Omega Dependence Research Articles

1D solitons in cubic-quintic fractional nonlinear Schrödinger model

We examine the properties of a soliton solution of the fractional Schrö dinger equation with cubic-quintic nonlinearity. Using analytical (variational) and numerical arguments, we have shown that the substitution of the ordinary Laplacian in the Schrödinger equation by its fractional counterpart with Lévy index alpha permits to stabilize the soliton texture in the wide range of its parameters (nonlinearity coefficients and alpha) values. Our studies of omega (N) dependence (omega is soliton frequency and N its norm) permit to acquire the regions of existence and stability of the fractional soliton solution. For that we use famous Vakhitov-Kolokolov (VK) criterion. The variational results are confirmed by numerical solution of a one-dimensional cubic-quintic nonlinear Schrödinger equation. Direct numerical simulations of the linear stability problem of soliton texture gives the same soliton stability boundary as within variational method. Thus we confirm that simple variational approach combined with VK criterion gives reliable information about soliton structure and stability in our model. Our results may be relevant to both optical solitons and Bose-Einstein condensates in cold atomic gases.

Stabilization of 1D solitons by fractional derivatives in systems with quintic nonlinearity

We study theoretically the properties of a soliton solution of the fractional Schrödinger equation with quintic nonlinearity. Under “fractional” we understand the Schrödinger equation, where ordinary Laplacian (second spatial derivative in 1D) is substituted by its fractional counterpart with Lévy index alpha. We speculate that the latter substitution corresponds to phenomenological account for disorder in a system. Using analytical (variational and perturbative) and numerical arguments, we have shown that while in the case of Schrödinger equation with the ordinary Laplacian (corresponding to Lévy index alpha =2), the soliton is unstable, even infinitesimal difference alpha from 2 immediately stabilizes the soliton texture. Our analytical and numerical investigations of omega (N) dependence (omega is soliton frequency and N its mass) show (within the famous Vakhitov–Kolokolov criterion) the stability of our soliton texture in the fractional alpha <2 case. Direct numerical analysis of the linear stability problem of soliton texture also confirms this point. We show analytically and numerically that fractional Schrödinger equation with quintic nonlinearity admits the existence of (stable) soliton textures at 2/3<alpha <2, which is in accord with existing literature data. These results may be relevant to both Bose–Einstein condensates in cold atomic gases and optical solitons in the disordered media.

Analysis of Ion Transport in Nanofiltration Using Phenomenological Coefficients and Structural Characteristics

The analysis of salt transport in nanofiltration using extended Nernst-Planck equations or similar models often suffers from the difficulties to establish and independently and transparently verify the consistency between the filtration results, assumed mechanism, and fitted values of parameters. As a general alternative, we propose here a procedure that reduces filtration data to two general phenomenological coefficients, concentration-dependent salt permeability omega(s) and Peclet coefficient A, which does not require that a specific exclusion mechanism be assumed and thus allows a transparent test on consistency with commonly used models. This approach was demonstrated using concentration polarization-corrected filtration data for NF-200 membrane and four monovalent salts, NaCl, NaBr, KBr, and KCl. The coefficient A was found to be very small, which points to the negligible contribution of convection to salt transport. The smallness of A was verified through estimates of the effective pore radius of the membrane, found to be between 0.2 and 0.3 nm, and comparing them with similar independent estimates from the hydraulic permeability L(p) using the data on the thickness and swelling of the selective polyamide layer obtained by AFM. The concentration dependence of omega(s) and its variation for different salts suggested that in the concentration range above 0.01 M the salt exclusion may be dominated by a combination of Donnan and dielectric mechanisms. The values of omega(s) obtained for single salts were also consistent with the selectivity observed for equimolar feed mixtures of NaCl and NaBr. However, the observed variation of omega(s) with concentrations of single salts below 0.01 M reveals a new regime that is inconsistent with all commonly used models of NF based on a Donnan mechanism modified with dielectric and steric effects. In particular, omega(s) appeared to approach a constant value at low salt concentrations, whereas the standard mechanisms predict a linear or even steeper decrease as concentration decreases. This puzzling discrepancy could have passed unnoticed in the standard multiparameter fitting extended Nernst-Planck equations and demonstrates the benefits of the present phenomenological analysis.

