Behavior Of Function Research Articles

Decomposition and factorisation of transients in functional graphs

Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be quite large, it is interesting to decompose and factorise them into several subgraphs acting together. Polynomial equations over functional graphs provide a formal way to represent this decomposition and factorisation mechanism, and solving them validates or invalidates hypotheses on their decomposability. The current solution method breaks down a single equation into a series of basic equations of the form A×X=B (with A, X, and B being FGs) to identify the possible solutions. However, it is able to consider just FGs made of cycles only. This work proposes an algorithm for solving these basic equations for general connected FGs. By exploiting a connection with the cancellation problem, we prove that the upper bound to the number of solutions is closely related to the size of the cycle in the coefficient A of the equation. The cancellation problem is also involved in the main algorithms provided by the paper. We introduce a polynomial-time semi-decision algorithm able to provide constraints that a potential solution will have to satisfy if it exists. Then, exploiting the ideas introduced in the first algorithm, we introduce a second exponential-time algorithm capable of finding all solutions by integrating several ‘hacks’ that try to keep the exponential as tight as possible.

Science Opportunities for IMAP-Lo Observations of Interstellar Neutral Hydrogen and Deuterium during a Maximum of Solar Activity

Direct-sampling observations of interstellar neutral gas, including hydrogen and deuterium, have been performed for more than one cycle of solar activity by IBEX. The IBEX viewing is restricted to directions perpendicular to the spacecraft–Sun line, which limits the observations to several months each year. This restriction is removed in the forthcoming mission called Interstellar Mapping and Acceleration Probe. The IMAP-Lo instrument will have the capability of adjusting the angle of its boresight with the spacecraft rotation axis. We continue a series of studies of the resulting science opportunities. We adopt the schedule of adjusting the boresight angle suggested by Kubiak et al. and focus on interstellar hydrogen and deuterium during solar maximum. Based on an extensive set of simulations, we identify the times during the calendar year and the elongation angles of the boresight needed to measure the abundance of D/H at the termination shock and to unambiguously observe interstellar H without a contribution from interstellar He. Furthermore, IMAP-Lo will be able to resolve the primary and secondary populations, in particular, to view the secondary population with little contribution from the primary. We show that the expected signal is sensitive to details of radiation pressure, particularly its dependence on the radial speed of the atoms, and to details of the behavior of the distribution function of the primary and secondary populations at the heliopause. Therefore, IMAP-Lo will be able to provide the observations needed to address compelling questions in heliospheric physics and even in general astrophysics.

Quantum non-Markovianity of a qubit in presence of state dependent bath

In the field of quantum information theory, the intersection of the complex dynamics related to non-Markovianity and information is a crucial frontier. Non-Markovian effects, which take memory and temporal correlations into account, challenge conventional wisdom in the fields of quantum biology, metrology, cryptography, and communication. In this work, we analyze the non-Markovian dynamics of a dephasing model in presence of initial system-bath (SB) correlations. These SB correlations are generated via projective measurements on a predefined equilibrium state. Using the non-Markovian measures based on trace distance and quantum Fisher information, it is shown that these correlations have significant impact in the non-Markovian regime at high temperatures while it does not play any role in the Markovian case. Furthermore, it is shown that the oscillatory behaviour of the decoherence function does not always show non-Markovian behaviour.

The Dynamic Spatial Structure of Flocks.

Studies of collective motion have heretofore been dominated by a thermodynamic perspective in which the emergent "flocked" phases are analyzed in terms of their time-averaged orientational and spatial properties. Studies that attempt to scrutinize the dynamical processes that spontaneously drive the formation of these flocks from initially random configurations are far more rare, perhaps owing to the fact that said processes occur far from the eventual long-time steady state of the system and thus lie outside the scope of traditional statistical mechanics. For systems whose dynamics are simulated numerically, the nonstationary distribution of system configurations can be sampled at different time points, and the time evolution of the average structural properties of the system can be quantified. In this paper, we employ this strategy to characterize the spatial dynamics of the standard Vicsek flocking model using two correlation functions common to condensed matter physics. We demonstrate, for modest system sizes with 800 to 2000 agents, that the self-assembly dynamics can be characterized by three distinct and disparate time scales that we associate with the corresponding physical processes of clustering (compaction), relaxing (expansion), and mixing (rearrangement). We further show that the behavior of these correlation functions can be used to reliably distinguish between phenomenologically similar models with different underlying interactions and, in some cases, even provide a direct measurement of key model parameters.

