Nonzero Number Research Articles

Stepanov and Weyl Classes of c-Almost Periodic Type Functions

As an extension of some classes of generalized almost periodic functions, in this paper we develop the notion of c-almost periodicity in the sense of Stepanov and Weyl approaches. In fact, we extend some basic results of this theory which were already demonstrated for the standard cases. In particular, we prove that every c-almost periodic function in the sense of Stepanov approach (in the sense of equi-Weyl or Weyl approaches, respectively) is also c^m-almost periodic in the sense of Stepanov approach (in the sense of equi-Weyl or Weyl approaches, respectively) for each non-zero integer number m. This study is performed for both representative cases of functions defined on the real axis and with values in a Banach space and the complex functions defined on vertical strips in the complex plane.

A comparative study of electromagnetically induced transparency (EIT) in Λ-, V-, and Ξ-type systems using Laguerre–Gaussian (LG) laser beams

In this paper, a theoretical investigation of electromagnetically induced transparency (EIT) using Laguerre–Gaussian (LG) beams has been carried out for the three canonical atom-laser coupled systems (e.g. [Formula: see text]-, V-, and [Formula: see text]-type) in [Formula: see text]Rb atom. The required optical Bloch equations (OBEs) are derived for each system. The OBEs are analytically solved in steady-state condition under the weak probe field approximation. We have used the iterative perturbative technique to obtain the probe coherence term. The probe response w.r.t. probe detuning for different orders of the orbital angular momentum (OAM) number of both the pump and probe LG beams has been studied. We have also studied the effect of the OAM number on probe response in both Doppler-free and Doppler-broadened mediums. It has been observed that the EIT signal is squeezed for nonzero OAM number of the pump beam with arbitrary OAM number of the probe beam. It is found that for higher-order OAM number, the EIT signal is further squeezed. The modification of the EIT signal is attributed because of the spatial-dependent Rabi frequency. Our study demonstrates that the dynamic of the probe field inside an atomic medium may be controlled by tuning the OAM number of the LG beam.

Non-existence of quasi-symmetric designs having certain pseudo-geometric block graphs

The block graph of a quasi-symmetric design is strongly regular. It is a challenging problem to decide which strongly regular graphs are block graphs of quasi-symmetric designs. We rule out the possibility of quasi-symmetric designs with non-zero intersection numbers whose block graphs have the parameters as certain pseudo-geometric graphs.

Algebraic independence of values of quasi-modular forms

In this paper, we discuss the algebraic independence of special values of quasi-modular forms. We show that for three algebraically independent quasi-modular forms with algebraic Fourier coefficients, if one of e2πiz and their values at z in the upper half plane is a non-zero algebraic number, then the other three numbers are algebraically independent over Q. We also provide a condition for determining when quasi-modular forms are algebraically independent. Moreover, based on the theorem proved in the paper, we prove the algebraic independence of values of derivatives of modular forms with algebraic Fourier coefficients.

Cardinality optimization in constraint-based modelling: application to human metabolism.

Several applications in constraint-based modelling can be mathematically formulated as cardinality optimization problems involving the minimization or maximization of the number of nonzeros in a vector. These problems include testing for stoichiometric consistency, testing for flux consistency, testing for thermodynamic flux consistency, computing sparse solutions to flux balance analysis problems and computing the minimum number of constraints to relax to render an infeasible flux balance analysis problem feasible. Such cardinality optimization problems are computationally complex, with no known polynomial time algorithms capable of returning an exact and globally optimal solution. By approximating the zero-norm with nonconvex continuous functions, we reformulate a set of cardinality optimization problems in constraint-based modelling into a difference of convex functions. We implemented and numerically tested novel algorithms that approximately solve the reformulated problems using a sequence of convex programs. We applied these algorithms to various biochemical networks and demonstrate that our algorithms match or outperform existing related approaches. In particular, we illustrate the efficiency and practical utility of our algorithms for cardinality optimization problems that arise when extracting a model ready for thermodynamic flux balance analysis given a human metabolic reconstruction. Open source scripts to reproduce the results are here https://github.com/opencobra/COBRA.papers/2023_cardOpt with general purpose functions integrated within the COnstraint-Based Reconstruction and Analysis toolbox: https://github.com/opencobra/cobratoolbox.