High spin baryon in hot strongly coupled plasma

We consider a strings-junction holographic model of a probe baryon in the finite-temperature supersymmetric Yang-Mills dual of the AdS-Schwarzschild black hole background. In particular, we investigate the screening length for a high spin baryon composed of rotating N-c heavy quarks. To rotate quarks by finite force, we put a hard infrared cutoff in the bulk and give quarks a finite mass. We find that N-c microscopic strings are embedded reasonably in the bulk geometry when they have finite angular velocity omega, similar to the meson case. By defining the screening length as the critical separation of quarks, we compute the omega dependence of the baryon screening length numerically and obtain a reasonable result which shows that baryons with high spin dissociate more easily. Finally, we discuss the relation between J and E-2 for baryons.

Mössbauer study of reduced rubredoxin as purified and in whole cells. Structural correlation analysis of spin Hamiltonian parameters.

The [Fe(II)(Cys)(4)](2-) site of rubredoxin from Clostridium pasteurianum (Rd(red)) has been studied by Mössbauer spectroscopy in both purified protein and whole cells of Escherichia coli overproducing it. Excellent fits were obtained to an S = 2 spin Hamiltonian for D = 5.7(3) cm(-1), E/D = 0.25(2), delta = 0.70(3) mm/s, DeltaE(Q) = -3.25(2) mm/s, eta = 0.75(5), A(x) = -20.1(7) MHz, A(y) = -11.3(2) MHz, and A(z) = -33.4(14) MHz. These parameters were analyzed with crystal-field theory for the (5)D manifold of iron(II), revealing a d(z(2)) orbital ground state that is admixed by approximately 0.21 d(x(2) - y(2)). The spin-Hamiltonian parameters are consistent within the (5)D theory, apart from the zero-field splitting parameter, D. This problem was solved by extending the crystal-field treatment with spin-orbit coupling to spin-triplet d-d excited states of the iron. Theoretical estimates are given for the spin-triplet (D(T)) and spin-quintet contributions (D(Q)) to D based on excitation energies derived from time-dependent density functional theory, TD-DFT. The computational results were interpreted in terms of crystal-field theory, yielding the Racah parameters B = 682 cm(-1) and C = 2583 cm(-1). The theoretical analysis gives the relative magnitudes D(Q):D(T):D(ss) = 51%: 42%:7% (D(ss) originates from spin-spin interaction). The DFT analysis corroborates the pivotal role of the torsion angles (omega(i)) of the C-S(i) bonds in shaping the electronic structure of the iron(II) site. Rd(red) in overexpressing whole cells accounts for 60% of the Mössbauer absorption. The Rd(red) spectra from whole cells are virtually identical to those of the purified protein. By using the theoretical omega dependence of the spin Hamiltonian parameters, the torsions for Rd(red) in whole cells and purified protein samples are estimated to be the same within 2 degrees. These findings establish Mössbauer spectroscopy as a structural tool for investigating iron sites in whole cells.

The Omega dependence in equations of motion

We show that the equations of motion governing the evolution of a collisionless gravitating system of particles in an expanding universe can be cast in a form which is almost independent of the cosmological density parameter, $\Omega$, and the cosmological constant, $\Lambda$. The new equations are expressed in terms of a time variable $\tau\equiv \ln D$, where $D$ is the linear rate of growth of density fluctuations. The weak dependence on the density parameter is proportional to $\epsilon=\Omega^{-0.2}-1$ times the difference between the peculiar velocity (with respect to $\tau$) of particles and the gravity field. In the general case, the effect of this weak $\Omega$ dependence is to enhance the rate of evolution of density perturbations in dense regions. In a flat universe with $\Lambda\ne 0$, this enhancement is less pronounced than in an open universe with $\Lambda=0$ and the same $\Omega$. Using the spherical collapse model, we find that the increase of the $rms$ density fluctuations in a low $\Omega$ universe relative to that in a flat universe with the same linear normalization is $\sim 0.01 \epsilon(\Omega) $, where $\delta$ is the density field in the flat universe. The equations predict that the smooth average velocity field scales like $\Omega^{0.6}$ while the local velocity dispersion (rms value) scales, approximately, like $\Omega^{0.5}$. High resolution N-body simulations confirm these results and show that density fields, when smoothed on scales slightly larger than clusters, are insensitive to the cosmological model. Halos in an open model simulation are more concentrated than halos of the same $M/\Omega$ in a flat model simulation.

