonscher’s universal power law equation σ(ω)=σ _dc+Aω ^s , was analyzed as a function of temperature for the sample containing 30 wt% of EC. The analysis suggests that the conduction mechanism follows that proposed by the overlapping large polaron tunneling model.