Preasymptotic Region Research Articles

Non-Fermi-liquid behavior consistent with a preasymptotic disorder-tuned ferromagnetic quantum critical point in the heavy fermion system CeTi1−xVxGe3

An investigation of the thermodynamic and electrical transport properties of the isoelectronic chemical substitution series CeTi1−xVxGe3 (CTVG) single crystals is reported. As x increases, the ferromagnetic (FM) transition temperature is suppressed, reaching absolute zero at the critical concentration x=0.4, where a non-Fermi-liquid low-temperature specific heat and electrical resistivity, as well as the hyperscaling of specific heat and magnetization, are found. Our study suggests the presence of an FM quantum critical point (QCP) in CTVG. The obtained critical exponents indicate that CTVG falls in the preasymptotic region of the disorder-tuned FM QCP predicted by the Belitz-Kirkpatrick-Vojta theory. Published by the American Physical Society 2024

Preasymptotic analysis of the generalization of the classical scheme of particle allocation by sets with conditions

Generalization of the classical scheme of allocating particles into cells by sets implies extending its conditions to allow different sizes of sets. This allocation scheme is studied separately for cases without empty cells and by selected cells. The study is carried out by the enumeration method based on the construction and analysis of an iterative random process of direct non-repetitive numbered enumeration of its outcomes in the pre-asymptotic region of parameter change in the following directions: solving the numbering problem in direct and inverse formulations which consist in finding one-to-one correspondence between the numbers and types of outcomes of the scheme, determining the probabilistic distribution of the number of empty cells and on the set of outcomes of the scheme according to the introduced probabilities of iterative transitions of the process of their enumeration and developing a procedure for their modeling

Hyperscaling analysis of a disorder-induced ferromagnetic quantum critical point in Ni1−xRhx with x=0.375

Here we report on hyperscaling analysis on thermodynamic measurements as a function of temperature and magnetic field for Ni$_{1-x}$Rh$_{x}$ with $x = 0.375$ where a ferromagnetic quantum critical point has been recently identified [Phys. Rev. Lett. $\textbf{124}$, 117203 (2020)]. The obtained critical exponents agree well with the theory proposed by Belitz, Kirkpatrick, and Vojta for disorder tuned quantum critical point in the preasymptotic region.

Increasing effective intensity of soft strong interactions

We suggest definition of effective interaction intensity for soft hadron collisions and discuss its energy dependence in the preasymptotic region. Practical importance of this quantity consists in separation of rising interaction radius from effective interaction intensity increase both contributing to the total cross-section growth. It would be helpful for understanding the origin of this growth at the accelerator energies. The essential feature is that the effective interaction intensity is an experimentally measurable quantity.

Goal-based angular adaptivity for Boltzmann transport in the presence of ray-effects

Boltzmann transport problems often involve heavy streaming, where particles propagate long distance due to the dominance of advection over particle interaction. If an insufficiently refined non-rotationally invariant angular discretisation is used, there are areas of the problem where no particles will propagate. These “ray-effects” are problematic for goal-based error metrics with angular adaptivity, as the metrics in the pre-asymptotic region will be zero/incorrect and angular adaptivity will not occur. In this work we use low-order filtered spherical harmonics, which are rotationally invariant and hence not subject to ray-effects, to “bootstrap” our error metric and enable highly refined anisotropic angular adaptivity with a Haar wavelet angular discretisation. We test this on three simple problems with pure streaming in which traditional error metrics fail. We show our method is robust and produces adapted angular discretisations that match results produced by fixed a priori refinement with either reduced runtime or a constant additional cost even with angular refinement.

Taming of preasymptotic small x evolution within resummation framework

It is well understood that the leading logarithmic approximation for the amplitudes of high energy processes is insufficient and that the next-to-leading logarithmic effects are very large and lead to instability of the solution. The resummation at low x, which includes kinematical constraints and other corrections leads to stable result. Using previously established resummation procedure we study in detail the preasymptotic effects which occur in the solution to the resummed BFKL equation when the energy is not very large. We find that in addition to the well known reduction of the intercept, which governs the energy dependence of the gluon Green’s function, resummation leads to the delay of the onset of its small x growth. Moreover the gluon Green’s function develops a dip or a plateau in wide range of rapidities, which increases for large scales. The preasymptotic region in the gluon Green’s function extends to about 8 units in rapidity for the transverse scales of the order of 30–100 GeV. To visualize the expected behavior of physical processes with two equal hard scales we calculate the cross section of the process gamma ^{*}+gamma ^{*}rightarrow X to be probed at future very high-energy electron-positron colliders. We find that at gamma ^*gamma ^* energies below 100 ; mathrm{{GeV}} the BFKL Pomeron leads to smaller value of the cross section than the Born approximation, and only starts to dominate at energies about 100 ; mathrm{{GeV}}. This pattern is significantly different from the one which we find using LLx approximation. We also analyze the transverse momentum contributions to the cross section for different virtualities of the photons and find that the dominant contributions to the integral over the transverse momenta comes from lower values than the the external scales in the process under consideration.