The Ω dependence of the velocity divergence distribution

Analytical studies based on perturbative theory have shown that the moments of the Probability Distribution Function (PDF) of the local smoothed velocity divergence are expected to have a very specific dependence on the density parameter Omega in the quasi-linear regime. This dependence is particularly interesting as it does not involve the possible bias between the galaxy spatial distribution and the underlying mass distribution. This implies a new and promising method for determining a bias-independent value of Omega based on a reliable determination of the velocity divergence PDF. In this paper we study the Omega dependence of the velocity divergence PDF and its first moments in a set of N-body simulations, using the so-called Voronoi and Delaunay methods. We show that this dependence is in agreement with the theoretical prediction, even while the number density of velocity field tracers has been diluted to a value comparable to that available in current galaxy catalogues. In addition, we demonstrate that a sufficiently reliable determination of these statistical quantities is also possible when the measurement of the galaxy peculiar velocities is restricted to the one component along the line-of-sight. Under ideal, noise-free circumstances we can successfully discriminate between low and high Omega.

The cosmological dependence of cluster density profiles

We use N-body simulations to study the shape of mean cluster density and velocity profiles in the nonlinear regime formed via gravitational instability. The dependence of the final structure on both cosmology and initial density field is examined, using a grid of cosmologies and scale-free initial power spectra P(k) varies as k(exp n). Einstein-de Sitter, open (Omega(sub 0) = 0.2 and 0.1) and flat, low density (Omega(sub 0) = 0.2 lambda(sub 0) = 0.8) models are examined, with initial spectral indices n = -2, -1 and 0. For each model, we stack clusters in an appropriately scaled manner to define an average density profile in the nonlinear regime. The profiles are well fit by a power law rho(r) varies as r(exp -alpha) for radii whereat the local density contrast is between 100 and 3000. This covers 99% of the cluster volume. We find a clear trend toward steeper slopes (larger alphas) with both increasing n and decreasing Omega(sub 0). The Omega(sub 0) dependence is partially masked by the n dependence; there is degeneracy in the values of alpha between the Einstein-de Sitter and flat, low-density cosmologies. However, the profile slopes in the open models are consistently higher than the Omega = 1 values for the range of n examined. Cluster density profiles are thus potentially useful cosmological diagnostics. We find no evidence for a constant density core in any of the models, although the density profiles do tend to flatten at small radii. Much of the flattening is due to the force softening required by the simulations. An attempt is made to recover the unsoftened profiles assuming angular momentum invariance. The recovered profiles in Einstein-de Sitter cosmologies are consistent with a pure power law up to the highest density contrasts (10(exp 6)) accessible with our resolution. The low-density models show significant deviation from a power law above density contrasts approximately 10(exp 5). We interpret this curvature as reflecting the non-scale-invariant nature of the background cosmology in these models. These results are at the limit of our resolution and so should be tested in the future using simulations with larger numbers of particles. Such simulations will also provide insight on the broader problem of understanding, in a statistical sense, the full phase space structure of collapsed, cosmological halos.

Self-energy calculations in the Hubbard model

The authors have calculated the electronic self-energy of the two-dimensional Hubbard model as a function of frequency and momentum for various band fillings. They present this up to second order in the interaction parameter and also up to infinite order for ladder diagrams in the two-particle scattering channel. The authors have carried out direct k-space integrations using a triangle method. For a half-filled perfectly nested band, the imaginary part, lm Sigma (kf, omega ), has a linear- omega dependence for nested Fermi surfaces which is consistent with the marginal Fermi liquid phenomenology for high-Tc superconductors. At, and near, half-filling there is a strong low-energy peak in lm Sigma (2)(k, omega ) when k is off the Fermi surface. The physical origin of this peak is discussed. The peak is enhanced in the ladder approximation. The corresponding structure in Re Sigma (2)(k, omega ) leads to multiple solutions of the Dyson equation for a wide range of values of the parameters. This leads to an appealing explanation of observed structure in some experimental angle-resolved photoemission spectra of high-Tc materials. The authors also find anti-bound states split off from the band in the two-particle scattering ladders consistent with the suggestion of Anderson.

The Omega dependence of peculiar velocities induced by spherical density perturbations

La vitesse d'une enveloppe entourant une perturbation de densite spherique avec une sur-densite fractionnaire moyenne Δρ/ρ, dans un univers de Friedmann, peut etre developpee en puissance de Δρ/ρ. En considerant que v est la vitesse d'une enveloppe non-perturbee de meme rayon, le changement de vitesse fractionnaire de l'enveloppe perturbee est donnee par Δv/v -1/3×f 1 (Ω)×(Δρ/ρ) + 4/63×f 2 (Ω)×(Δρ/ρ) 2 + O(Δρ/ρ) 3 . Les coefficients f 1 (Ω) et f 2 (Ω) sont determines pour Ω 1.