Unleashing the Power of Graph Spectral Sparsification for Power Grid Analysis via Incomplete Cholesky Factorization

Graph spectral sparsification based preconditioning technique has shown promising results for power grid analysis. However, the conventional methods converge slowly for high accuracy requirement. In this work, we propose an efficient approach to address this issue. Instead of using Cholesky factorization, we employ incomplete Cholesky factorization to factorize the spectral sparsifier. We also propose a concept of graph spectral pattern, which can further reduce the preconditioned conjugate gradient (PCG) iterations using less number of nonzeros. Experiments show that under 10-6 relative tolerance, our proposed preconditioning technique achieves 1.17× speedup compared to AMGPCG in average; compared to the conventional spectral sparsification based preconditioning techniques, our proposed approach achieves up to 8.53× speedup of the factorization, 8.74× speedup of the PCG iteration, and 5.6× speedup of the total time. Moreover, the speedup of the total time continues to enlarge for higher accuracy requirement, e.g., 10-12. Last, but not the least, our method is compatible with existing graph spectral sparsification algorithms for power grid analysis.

Schrödinger and Klein–Gordon theories of black holes from the quantization of the Oppenheimer and Snyder gravitational collapse

The Schrödinger equation of the Schwarzschild black hole (BH) has been recently derived by the author and collaborators. The BH is composed of a particle, the ‘electron’, interacting with a central field, the ‘nucleus’. Via de Broglie’s hypothesis, one interprets the ‘electron’ in terms of BH horizon’s modes. Quantum gravity effects modify the BH semi-classical structure at the Schwarzschild scale rather than at the Planck scale. The analogy between this BH Schrödinger equation and the Schrödinger equation of the s states of the hydrogen atom permits us to solve the same equation. The quantum gravitational quantities analogous of the fine structure constant and of the Rydberg constant are not constants, but the dynamical quantities have well-defined discrete spectra. The spectrum of the ‘gravitational fine structure constant’ is the set of non-zero natural numbers. Therefore, BHs are well-defined quantum gravitational systems obeying Schrödinger’s theory: the ‘gravitational hydrogen atoms’. By identifying the potential energy in the BH Schrödinger equation as being the gravitational energy of a spherically symmetric shell, a different nature of the quantum BH seems to surface. BHs are self-interacting, highly excited, spherically symmetric, massive quantum shells generated by matter condensing on the apparent horizon, concretely realizing the membrane paradigm. The quantum BH described as a ‘gravitational hydrogen atom’ is a fictitious mathematical representation of the real, quantum BH, a quantum massive shell having a radius equal to the oscillating gravitational radius. Nontrivial consequences emerge from this result: (i) BHs have neither horizons nor singularities; (ii) there is neither information loss in BH evaporation, nor BH complementarity, nor firewall paradox. These results are consistent with previous ones by Hawking, Vaz, Mitra and others. Finally, the special relativistic corrections to the BH Schrödinger equation give the BH Klein–Gordon equation and the corresponding eigenvalues.

Angular Adaptivity in P0 Space and Reduced Tolerance Solves for Boltzmann Transport

