Exact Solutions of the Gardner Equation and their Applications to the Different Physical Plasmas

Traveling wave solution of the Gardner equation is studied analytically by using the two dependent (G^′/G,1/G)-expansion and (1/G^′)-expansion methods and direct integration. The exact solutions of the Gardner equations are obtained. Our analytic solutions are applied to the unmagnetized four-component and dusty plasma systems consisting of hot protons and electrons to investigate dynamical features of the solitons and shock waves produced in these systems. A wide variety of parameters of the plasma is used, and the basic features of the Gardner solitons that are beyond the existing study in literature are found. It is observed that the analytic solutions from (G^′/G,1/G)-expansion and (1/G^′)-expansion methods only produce shock waves but the solitary waves are found from the analytic solutions derived from the direct integration. It is also noted that the superhot electrons and relative mass density of the electrons significantly effect the soliton’s amplitude, width, and position. We have also numerically proved that the combination of every value of nomalized density μ₁ or temperature ratio σ₁ with the other sets of plasma parameters creates a region where the solutions have similar physical properties. The time-dependent behavior of the soliton is also studied, and a periodic motion of soliton along the phase variable η is found during the evolution. The investigations and the limits presented in this study may be helpful for studying and understanding the nonlinear properties of the solitary and shock waves seen in various physical and astrophysical plasma systems.     

GA/GV measured in the decay of polarized neutrons

A measurement of [G_A/G_V] in the decay of polarized neutrons, basically quite similar to our 1968 one, gives a value of 1.258±0.015. The asymmetry coefficient, A, is ?0.113±0.006. These results include the 1968 data.     

Step algebras of semi-simple subalgebras of Lie algebras

For each pair (G,K) where G is a complex finite-dimensional Lie algebra and K a semi-simple subalgebra of G, we construct an associative algebra (step algebra) $\text{Y}$ (G,K) and a homomorphism i_*: $\text{Y}$ (G,K)→E(G) is the enveloping algebra of G. $\text{Y}$ (G,K) has the following properties: (1) If V is any G-module and x ? V a K-maximal vector, then sx = i_* (s)x is K-maximal for any s ? $\text{Y}$ (G,K); (2) If V is irreducible and a certain simple criteria is fulfilled, then any K-maximal vector can be written in the form sx_m, s ? $\text{Y}$ (G,K), where x_m is some fixed K-maximal vector. Because of these properties $\text{Y}$ (G,K) has great practical value when constructing irreducible representations of Lie algebras in a form which makes the reduction with respect to a semi-simple subalgebra explicit.     

Online multi-parameter phase-curve fitting and application to a large corpus of asteroid photometric data

We apply the new H,G₁₂ and H,G₁,G₂ phase functions to a large corpus of asteroid photometric data. We make use of low-precision (generally rounded to 0.1 mag) and low-accuracy (rms magnitude uncertainties of ±0.2-0.3 mag) data obtained from the Minor Planet Center and modified at Lowell Observatory. We find (1) a correlation between G₁,G₂ values derived for asteroid families and albedos; (2) G₁₂ homogeneity in families. In addition, we make available an online Java applet (titled Asteroid Phase Function Analyzer). The applet may be used to compute asteroid absolute magnitudes and slope parameters using three different phase functions: the H,G, H,G₁,G₂, and H,G₁₂. The tool also includes non-Gaussian error analysis using Monte Carlo methods. The applet is available at http://asteroid.astro.helsinki.fi/astphase/.     

Theory of the local field correction in an electron gas

The wave-vector- and frequency-dependent dielectric function ?(k,ω) of an electron gas can be expressed in terms of Lindhard's function and a complex local field correctionG(k,ω) which incorporates all the effects of dynamic exchange and correlation in the system. The general properties ofG(k,ω) are discussed, in particular the static and high-frequency limits. It is shown that for smallk, bothG(k, 0) andG(k, ∞) vary ask ², with different coefficients, but both determined by the average kinetic and potential energies per particle. For largek,G(k, ∞) varies again ask ² and it is argued that the same holds true forG(k, 0), with both coefficients (though different) determined by the average kinetic energy per particle. General formulas for the plasma dispersion relation and damping, involving, respectively, the real and imaginary parts ofG(k,ω), are given. The term in the plasma frequency which is proportional tok ² is given directly in terms of the average kinetic and potential energies per particle, a result true at all temperatures. A calculation of the frequency dependence ofG(k,ω), starting from the exact equation of motion for the particle-hole operator and employing a decoupling approximation introduced previously by Toigo and Woodruff, is presented. Explicit results forG(k,ω) are obtained for smallk and allω. The complete expressions forG(k, 0) andG(k, ∞) in this approximation have been obtained and are plotted.     

Group actions on quantum bundles

Suppose we are given a group G acting through canonical transformations on a symplectic manifold (M, ω). If there is a quantum bundle over (M, ω), a carrier for wave functions in the geometric quantization theory, then G acts infinitesimally on the bundle in a natural way. We give a necessary and sufficient condition for the infinitesimal G-action to integrate up to a global G-action. This is used for an investigation how the choice of the quantum bundle over (M, ω) influences the integrability of the corresponding infinitesimal G-action. The relationship to group representations is briefly mentioned.     

