Limit Of Small Field Research Articles

Nonlinear evolution off(R)cosmologies. III. Halo statistics

The statistical properties of dark matter halos, the building blocks of cosmological observables associated with structure in the Universe, offer many opportunities to test models for cosmic acceleration, especially those that seek to modify gravitational forces. We study the abundance, bias, and profiles of halos in cosmological simulations for one such model: the modified action $f(R)$ theory. The effects of $f(R)$ modified gravity can be separated into a large- and small-field limit. In the large-field limit, which is accessible to current observations, enhanced gravitational forces raise the abundance of rare massive halos and decrease their bias but leave their (lensing) mass profiles largely unchanged. This regime is well described by scaling relations based on a modification of spherical collapse calculations. In the small-field limit, the enhancement of the gravitational force is suppressed inside halos and the effects on halo properties are substantially reduced for the most massive halos. Nonetheless, the scaling relations still retain limited applicability for the purpose of establishing conservative upper limits on the modification to gravity.

First-principles conductance of nanoscale junctions from the polarizability of finite systems

A method for the calculation of the conductance of nanoscale electrical junctions is extended to ab initio electronic structure methods that make use of the periodic supercell technique and applied to realistic models of metallic wires and break junctions of sodium and gold. The method is systematically controllable and convergeable and can be straightforwardly extended to include more complex processes and interactions. Important issues, about the order in which the thermodynamic and static (small field) limits are taken, are clarified, and characterized further through comparisons to model systems.

Models off(R)cosmic acceleration that evade solar system tests

We study a class of metric-variation $f(R)$ models that accelerates the expansion without a cosmological constant and satisfies both cosmological and solar-system tests in the small-field limit of the parameter space. Solar-system tests alone place only weak bounds on these models, since the additional scalar degree of freedom is locked to the high-curvature general-relativistic prediction across more than 25 orders of magnitude in density, out through the solar corona. This agreement requires that the galactic halo be of sufficient extent to maintain the galaxy at high curvature in the presence of the low-curvature cosmological background. If the galactic halo and local environment in $f(R)$ models do not have substantially deeper potentials than expected in $\ensuremath{\Lambda}\mathrm{CDM}$, then cosmological field amplitudes $|{f}_{R}|\ensuremath{\gtrsim}{10}^{\ensuremath{-}6}$ will cause the galactic interior to evolve to low curvature during the acceleration epoch. Viability of large-deviation models therefore rests on the structure and evolution of the galactic halo, requiring cosmological simulations of $f(R)$ models, and not directly on solar-system tests. Even small deviations that conservatively satisfy both galactic and solar-system constraints can still be tested by future, percent-level measurements of the linear power spectrum, while they remain undetectable to cosmological-distance measures. Although we illustrate these effects in a specific class of models, the requirements on $f(R)$ are phrased in a nearly model-independent manner.

Ionic contribution to the electric current in an electrolytic cell submitted to an external voltage

The ionic contribution to the electrical current in an electrolytic cell submitted to an external voltage linearly increasing with the time is evaluated. The investigation is performed in the limit of small and large electric field, in which the density of ions depends on the actual electric field in the sample. In the analysis, it is assumed that the ionic separation induced by an external field can be described by a surface density of charge. We show that the ions are responsible for a peak in the current, followed by a delay in the application of the external voltage. From the analysis of the peak and its delay, it is possible to obtain information on the density of ions in thermodynamical equilibrium, and on the mobility of the ions in the considered liquid.