Previously, we developed an adaptive method in angle that is based on solving in Haar wavelet space with a matrix-free multigrid for Boltzmann transport problems. This method scalably mapped to the underlying P0 space during every matrix-free matrix-vector product; however, the multigrid method itself was not scalable in the streaming limit. To tackle this, we recently built an iterative method based on using an Approximate Ideal Restriction multigrid with GMRES polynomials (AIRG) for Boltzmann transport that showed scalable work with uniform P0 angle in the streaming and scattering limits. This paper details the practical requirements of using this new iterative method with angular adaptivity. Hence, we modify our angular adaptivity to occur directly in P0 space rather than the Haar space. We then develop a modified stabilization term for our Finite Element Method that results in scalable growth in the number of nonzeros in the streaming operator with P0 adaptivity. We can therefore combine the use of this iterative method with P0 angular adaptivity to solve problems in both the scattering and the streaming limits, with close to fixed work and memory use.We also present a coarse-fine splitting for multigrid methods based on element agglomeration combined with angular adaptivity, which can produce a semicoarsening in the streaming limit without access to the matrix entries. The equivalence between our adapted P0 and Haar wavelet spaces also allows us to introduce a robust convergence test for our iterative method when using regular adaptivity. This allows the early termination of the solve in each adapt step, reducing the cost of producing an adapted angular discretization.

Soret-induced convection of ternary fluid in a horizontal porous layer heated from below

The present paper deals with the investigation of the Soret-induced convection of a three-component mixture of hydrocarbons in a horizontal porous layer. This problem is important for geological applications. The first part of the paper is devoted to the linear stability of the conductive state. The longwave instability is studied analytically by the expansion into the power series with respect to the wave number. A new long-wave oscillatory instability mode existing at negative separation ratios is found out. It is shown that this mode is more dangerous than the long-wave monotonic instability mode in the entire range of its existence. The instability to the perturbations with nonzero wave numbers is studied numerically by the shooting method. Stability map is obtained. The results confirm the predictions of the longwave analysis. In the second part of the paper, the nonlinear convection regimes are studied by the finite difference method. The calculations give the results consistent with the linear stability analysis. It is found that the primary bifurcation as a result of which the conductive state losses its stability is supercritical. The transformations of the convective flow structure with the change in the Rayleigh–Darcy number are accompanied by the hysteresis phenomena.

Probing the symmetry breaking of a light–matter system by an ancillary qubit

Hybrid quantum systems in the ultrastrong, and even more in the deep-strong, coupling regimes can exhibit exotic physical phenomena and promise new applications in quantum technologies. In these nonperturbative regimes, a qubit–resonator system has an entangled quantum vacuum with a nonzero average photon number in the resonator, where the photons are virtual and cannot be directly detected. The vacuum field, however, is able to induce the symmetry breaking of a dispersively coupled probe qubit. We experimentally observe the parity symmetry breaking of an ancillary Xmon artificial atom induced by the field of a lumped-element superconducting resonator deep-strongly coupled with a flux qubit. This result opens a way to experimentally explore the novel quantum-vacuum effects emerging in the deep-strong coupling regime.

Dynamical Love numbers for area quantized black holes

We study the tidal deformability of horizonless exotic compact objects, with implications for area quantized black holes. Since, any such horizonless compact object, including an area quantized black hole, possesses a nonzero reflectivity, it follows that they inherit a nonzero tidal Love number which varies as a function of the perturbing frequency. The reflectivity of the horizon for an area quantized black hole has a distinct shape and unmistakable features, which are also present in the frequency-dependent tidal Love numbers, and therefore is a smoking gun test for such quantum black holes. The existence of these features also promotes the dynamical Love number to be a crucial observational tool to not only distinguish area quantized black holes from other models of horizonless compact objects, but also to differentiate between black holes with distinct schemes of area quantization. We further discuss implications of the same for the present and the future gravitational wave detectors.

Vanishing Love numbers of black holes in general relativity: From spacetime conformal symmetry of a two-dimensional reduced geometry