Taking account of loudness constancy for the loudness criterion for concert halls

One of the surprises from analysis of results of an objective and subjective study of British concert halls (1988 Acustica 66, 1–14) was that the subjective judgement of loudness in concert halls is influenced not only by sound level but also by the source–receiver distance. This response implies that the same sound level is judged louder at positions further from the orchestra platform. Whereas level decreases with distance in actual halls, loudness is judged more-or-less independent of position in average halls (except at positions close to the platform and seats overhung by balconies). As an observation it ties in with evidence from experimental psychologists for loudness constancy throughout a space. The sound strength G is the sound level in an auditorium normalised to the sound power level of the source; the traditional criterion of acceptability for level is that G ? 0 dB. The paper proposes that, on the basis of subjective evidence and objective behaviour in auditoria, the criterion for G should not be a unique value of G but rather a function of source–receiver distance.     

Random walk on the homogeneous spaces of a group and generalized coherent states

The evolution of a quantum system characterized by a dynamical group G and subjected to random interactions can be reduced, through the use of the generalized coherent states associated with a group $\text{G}$, whose algebra is an ideal of the algebra of G, to a random walk on some homogeneous space S of $\text{G}$. G is the group of automorphisms of S. The connection between the symmetry properties of such a random walk and the structure of G are discussed, showing that it is always possible to map the original process into an equivalent process taking place in the manifold of G. The investigation of the general properties of this mapping quite naturally provides a deep characterization of the role played by G in determining the basic transient and stationary features of the evolution of the system.     

Weighted Graph Colorings

We study two weighted graph coloring problems, in which one assigns q colors to the vertices of a graph such that adjacent vertices have different colors, with a vertex weighting w that either disfavors or favors a given color. We exhibit a weighted chromatic polynomial Ph(G,q,w) associated with this problem that generalizes the chromatic polynomial P(G,q). General properties of this polynomial are proved, and illustrative calculations for various families of graphs are presented. We show that the weighted chromatic polynomial is able to distinguish between certain graphs that yield the same chromatic polynomial. We give a general structural formula for Ph(G,q,w) for lattice strip graphs G with periodic longitudinal boundary conditions. The zeros of Ph(G,q,w) in the q and w planes and their accumulation sets in the limit of infinitely many vertices of G are analyzed. Finally, some related weighted graph coloring problems are mentioned.     

Determination of the gravitational constant G

A precise knowledge of the Newtonian gravitational constant G has an important role in physics and is of considerable meteorological interest. Although G was the first physical constant to be introduced and measured in the history of science, it is still the least precisely determined of all the fundamental constants of nature. The 2002 CODATA recommended value for G, G = (6.6742 ± 0.0010) × 10⁻¹¹m³ · kg⁻¹ · s⁻², has an uncertainty of 150 parts per million (ppm), much larger than that of all other fundamental constants. Reviewed here is the status of our knowledge of the absolute value of G, methods for determining G, and recent high precision experiments for determining G.     

Investigation of zero-frequency solutions to the pion dispersion equation

The instability of nuclear matter is considered for the case where it is generated by the vanishing of the frequencies of collective excitations belonging to specific types (specifically, excitations that have the pion quantum numbers J ^π = 0^?). The behavior of zero-frequency solutions to the pion dispersion equation is analyzed versus the strength G′ of spin—isospin particle—hole interaction. It is shown that there exists a strength value G′_tr (|G′_tr| ? 1) such that, for G′ < G′_tr, zero-frequency solutions are excitations of the ω _P type, while, for G′ ≥ G′_tr, such solutions are excitations of the ω _c type. Excitations of the ω _P type for G′ < ?1 describe the instability of nuclear matter against small density fluctuations (Pomeranchuk’s instability), while excitations of the ω _c type are responsible for the instability associated with pion condensation at G′ ≈ 2. For stable nuclear matter, the solutions ω _P(κ) and ω _c (κ) lie on unphysical sheets of the complex plane of frequency.     

Normal forms generalizing action-angle coordinates for Hamiltonian actions of Lie groups

Let (M, Ω) be a symplectic manifold on which a Lie group G acts by a Hamiltonian action. Under some restrictive assumptions, we show that there exists a symplectic diffeomorphism ψ of a G-invariant open neighbourhood U of a given G-orbit in M, onto an open subset ψ(U) of a vector bundle F ^*, with base space G. Explicit expressions are given for the symplectic 2-form, for the momentum map and for a Hamiltonian vector field whose Hamiltonian function is G-invariant, on the model symplectic manifold ψ(U).     

Orbifold conformal blocks and the stack of pointed G-covers

Starting with a vertex algebra V, a finite group G of automorphisms of V, and a suitable collection of twisted V-modules, we construct (twisted) D-modules on the stack of pointed G-covers, introduced by Jarvis, Kaufmann, and Kimura. The fibers of these sheaves are spaces of orbifold conformal blocks defined in joint work with Edward Frenkel. The key ingredient is a G-equivariant version of the Virasoro uniformization theorem.     