Universal interpolating function for the dispersion coefficient of DNA fragments in sieving matrices

The separation of DNA fragments by (slab or capillary) gel electrophoresis has been studied extensively. To characterize the separation achieved by such systems, one needs to understand the impact (and their dependency upon the experimental quantities) of two physical parameters: the electrophoretic mobility mu and the diffusion coefficient D. Three different regimes have been shown to exist for both mu and D: the Ogston regime, the reptation regime and the reptation with orientation regime (note that separation is only possible for the first two regimes). In the small electric field limit, both mu and D are apparently well described by theories for all three regimes. Unfortunately this results in disjointed scaling laws and no theory-based general equations can apply to all regimes. Recently, an empirical interpolating formula has been proposed that adequately fits the low electric field mobility mu of dsDNA fragments across all three regimes and is compatible with accepted theories. In this article we review and clarify the current state of knowledge regarding the size dependence of the mobility and the diffusion coefficient and propose an interpolating formula for molecular size dependence of the low field diffusion coefficient D. With formulas for both the mobility and the diffusion coefficient as a function of the experimental conditions one could, in principle, optimize any gel/polymer matrix-based electrophoresis system for a wide range of DNA molecular sizes.

Rates of neutrino absorption on nucleons and the reverse processes in strong magnetic fields

The rates of ${\ensuremath{\nu}}_{e}+n\ensuremath{\rightleftharpoons}{e}^{\ensuremath{-}}+p$ and ${\overline{\ensuremath{\nu}}}_{e}+p\ensuremath{\rightleftharpoons}{e}^{+}+n$ are important for understanding the dynamics of supernova explosion and the production of heavy elements in the supernova environment above the protoneutron star. Observations and theoretical considerations suggest that some protoneutron stars may be born with strong magnetic fields. In a previous paper we calculated the above rates in supernova environments with magnetic fields up to $\ensuremath{\sim}{10}^{16}\text{ }\text{ }\mathrm{G}$ assuming that the nucleon mass ${m}_{N}$ is infinite. We also applied these rates to discuss the implications of such strong fields for supernova dynamics. In the present paper we take into account the effects of a finite ${m}_{N}$ and develop a numerical method to recalculate the above rates in similar environments. This method is accurate to $\mathcal{O}(1/{m}_{N})$ and such an accuracy is required for application to supernova nucleosynthesis. We show that our results have the correct behavior in the limit of high neutrino energy or small magnetic field. Based on comparison of our results with various approximations, we recommend efficient estimates of the above rates for use in models of supernova nucleosynthesis in the presence of strong magnetic fields.

Analysis of the diffuse layer potential drop in the limit of small fields on the basis of a generalized mean spherical approximation

Analytical expressions have been derived for the functions Ξ o and H o which arise in the description of the diffuse double layer using a generalized mean spherical approximation (GMSA). The analytical expressions are shown to provide a very good alternate method to estimate Ξ o and H o which were calculated on the basis of numerical evaluation of integrals in previous work. They are valid in the limit of small electrical fields, a region in which the GMSA itself is valid. The GMSA results are compared to data obtained in Monte Carlo simulations carried out at the primitive level as a function of ion size and concentration for a 1–1 electrolyte.

Strong wiggler field assisted amplification in a second-harmonic waveguide free electron laser

As a technique to reduce the size of compact waveguide free electron lasers (FELs) operated from microwave to the far infrared, a longitudinal interaction mechanism was recently proposed to operate waveguide FELs at the second harmonic. With a gain formulation based on Madey's theorem in the limit of small wiggler field, it was shown analytically that second harmonic waveguide FELs can reduce significantly the electron energy required for radiation at a given frequency. As it is advantageous to operate second harmonic waveguide FELs with strong wiggler field, Madey's theorem is used here to reformulate their interaction gain for strong wiggler fields up to a/sub /spl omega///sup 2///spl gamma//sub 0//sup 2//spl beta//sub z0//sup 2/=1with the axial electron velocity Taylor expanded to the eighth order of the wiggler field. Given that Madey's theorem has not been established for second harmonic waveguide FELs, their interaction gain is also formulated independently by solving their pendulum equation without recourse to Madey's theorem. These two gain formulas are not analytically identical, but numerically they lead to an excellent agreement over a wide range of system parameters, thus confirming the applicability of Madey's theorem. The interaction analyses presented form a thorough and detailed description of second harmonic waveguide FELs in the small-signal regime and for wiggler field that is both practical and beneficial.