We study the underlying structure of the vanishing of the Love numbers of both Schwarzschild and Kerr black holes in terms of spacetime conformal symmetry in a unified manner for the static spin-$s$ fields. The perturbations can be reduced with the harmonic decomposition to a set of infinite static scalar fields in a two-dimensional anti--de Sitter spacetime $({\text{AdS}}_{2})$. In the reduced system, each scalar field is paired with another, implying that all multipole modes of the perturbation can be regarded as symmetric partners, which can be understood from the property of the supersymmetry algebra. The generator of the supersymmetric structure is constructed from a closed conformal Killing vector field of ${\text{AdS}}_{2}$. The associated conserved quantity allows one to show no static response, i.e., vanishing of the Love and dissipation numbers. We also discuss the vanishing Love numbers of the Kerr black hole with the nonzero dissipation numbers for the nonaxisymmetric perturbations in terms of a radial constant found in a parallel manner as the axisymmetric field case even though the interpretation for the structure is controversial. The symmetric structure corresponds to the ``ladder'' symmetry in [Hui et al., J. Cosmol. Astropart. Phys. 01 (2022) 032] although the geometrical origin is different. Our ladder operator includes the generators of hidden symmetries in previous works.

Minimum number of Weyl point phonons in mixed-metal periodate RbGeIO6

In topology physics, the prediction of Weyl systems with the minimum nonzero number of Weyl points (WPs) remains challenging. In this study, for the first time, we propose the P312 type RbGeIO6 as a material candidate with the minimum number of WPs in its phonon curves. Based on first-principles calculations and symmetry analysis, we confirm that the RbGeIO6 exhibits only two charge-two (C-2) WPs at the Γ and A time-reversal-invariant momenta points in the 3D Brillouin zone (BZ). Furthermore, the two C-2 WP phonons at the Γ and A result in the formation of the clean and long phononic double surface state on the (010) surface. The phononic double surface state spans the entire first surface BZ of the (010) surface, facilitating their detection in future experimental studies.

On application of the regularized lattice Boltzmann method for isothermal flows with non-vanishing Knudsen numbers

Despite the advances in microscale modelling capabilities, physically observed non-zero Knudsen number (Kn) effects still elude the lattice Boltzmann method (LBM). This article details various Regularized LBM (RLBM) strategies used to model microscale flows and presents a thorough analysis on their applicability for the force-driven Poiseuille flow problem. In particular, we compare the formulations of eight schemes: Projected RLBM (P-RLBM), standard and Galilean Invariant Filtered Collision RLBM, Kn-dependant P-RLBM, Recursively Regularized LBM (R-RLBM), Hybrid R-RLBM, Central-Moment RLBM, and Onsager-Regularized LBM. We demonstrate, at different Kn with discrete Maxwell’s diffuse kinetic wall boundary conditions, the numerical equivalence of the considered RLBM schemes for hard sphere molecules on the D2Q9 lattice. Thereafter, we include a Kn-dependant wall-modified mean-free-path and extend the characterization onto higher-order D2Q17, D2Q21 and Q2Q25-Zero-One-Three, Q2Q49-Zero-One-Two-Three lattices. The study indicates that RLBM schemes are Navier-Stokes solvers which fail to entirely capture all the non-equilibrium phenomenon of slip/transition regime flows.

Far-off-equilibrium expansion trajectories in the QCD phase diagram

We consider the hydrodynamic evolution of a quark-gluon gas with nonzero quark masses and net baryon number in its phase diagram. For far-off-equilibrium initial conditions the expansion trajectories appear to violate simple rules based on the second law of thermodynamics that were previously established for ideal or weakly dissipative fluids. For Bjorken flow we present a detailed analysis within kinetic theory that provides a full microscopic understanding of these macroscopic phenomena and establishes their thermodynamic consistency. We point out that, for certain far-off-equilibrium initial conditions, the well-known phenomenon of ``viscous heating'' turns into ``viscous cooling'' where, driven by dissipative effects, the temperature decreases faster than in adiabatic expansion.

The effect of thermal photons on exceptional points in coupled resonators

We analyse two quantum systems with hidden parity-time ({mathscr {P}mathscr {T}}) symmetry: one is an optical device, whereas another is a superconducting microwave-frequency device. To investigate their symmetry, we introduce a damping frame (DF), in which loss and gain terms for a given Hamiltonian are balanced. We show that the non-Hermitian Hamiltonians of both systems can be tuned to reach an exceptional point (EP), i.e., the point in parameter space at which a transition from broken to unbroken hidden {mathscr {P}mathscr {T}} symmetry takes place. We calculate a degeneracy of a Liouvillian superoperator, which is called the Liouvillian exceptional point (LEP), and show that, in the optical domain, LEP is equivalent to EP obtained from the non-Hermitian Hamiltonian (HEP). We also report breaking the equivalence between LEP and HEP by a non-zero number of thermal photons for the microwave-frequency system.