Измерение величины R в предасимптотической области энергий

Измерение величины R в предасимптотической области энергий

Analysis of combinatorial schemes in the pre-asymptotic region of parameter change

The paper discusses the specific features and presents the procedure and the results of studying a wide variety of specific combinatorial schemes in the pre-asymptotic region of their parameter change. It is suggested that the schemes are analyzed by an unconventional quality analysis of their outcomes, the result of which include quantitative characteristics.

Parametric Model-Order Reduction for Accelerating the Gradient-Based Optimization of Microwave Structures Using Finite-Elements

A numerical method for optimizing the frequency response of linear time-invariant microwave structures at the fields level is presented. It is based on the finite-element method in the frequency-domain, a quasi-Newton optimizer, and the reduced-basis method. The reduced-order model is constructed adaptively, in the course of the optimization process, and its validity is restricted to some neighborhood of the trajectory drawn by the optimizer in parameter space. The computational complexity of the method is independent of the number of design variables. The present study is restricted to material parameters which lead to affine parameterization. Numerical results demonstrate that the number of finite-element evaluations, which are computationally expensive, is greatly reduced, even in the pre-asymptotic region of the optimization process. Moreover, it is shown that computing the gradient of the cost function analytically provides significant savings in computer runtime over finite-difference approximations.

The impact of target mass correction on polarized parton distribution functions

Considering the nonzero mass effect of the target in extracting polarized parton distribution functions (PPDFs) in preasymptotic region is not negligible. We extract PPDFs from available proton structure function data and study the numerical effects of target mass corrections (TMCs). PPDFs with and without this correction are compared.

Some remarks on methods of QCD analysis of polarized DIS data

The results on polarized parton densities obtained using different methods of QCD analysis of the present polarized DIS data are discussed. Their dependence on the method used in the analysis, accounting or not for the kinematic and dynamic 1=Q 2 corrections to spin structure function g1, is demonstrated. It is pointed out that the precise data in the preasymptotic region require a more careful matching of the QCD predictions to the data in this region in order to determine the polarized parton densities correctly.

An Improved Jacobi-Davidson Method With Multi-Level Startup Procedure

The Jacobi-Davidson method is very attractive for the large-scale finite element simulation of electromagnetic cavity problems, because it just requires approximate solutions to some auxiliary systems of linear equations, which are easily obtained by iterative solvers. Moreover, rates of convergence are quadratic to cubic. In consequence, the time spent within the pre-asymptotic region at the early stages of the iteration may have strong impact on overall performance, particularly when the number of eigenvalues sought is small. Therefore, we propose a startup procedure that utilizes p hierarchical finite element spaces to reduce the cost of bridging the pre-asymptotic region.

Upscaling, relaxation and reversibility of dispersive flow in stratified porous media

Dispersive tracer released in a unidirectional velocity field belonging to a stratified porous of finite height describes a transition, called relaxation, from a convective dominated behaviour for short times to Fickian behaviour for asymptotic long times. The temporal relaxation state of the tracer is controlled by the transverse mixing term. In most practical applications, the orders of the time and length scales of the relaxation mechanism are such that in an upscaled model of a stratified medium the dispersive flux is in a pre-asymptotic state. Explicit modelling of the relaxation of the dispersive flux in the pre-asymptotic region is required to improve the accuracy. This paper derives a pre-asymptotic one-dimensional upscaled model for the transverse averaged tracer concentration. The model generalises Taylor dispersion (Proc. R. Soc. London 219, 186–203 (1953)) and extends the method of Camacho (Phys. Rev. E 47(2), 1049–1053 (1993a); Phys. Rev. E 48 (1993b)) to dispersion tensors that may vary as function of the transverse direction. In the averaging step, the governing two-dimensional equation is first spectrally decomposed in terms of the eigenfunctions of the transverse mixing term. Next, the resulting modal relaxation equations are combined into an effective relaxation equation for the extended dispersive Taylor flux. Contrary to the one-dimensional Fickian approach, the upscaled model approximates the multi-scale relaxation behaviour as a single scale relaxation process and accounts for the partial reversibility of convective dispersion upon reversal of the flow direction. The upscaled model is evaluated against the original two-dimensional model by means of moment analysis. The longitudinal tracer variance predicted by our model is quantitatively correct in the short and long time limits and is qualitatively correct for intermediate times.