Comment on “Origin of low-frequency dielectric dispersion inKH2PO4andRbH2PO4ferroelectric crystals”

Kim and Kim [Phys. Rev. B 59, 13 509 (1999)] have studied the frequency dependence of the complex permittivity of ${\mathrm{KH}}_{2}{\mathrm{PO}}_{4}$ and ${\mathrm{RbH}}_{2}{\mathrm{PO}}_{4}$ in the ferroelectric phase. In the low-frequency regime $(fl10 \mathrm{kHz})$ they found a dispersion consisting of at least three distinctive components. Considering the temperature dependence of those relaxational modes they claim that each of them is associated with domain wall motion, and not with a heat diffusion central peak (HDCP). The aim of this Comment is twofold: First we want to demonstrate the importance and influence of the ac measuring field on the dielectric properties, in particular in the temperature range $Tl{T}_{f}=100 \mathrm{K}l{T}_{c}$ of domain freezing. Second, by investigating the dielectric nonlinearity in the limit of small ac fields we exclude HDCP contributions in the low-frequency part of the spectrum.

Electrical current density in a sheared dilute gas

Electrical current density of charged particles across a rarefied gas of neutral particles under shear flow is analyzed in the limit of small electric fields. The concentration of the charged species is assumed to be much smaller than that of the neutral species so that the interactions of charged–neutral and neutral–neutral type are the dominant ones. The study is made from the exact Boltzmann equation for Maxwell molecules as well as from a kinetic model for general repulsive interactions. By performing a perturbation expansion around a nonequilibrium state, the current density is explicitly evaluated in the first order of the external field. We get a generalized Ohm's law, where an electrical conductivity tensor can be identified. The nonzero elements of this tensor are nonlinear functions of the shear rate, the mass ratio, the force constant ratio, and the interaction parameter.

Dynamic scaling of hysteresis loop areas in ferroelectric KDP crystal

Hysteresis loop area A was observed in ferroelectric KDP crystal as a function of the field amplitude E and frequency ω to derive a scaling behaviour of A ∞ E1.55 ω0.20 (α=1.55, β=0.20) in small field and low frequency limits. The old Steinmetz law, which has been in disparity with both recent theoretical values and related thin film experiments, is found to be obeyed in our ferroelectric hysteresis curves of a KDP bulk crystal when we prevent our measurements properly from the distortion due to the resistive dielectric loss by going to low temperature below the domain wall freezing temperature.

Thermodynamic properties of a two-dimensional electron gas in the presence of a weak spatially modulated periodic potential

A systematic investigation on the influence of an additional periodic modulation potential which is weak, either electric or magnetic in nature, and spatially modulated along one dimension, on the equilibrium thermodynamic properties of a two-dimensional electron gas in an externally applied magnetic field is presented. The application of such an additional modulation potential results in a broadening of the Landau level energy spectrum into bands whose widths oscillate as a function of the externally applied magnetic field. Such oscillations are found to reflect the commensurability of the two different length scales present in the system, namely the cyclotron diameter at the Fermi level and the period of the modulation. We show that such commensurability effects are also to be found in all thermodynamic quantities of the system. They appear at low magnetic fields as an amplitude modulation of the well-known de Haas-van Alphen-type oscillations, familiar from the homogeneous two-dimensional electron gas system in an external magnetic field, which may or may not be resolved depending on temperature and are only weakly dependent on temperature. Their origin lies in the oscillations occurring in the bandwidths and they are consequently completely different in origin from the usual de Haas-van Alphen-type oscillations. In particular, we show that commensurability oscillations are to be found in the chemical potential, Helmholtz free energy, internal energy, electronic entropy, electronic specific heat, orbital magnetization and orbital magnetic susceptibility of such weakly modulated systems. We find that the resulting commensurability oscillations in each thermodynamic function exhibit well-defined phase relations between the electric and magnetic modulations except in the case of the orbital magnetization and the orbital magnetic susceptibility. Explicit asymptotic expressions for the chemical potential, Helmholtz free energy and orbital magnetization, in the quasi-classical limit of small magnetic fields and small but finite temperatures, are also given.