Third-order accurate 13-moment equations for non-continuum transport phenomenon

The derivation of analytical equations of non-continuum macroscopic transport phenomena is underpinned by approximate descriptions of the particle distribution function and is required due to the inability of the Navier–Stokes equations to describe flows at high Knudsen number (Kn ∼ 1). In this paper, we present a compact representation of the second-order correction to the Maxwellian distribution function and 13-moment transport equations that contain fewer terms compared to available moment-based representations. The intrinsic inviscid and isentropic assumptions of the second-order accurate distribution function are then relaxed to present a third-order accurate representation of the distribution function, using which corresponding third-order accurate moment transport equations are derived. Validation studies performed for Grad’s second problem and the force-driven plane Poiseuille flow problem at non-zero Knudsen numbers for Maxwell molecules highlight an improvement over results obtained by using the Navier–Stokes equations and Grad’s 13-moment (G13) equations. To establish the ability of the proposed equations to accurately capture the bulk behavior of the fluid, the results of Grad’s second problem have been validated against the analytical solution of the Boltzmann equation. For the planar Poiseuille flow problem, validations against the direct simulation Monte Carlo method data reveal that, in contrast to G13 equations, the proposed equations are capable of accurately capturing the Knudsen boundary layer.

An Agent-Based Model of Sex and Sexual Orientation Differences in Short-Term Mating Behaviors as a Result of Mating Preferences

ABSTRACT Sex differences in short-term mating behaviors are well-documented in human sexuality research. Existing studies usually explain sex differences in sexual behaviors through differences in mating preferences, which is theoretically problematic. Using an agent-based model, we investigated the circumstances under which males’ and females’ differential preferences for short-term mating would result in sex differences in short-term mating behaviors. The model showed that when all individuals in a closed heterosexual population were considered, males and females had the same average number of short-term mating experiences and short-term mates even when males had stronger preferences for short-term mating. Males (vs. females) had a higher average number of both experiences and mates when analyses were limited to only heterosexual males and females who successfully participated in the mating pool (i.e., those with a non-zero number of short-term mating experiences). Moreover, when males (vs. females) had stronger preferences for short-term mating, gay males had a higher average number of experiences and mates compared to both lesbian females and heterosexual males. These results suggest that even when sex differences in mating preferences exist, the sex differences in short-term mating behaviors only occur among particular populations, or when males’ preferences for short-term mating are not constrained by those of females. Suggestions for future research in human mating psychology and behaviors were provided.

Formation of Diophantine Triples Involving Heptagonal Pyramidal Numbers

Abstract: In this paper, we seek for three specific polynomials with integer coefficients to such an extent that the product of any two numbers expanded by a non-zero number (or polynomials with integer coefficients) is a perfect square.

Maximally charged single-pair multi-Weyl point phonons in P23 -type BeH2

The realization of multi-Weyl systems with the minimum nonzero number of Weyl points and the maximum charge number remains challenging in topology physics. In this work, based on first-principles calculations, we propose that ${\mathrm{BeH}}_{2}$ is thermodynamically, mechanically, and dynamically stable in a cubic crystal structure with the $P23$ space group. Importantly, this is the first work to report the appearance of single-pair multi-Weyl point phonons with the maximum charge number in $P23$-type ${\mathrm{BeH}}_{2}$. Furthermore, the number and charge of the Weyl points and the phononic surface modes can be tuned by applying $1%$ and $2%$ uniaxial strains along the [100] and [111] directions, respectively. Finally, we report that clean charge-two single-pair triple-point phonons appear in $P23$-type ${\mathrm{BeH}}_{2}$ and investigate the related chiral phonon transition under the uniaxial strains.