Energy functional dependence of exchange coupling and magnetic properties ofFe∕Nbmultilayers

We present an ab initio calculation of the exchange coupling for $\mathrm{Fe}∕\mathrm{Nb}$ multilayers using the self-consistent full-potential linearized augmented plane-wave method. The exchange correlation potential has been treated in the local spin density approximation (LSDA) as well as generalized gradient approximation (GGA). We find that for the LSDA as well as the GGA the exchange coupling oscillates with a period of $6.0\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ of Nb spacer thickness which is close to the experimental value in the pre-asymptotic region. This is also close to the earlier calculated period (i.e., $4.5\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$) by augmented spherical wave method. The LSDA shows antiferromagnetic coupling for 2 and $5\phantom{\rule{0.3em}{0ex}}\mathrm{Nb}$ monolayers but the GGA shows the ferromagnetic coupling for all Nb spacer layers. The period of oscillation is found to be in good agreement with the period calculated using the Ruderman-Kittel-Kasuya-Yosida and quantum well models. The magnetic moment of Fe is found to be higher in the GGA than the LSDA. Fe magnetic moment also shows strong oscillations as a function of the spacer layer thickness, in agreement with the experimental results. We find that the GGA results show better agreement with the experiment than the LSDA results.

The running QCD coupling in the pre-asymptotic region

We study deviations from the perturbative asymptotic behaviour in the running QCD coupling by analysing non-perturbative measurements of α s ( p) at low momenta ( p ≈ GEV) as obtained from the lattice three-gluon vertex. Our exploratory study provides some evidence for power corrections to the perturbative running proportional to 1 p 2 .

Positive-definite Toeplitz completion in DOA estimation for nonuniform linear antenna arrays. I. Fully augmentable arrays

This paper considers the problem of direction-of arrival (DOA) estimation for multiple uncorrelated plane waves incident on so-called fully augmentable sparse linear arrays. In situations where a decision is made on the number of existing signal sources (m) prior to the estimation stage, we investigate the conditions under which DOA estimation accuracy is effective (in the maximum-likelihood sense). In the case where m is less than the number of antenna sensors (M), a new approach called MUSIC-maximum-entropy equalization is proposed to improve DOA estimation performance in the preasymptotic region of finite sample size (N) and signal-to-noise ratio. A full-sized positive definite (p.d.) Toeplitz matrix is constructed from the M/spl times/M direct data covariance matrix, and then, alternating projections are applied to find a p.d. Toeplitz matrix with m-variate signal eigensubspace (signal subspace truncations). When m/spl ges/M, Cramer-Rao bound analysis suggests that the minimal useful sample size N is rather large, even for arbitrarily strong signals. It is demonstrated that the well-known direct augmentation approach (DAA) cannot approach the accuracy of the corresponding Cramer-Rao bound, even asymptotically (as N/spl rarr//spl infin/) and, therefore, needs to be improved. We present a new estimation method whereby signal subspace truncation of the DAA augmented matrix is used for initialization and is followed by a local maximum-likelihood optimization routine. The accuracy of this method is demonstrated to be asymptotically optimal for the various superior scenarios (m/spl ges/M) presented.

Hadronic transitions among quarkonium states in a soft-exchange-approximation. Chiral breaking and spin symmetry breaking processes

Although no asymptotic heavy quark spin symmetry, and even more no flavor symmetry, are expected for systems such as quarkonium, a numerical discussion shows that for some processes and in a preasymptotic region which may roughly include charmonium and bottomonium, the use of the spin-symmetry may be useful in conjunction with chiral symmetry for light hadrons (soft-exchange-approximation regime, SEA). We continue our discussion of hadronic transitions in the SEA-regime by studying in particular chiral breaking transitions such as 3P′ → 3Pπ 0, 3Pη , level splittings and transitions which break both chiral and spin symmery, such as ψ′ → J/ ψπ 0, J/ ψη and 1 P 1 → J/ ψπ 0.

Preasymptotic corrections to the exchange coupling in magnetic multilayers

The oscillations in the exchange coupling J( z), are derived for magnetic multilayers described by the generalized Anderson model. In the preasymptotic region, which is relevant for multilayers studied experimentally, J( z) deviates markedly from the asymptotic form. For short spacer layers J( z) differs in sign, its attenuation is much slower and the period is much longer than what is predicted by the asymptotic theory. For the quantitative analysis, the parameters of the Anderson (or Wolff) model, used here to estimate the distance dependence of the coupling, should be derived from the ab initio band structure calculations for a single 3 d magnetic layer in a nonmagnetic host.

A new point-ion pseudizing potential for s-p bonded metals

The authors have developed a new point-ion pseudizing potential appropriate for the s-p bonded metals. The electron-ion contribution to the effective potential has been calculated self-consistently. The essential feature of this description is the occurrence of the true field rather than a coulombic form in the pre-asymptotic region. The orthogonalizing contributions that arise from repulsive s scattering and attractive p scattering are calculated in terms of delta functions of strengths suitable for achieving the necessary s and p pseudizations respectively. The new potential is successfully applied to calculate a number of solid and liquid state properties of certain s-p bonded systems.

Theory of generalized bessel functions.-II

In this paper we continue the systematic study of the generalized Bessel functions (GBF) recently introduced and often encountered in problems of scattering for which the dipole approximation is inadequate. We analyse the relations among different GBF and discuss their importance for the solution of differential finite-difference equation of the Raman-Nath type. We present numerical results for the first-kind cylinder GBF in the preasymptotic region and also a preliminary analysis of the asymptotic properties of the modified GBF.