Electrical conductivity in a dilute gas far from equilibrium

Electrical conductivity of a minor constituent of charged particles through a background of neutral particles is studied in the limit of small electrical fields. The neutral gas is in a steady state with both arbitrary velocity and temperature gradients. The results are obtained from the Gross-Krook model [Phys. Rev. 102, 593 (1956)] of the Boltzmann equation for a binary mixture. The transport properties of the charged species are obtained from a perturbation expansion in powers of the electrical field. In the first order, the current density obeys a generalized Ohm's law where an electrical conductivity tensor is identified. The nonzero elements of this tensor are nonlinear functions of the shear rate, the mass ratio, and the force constant ratio. The results show that, in general, the presence of the shear produces an inhibition in the diffusion of charged particles.

Non-Ohmic effects in hopping conduction in doped silicon and germanium between 0.05 and 1 K

We have studied non-Ohmic effects in hopping conduction in moderately compensated ion-implanted Si:P, B (both $n$- and $p$-type) and neutron-transmutation-doped Ge:Ga,As over the temperature range 0.05--0.8 K and up to moderately strong electric fields. In the limit of small fields, where the current is proportional to applied voltage, the resistivities of these materials are approximated over a wide temperature range by the model of variable range hopping with a Coulomb gap: $\ensuremath{\rho}={\ensuremath{\rho}}_{0}\mathrm{exp}{(T}_{0}{/T)}^{1/2}.$ The samples included in this study have characteristic temperatures ${T}_{0}$ in the range 1.4--60 K for silicon, and 22--60 K for germanium. We have compared our data to exponential and ``hyperbolic-sine'' field-effect models of the electrical nonlinearity: $\ensuremath{\rho}(E)=\ensuremath{\rho}{(0)e}^{\ensuremath{-}x}$ and $\ensuremath{\rho}(E)=\ensuremath{\rho}(0)x/\mathrm{sinh}(x),$ where $x\ensuremath{\equiv}eEl/kT,$ and to an empirical hot-electron model. The exponential field-effect model tends to be a good representation for the samples with high ${T}_{0}$ at low $T.$ The sinh model can match the data only at low fields. The hot-electron model fits our data well over a wide range of power in the low-${T}_{0}$--high-$T$ regime. We discuss the quantitative implications of these results for the application of these materials as thermometers for microcalorimeters optimized for high-resolution spectroscopy.

On the Bernstein–Landau paradox

The essence of the Bernstein–Landau paradox is that in a stable unmagnetized plasma electrostatic waves exhibit collisionless Landau damping, while in a magnetized plasma the Bernstein modes, perpendicular to the magnetic field, are exactly undamped, independent of the strength of the magnetic field. This problem is the subject of the present study. An analytical solution of the initial value problem for perturbations perpendicular to the magnetic field is given, which is a generalization of the well-known Landau work to magnetized plasmas. By introducing, according to Plemelj’s prescription, plus- and minus-functions, having unique analytical properties, the character of the short-term and long-term plasma response is revealed, showing in the small magnetic field limit Landau damping in the first gyroperiod, followed by recurrence, and exhibiting irregular behavior with no damping at large times. The initial damping rate is seen to be close to the commonly used Landau damping rate for unmagnetized plasmas, however with a significant systematic deviation. A corrected expression for the Landau damping rate is found which yields a perfect description of the initial damping of oscillations perpendicular to a weak magnetic field. An alternative approach, expansion over Bernstein modes, is also employed. It is found that a zero-frequency (convective) mode, revealed earlier in particle simulations, is included in the complete linear treatment.