The importance of the local structure of fractal aggregates

The pair correlation function, g(r), is a fundamental descriptor of the inner structure of fractal aggregates of monomers. It provides a natural tool for studying physical properties involving two-point interaction (e.g. optics of aggregates). Several domains of distances between pairs of monomers have been identified. The fractal domain (in which g(r) is a power-law) is generally dominant for large aggregates. We show here that the local behavior of g(r)—involving monomers tangent to a given monomer—is necessary for most of the quantitative applications, even if that local domain is not directly related to fractal morphology. We derive a simple generic pair correlation function for fractal aggregates, depending on three structural parameters only: the fractal dimension, df ; the prefactor, kf ; the local mean coordination number, Zˉ . Unlike the fractal dimension, the prefactor and the mean coordination number are not universal since they depend on many parameters of the generation process. We discuss the impact of the definite shape of g(r) on the aggregate structure factor profile (a measurable quantity through small-angle x-ray scattering). Improvement from the new g(r) shape is also illustrated deriving an analytical expression of the geometric cross section, G, of aggregates for fractal dimension <2 . Accuracy is checked by comparing with numerical data from aggregates of fractal dimension df=1.9 . On the up-to-date analytical expression of G, the contributions of the short- and long-range behaviours of g(r) are well separated, and it is clear that the local behavior of the pair correlation function is required to obtain accurate values of the geometric cross section. Thus, in addition to the fractal structure of aggregates, the local structure of aggregates (to which the prefactor kf and the g(r) divergence at short distances are related) also appears important to accurately describe their physical features.

Ralph Kenna's Scaling Relations in Critical Phenomena.

In this note, we revisit the scaling relations among "hatted critical exponents", which were first derived by Ralph Kenna, Des Johnston, and Wolfhard Janke, and we propose an alternative derivation for some of them. For the scaling relation involving the behavior of the correlation function, we will propose an alternative form since we believe that the expression is erroneous in the work of Ralph and his collaborators.

The impact of Caputo-Fabrizio fractional derivative and the dynamics of noise on worm propagation in wireless IoT networks

The main objective of this article on Wireless sensor network of the Internet of Things (IoT). The wireless network, B bluetooth network, infrared network, and other networks are the key components of the Internet of Things (IoT). The major emphasis of this work was on the impact of Caputo-Fabrizio fractional derivative on worm propagation in heterogeneous susceptible-exposed-infected-recovered wireless IoT devices. We first determined the equilibrium points and fundamental reproduction number for the Caputo-Fabrizio HSEIR system, and then we discussed the stability of the system at the worm propagation equilibrium point. Using the Picard-Lindeof method, we determine the existence and unique solution for the fractional CF system of the heterogeneous SEIR model. Next, we use fixed point theory to judge the stability of the iterative method. We investigate the impact of the derivative order on the behaviour of the resultant functions and acquired numerical values by computing the model's findings for various fractional orders. In addition, we compute the integer-order model's results and contrast them with the results of the fractional-order model. We develop a periodically intermittent controller driven by white noise with the amazing benefits of reduced cost and more adaptable control technique to restrict the spread of worms in wireless IoT networks. To clearly define the conditions for stability in probability one, we employ the stochastic analysis technique. Our results show that the nonlinear worm propagation system may be stabilised by intermittent stochastic perturbation under the parameters of intermittent time linked to stochastic perturbation strength. Our theoretical conclusions may be used to analyse the observable processes of the worm, design countermeasures to prevent its spread, and evaluate the consequences of various system parameters.

Asymptotic analysis of the sojourn time of a batch in a M [X]/M/1 processor sharing queue

. In this article, we exploit recent results for the Laplace transform of the sojourn time Ω of an entire batch in the M [ X ] / M / 1 processor sharing queue in order to derive the asymptotic behavior of the distribution function of Ω, namely the behavior of ℙ(Ω > x) when x tends to infinity. Specifically, we show that, up to a multiplying factor, ℙ(Ω > x) has the same order of magnitude as ℙ(ω > x) for large x, where ω is the sojourn time of an arbitrary job in the system. From a practical point of view, this means that if a system has to be dimensioned to guarantee the processing time for jobs, then the system can also guarantee processing times for entire batches by introducing a marginal amount of processing capacity.

Finitely generated saturated multi-Rees algebras

We study the question of finite generation of saturated multi-Rees algebras and investigate the asymptotic behaviour of related length functions. In the setup of excellent local domains, we show that the saturated multi-Rees algebra of a finite collection of ideals is finitely generated when the analytic spread is not maximal and the associated length function eventually agrees with a polynomial. Similar results are obtained when we restrict to two-dimensional local UFDs with no restrictions on the analytic spread. We further prove that the saturated multi-Rees algebra of finitely many monomial ideals in a polynomial ring modulo an irreducible monomial ideal, is always finitely generated. In this case, the corresponding length function is shown to exhibit piecewise quasi-polynomial behaviour. We also produce multi-ideal versions of a theorem of Amao.

Coast effect in magnetotelluric soundings on the continental south of the Russian Far East

The manifestation of coast effect is studied based on the magnetotelluric (MT) soundings made on three profiles in the southern part of the Sikhote-Alin folded system (SAFS) surrounded by the Sea of Japan in the south and east. It is found that the coast effect is poorly expressed in the MT sounding amplitude curves while well pronounced in the behavior of the magnetovariation response functions. The analysis of the complex Wiese tipper and its real induction arrows in the north and east directions identified the intensity of the coast effect within the study area and the influence of the main deep faults and conductive zones in the Earth’s crust and upper mantle on the effect. Based on the three-dimensional (3D) numerical modeling, the main factors affecting the behavior of the amplitude MT sounding curves in the presence of coast effect are determined for the conditions of the southern part of SAFS and different geoelectric models.