A measurement of the ratio GE/GE of the proton form factors at very low momentum transfer

The ratioμG _EG_M of the proton form factors was determined by measuring the electron scattering cross section of the proton relative to that of¹²C. Data were taken atq ²=0.09, 0.16, 0.25, and 0.36 fm^?2, yielding a weighted mean ofμG _E/G_M=1.01±0.03.     

Finite-time future singularities in modified Gauss–Bonnet and ℱ(R,G) gravity and singularity avoidance

We study all four types of finite-time future singularities emerging in the late-time accelerating (effective quintessence/phantom) era from ?(R,G)-gravity, where R and G are the Ricci scalar and the Gauss–Bonnet invariant, respectively. As an explicit example of ?(R,G)-gravity, we also investigate modified Gauss–Bonnet gravity, so-called F(G)-gravity. In particular, we reconstruct the F(G)-gravity and ?(R,G)-gravity models where accelerating cosmologies realizing the finite-time future singularities emerge. Furthermore, we discuss a possible way to cure the finite-time future singularities in F(G)-gravity and ?(R,G)-gravity by taking into account higher-order curvature corrections. The example of non-singular realistic modified Gauss–Bonnet gravity is presented. It turns out that adding such non-singular modified gravity to singular Dark Energy makes the combined theory a non-singular one as well.     

Theoretical shear strength of FCC and HCP metals

The theoretical shear strength (τ _c ) and its temperature dependence for a series of FCC and HCP metals have been calculated. Despite the obtained differences in temperature dependences of τ _c , critical deformation (γ _c ), and shear modulus (G), the fact of a weak temperature dependence of ratio Gγ _c /τ _c relating these quantities is established for all studied materials. The deviation of Gγ _c /τ _c from the average value in the temperature ranges under consideration is no more than 12%.     

A first principle study of encapsulated and functionalized silicon nanotube of chirality (6,6) with monoatomically thin metal wires of Ag,Au and Cu

First principle calculations have been performed to study the influence of interaction of monoatomically thin metal nanowires of Ag, Au and Cu placed inside (encapsulation) and outside (functionalization) the silicon nanotube having armchair conformation with chirality (6,6). The cohesive energy for all the encapsulated and functionalized systems under study was found to be almost same. In comparison to the pristine silicon nanotube (SiNT) which is found to be semiconducting in nature, all the encapsulated and functionalized systems of SiNT are found to be metallic in nature. The calculated electronic band structures show that the conductance in case of Ag, Au and Cu nanowires encapsulation is 2G₀. However, its value for functionalized Ag, Au and Cu nanowires is found to be 1G₀, 2G₀ and 4G₀ for the outside positioning of nanowires respectively. Optical properties of all the encapsulated and functionalized SiNTs have been studied. All the systems under study show reflectivity in the infrared (IR) region and behave as non-absorbing transparent conductors in the visible region.     

The thermodynamics of solid solutions of argon and methane

The primary concern of this paper is with the estimation of the excess Gibbs energy G^E,S for solid solutions of two molecularly simple components which are completely miscible in the solid state. The method depends on combining information on the excess thermodynamic functions of liquid mixtures of the two components with a knowledge of the liquidus and solidus lines on the temperature-composition phase diagram. It is applied to the particular case of argon-methane. For this system, unit cell sizes and some heat of fusion measurements are also available, from which V^E,S and H^E,S have been calculated.A solid solution of argon and methane departs much more from ideality than does a liquid mixture of the same composition at the same temperature, the ratio r, = G^E,S/G^E,L, being about 3. Moreover, the concentration dependence of G^E,S is less symmetrical than that of G^E,L, and the ratio r increases markedly with increasing argon mole fraction. A dilute solution of methane (which has the larger molecules) in argon has a larger G^E,S than the corresponding dilute solution of argon in methane.For a solid solution at 71 K with an argon mole fraction of 0.60, H^E,S is ≈4801 Jmol^?1. This gives TS^E,S ≈ 220 J mol^?1, which is about the same as G^E,S. The solid solutions cannot therefore be regarded as even approximating to regular solutions.From the calculated G^E,S results, it is predicted that the face-centred cubic solid solutions of argon and methane should separate into two phases on cooling. The calculated coordinates of the upper critical solution point are T = 67 K and an argon mole fraction of 0.63, in reasonable agreement with the experimental values of 63 K and 0.65 respectively.     

Temperature-dependent conductance in single and multiple quantum dots: the role of the disorder

We present calculations of conductance, G, as a function of inverse temperature, 1 / T, for a quantum dot array with disorder, a clean quantum dot enclosed by soft boundaries and a simple two resonance model. The behavior in each case is qualitatively similar, with G appearing to increase exponentially provided one starts at a minimum. Unlike some recent experimental studies, we do not see any logarithmic behavior at low temperatures.