Non-Gaussian spectra in cosmic microwave background temperature anisotropies

Gaussian cosmic microwave background skies are fully specified by the power spectrum. The conventional method of characterizing non-Gaussian skies is to evaluate higher order moments, the n-point functions and their Fourier transforms. We argue that this method is inefficient, due to the redundancy of information existing in the complete set of moments. In this paper we propose a set of new statistics or non-Gaussian spectra to be extracted out of the angular distribution of the Fourier transform of the temperature anisotropies in the small field limit. These statistics complement the power spectrum and act as localization, shape, and connectedness statistics. They quantify generic non-Gaussian structure, and may be used in more general image processing tasks. We concentrate on a subset of these statistics and argue that while they carry no information in Gaussian theories they may be the best arena for making predictions in some non-Gaussian theories. As examples of applications we consider superposed Gaussian and non-Gaussian signals, such as point sources in Gaussian theories or the realistic Kaiser-Stebbins effect. We show that in these theories non-Gaussianity is only present in a ring in Fourier space, which is best isolated in our formalism. Subtle but strongly non-Gaussian theories are also written down for which only non-Gaussian spectra may accuse non-Gaussianity.

A new one-dimensional model for electrostrictive materials

Electrostrictive materials such as lead magnesium niobate (PMN) are currently being evaluated for use in high-powered sonar transducers and actuators. The principal characteristics which differentiate them from piezoelectric ceramics are nonlinear dependence of the strain on the applied electric field and saturation of the polarization at high electric fields. A new set of constitutive relations for the behavior of electrostrictive materials in one dimension is developed, using the stress and the electric field as the independent variables. These relations are derived from a Gibbs free energy function using thermodynamic definitions of the strain and the electric displacement. The nonlinearity of the strain and the saturation behavior are included explicitly in the formulation. The resulting equations reduce to the correct power series forms for a pure electrostrictor [G. H. Blackwood and M. A. Ealey, Smart. Mater. Struct. 2, 124–133 (1993)] in the limit of small fields and/or stresses. The theory will be shown to be consistent with experimental data on PMN obtained at NUWC. Comparisons with other electrostrictive material models, such as those using polarization as the independent variable [C. L. Hom and N. Shankar, J. Intell. Mater. Syst. and Struct. 5, 795–801 (1994)], will also be made.

Magnetic structure of superlattices with biquadratic interlayer exchange coupling

We calculate the magnetic structure of an infinitely extended magnetic superlattice in the presence of interlayer biquadratic exchange coupling and a 4-fold in-plane anisotropy. An external magnetic field is also applied in the plane of the layers. We consider ground state configurations with unit cells involving 1, 2, or 4 magnetic layers. At low fields a two-layer unit cell structure is found to be the ground state. At higher fields the ground state has the spins in all layers aligned so the unit cell is one layer. Analytic expressions for the magnetic equilibrium structures are obtained in the small field limit, as are expressions for the critical fields for a transition from one state to another. Numerical results are presented for magnetic fields of arbitrary size.

Photodetachment of an electron bound by a zero-range potential in magnetic fields of arbitrary strength.

The model problem of photodetachment of an electron initially bound by a zero-range potential in a homogeneous static magnetic field of arbitrary strength is solved exactly. Expressions for the cross sections are derived within the nonrelativistic theory for various photon polarizations. In particular, photodetachment from states that exist only in the presence of a magnetic field is studied. In the limit of small fields the results obtained agree with findings of other authors.

Vortex lattice melting, pinning and kinetics

The phenomenology of the high Tc superconductors is discussed both at the level of the thermodynamics of melting of the Abrikosov flux lattice and in terms of the melting and kinetics of the flux lattice for a pinned system. We review results on 3D melting obtained by a Monte Carlo simulation approach in which the 2D “pancake” vortices are treated as statistical variables. We discuss pinning in the context of the strong pinning regime in which the vortex density given in terms of the applied field B is small compared to that represented by an effective field Bpin measuring the pinning center density. We introduce a new criterion for the unfreezing of a vortex glass on increase of magnetic field or temperature, in the strong pinning, small field limit. We model this limit in terms of a single flux line interacting with a columnar pin. This model is studied both analytically and by computer simulation. By applying a tilt potential, we study the kinetics of the vortex motion in an external current and show that the resulting current-voltage characteristic follows a basic vortex glass-like scaling relation in the vicinity of the depinning transition.