Interactions between the sextet states of FeCl

Remarkable features ( Omega dependence of effective B values, non-equidistant spin-orbit separations, observations of Lambda -type doubling effects) found in analysing ultraviolet bands of FeCl are interpreted as arising from interactions between the sextet states of the (3d64s)Fe+ complex (for the X6 Delta ground state) and of the (3d64p pi )Fe+ complex (for the excited 6 Phi and 6 Pi states). Ab initio calculations are used to ascertain the nature of the observed transition (which are shown to be 4s-4p ion-like excitations) and to determine plausible values of the off-diagonal parameters involved in the energy matrices of the sextet states. Given these values a deperturbation analysis is carried out. The Lambda -type splittings observed in the X6 Delta 1/2, X6 Delta -1/2 and 6 Phi 1/2 components are quantitatively interpreted.

Nuclear spin dynamics near ferromagnetic phase transitions. I. Isotropic systems

The mode-coupling theory of critical dynamics has been applied to both electron and nuclear spin fluctuations of isotropic ferromagnets with electron-nuclear spin interactions. By treating nuclear and electron spin fluctuations in a similar manner, the influence of hyperfine interactions on nuclear as well as electron spin motion could be accounted for. It has thus been possible to derive the asymptotic q-k- omega dependence of the self-energies of electron and nuclear spin fluctuations in the entire critical region above Tc.

Nuclear spin dynamics near ferromagnetic phase transitions. II. Anisotropic systems

The mode-coupling theory of critical dynamics has been applied to both electron and nuclear spin fluctuations of isotropic ferromagnets with electron-nuclear spin interactions. By treating nuclear and electron spin fluctuations in a similar manner, the influence of hyperfine interactions on nuclear as well as electron spin motion could be accounted for. It has thus been possible to derive the asymptotic q-k- omega dependence of the self-energies of electron and nuclear spin fluctuations in the entire critical region above Tc.

Critical frequency dependence of spin correlation functions

If one is interested in the asymptotic q- kappa - omega dependence of frequency-dependent spin correlation functions it is shown that the intricacies of the corresponding mode-coupling equations are greatly reduced by assuming the validity of certain general properties of the correlation functions. A simplified version of the mode-coupling equations results for the frequency-dependent self-energy. The asymptotic solutions of these equations in the entire critical q- kappa - omega region of three-dimensional anisotropic ferromagnets above Tc are presented. The modifications in the omega -dependence brought about by the anisotropy are especially emphasised. The solutions satisfy the intrinsic assumptions self-consistently. The frequency dependence of the self-energy leads to deviations of the shape functions from a Lorentzian line shape. These anomalies are studied for some special cases. Finally the self-energy of isotropic ferro- and antiferromagnets for general dimensions d>2 are derived in order to compare the author's results with recent renormalisation group calculations valid near d=6 and d=4 respectively. The asymptotic q- kappa - omega dependences turn out to be identical in both procedures.

Thermal excitations of a bilipid membrane

Propagating modes of vibration of a bilipid membrane have been detected with light beating spectroscopy. The dependence of omega on q is consistent with a model of a fluid film of surface tension sigma = 2.5 +/- 0.5 dyn cm-1 surrounded by a medium with rho = 1 g cm-3 and eta = 1.01 X 10(-2) P.

General continuum analysis of transport through pores. I. Proof of Onsager's reciprocity postulate for uniform pore

The nonelectrolyte (Js) and volume (Jv) flux across a membrane is usually described in terms of two equations derived from the theory of irreversible thermodynamics: (see article) where delta c and delta P are the concentration and pressure difference; omega and Lp are the diffuse and hydraulic permeability; and sigma s and sigma v are the reflection coefficients. If Onsager's reciprocity postulate is assumed, it can be shown that signa s and sigma v are equal. This is an important assumption because it allows one to apply the continuum theory relationship between sigma s and the pore radius to experimental measurements of sigma v. In this paper, general continuum expressions for both the Jv (a new result) and Js equation will be derived and the equality of sigma s and sigma v proved. The proof uses only general hydrodynamic results and does not require explicit solutions for the drag coefficients or, for example, the assumption that the solute is in the center of the pore. The proof applys to arbitrarily shaped solutes and any pore whose shape is independent of axial position (uniform). In addition, new expressions for the functional dependence of omega and sigma on the pore radius are derived (including the effect of the particle lying off the pore axis). These expressions differ slightly from earlier results and are probably more accurate.