Polyharmonic potential theory on the Poincaré disk

We consider the open unit disk D equipped with the hyperbolic metric and the associated hyperbolic Laplacian L. For λ∈C and n∈N, a λ-polyharmonic function of order n is a function f:D→C such that (L−λI)nf=0. If n=1, one gets λ-harmonic functions. Based on a Theorem of Helgason on the latter functions, we prove a boundary integral representation theorem for λ-polyharmonic functions. For this purpose, we first determine nth-order λ-Poisson kernels. Subsequently, we introduce the λ-polyspherical functions and determine their asymptotics at the boundary ∂D, i.e., the unit circle. In particular, this proves that, for eigenvalues not in the interior of the L2-spectrum, the zeroes of these functions do not accumulate at the boundary circle. Hence the polyspherical functions can be used to normalise the nth-order Poisson kernels. By this tool, we extend to this setting several classical results of potential theory: namely, we study the boundary behaviour of λ-polyharmonic functions, starting with Dirichlet and Riquier type problems and then proceeding to Fatou type admissible boundary limits.

The study of electronic structure and magnetic properties of ferromagnetic Kondo-lattice CePd2P2 from the first-principles

The electronic structure of ferromagnetic CePd2P2 Kondo lattice crystallizing in the tetragonal ThCr2Si2-type structure is investigated by means of the Density Functional Theory (DFT) and Time-Depedent DFT (TDDFT) methods. The calculated electronic properties from DFT are presented and compared to those of the non-magnetic LaPd2P2 compound. The differences in the FS topologies upon changing magnetic states (paramagnetic → ferromagnetic) is also examined. Including the relativistic effects of without or with spin-orbit coupling, and Hubbard corrections in the calculations, ferromagnetic ground state with an ordered magnetic moment of ∼ 0.8-0.9 μB is corroborated. Meaningful changes in the magnetic moment and electronic properties of CePd2P2 are discussed in terms of effects brought by the Coulomb interaction (U), and the Hund coupling (J). In particular, the reduction in magnetic moment and simultaneously enhancement of DOS at the Fermi energy due to decreasing J are in quantitative concordance with the Kondo lattice characteristic. Furthermore, dynamical model used in TDDFT calculations exhibits that 4 f electrons in CePd2P2 tend to be delocalized. The frequency-temperature behavior of response function allows to estimate the Kondo temperature to amount 19 K.

Sectorial Mertens and Mirsky formulae for imaginary quadratic number fields

We extend formulae of Mertens and Mirsky on the asymptotic behaviour of the usual Euler function to the Euler functions of principal rings of integers of imaginary quadratic number fields, giving versions in angular sectors and with congruences.

An Interesting Correlation Between the Peak Slope and Peak Value of a Sunspot Cycle

The maximum slope of the sunspot number during the rising phase of a sunspot cycle has an excellent correlation with the maximum value of the sunspot number during that cycle. This is demonstrated using a Savitzky–Golay filter to both smooth and calculate the derivative of the sunspot-number data. Version 2 of the International Sunspot Number (S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$S$\\end{document}) is used to represent solar activity. The maximum of the slope during the rising phase of each cycle was correlated against the peaks of solar activity. Using three different correlation fits, the average predicted amplitude for Solar Cycle 25 is 130.7 ± 0.5, among the best correlations in solar predictions. A possible explanation for this correlation is given by the similar behavior of a shape function representing the time variation of the sunspot number. This universal function also provides the timing of the solar maximum by the time from the slope maximum to the peak in the function as late 2023 or early 2024. A Hilbert transform gives similar results, which are caused by the dominance of the 11-yr sunspot-cycle period in a Fourier fit of the sunspot number.

Operator dynamics in Lindbladian SYK: a Krylov complexity perspective

We use Krylov complexity to study operator growth in the q-body dissipative Sachdev-Ye-Kitaev (SYK) model, where the dissipation is modeled by linear and random p-body Lindblad operators. In the large q limit, we analytically establish the linear growth of two sets of coefficients for any generic jump operators. We numerically verify this by implementing the bi-Lanczos algorithm, which transforms the Lindbladian into a pure tridiagonal form. We find that the Krylov complexity saturates inversely with the dissipation strength, while the dissipative timescale grows logarithmically. This is akin to the behavior of other \U0001d52e-complexity measures, namely out-of-time-order correlator (OTOC) and operator size, which we also demonstrate. We connect these observations to continuous quantum measurement processes. We further investigate the pole structure of a generic auto-correlation and the high-frequency behavior of the spectral function in the presence of dissipation, thereby revealing a general principle for operator growth in dissipative quantum chaotic systems.

Accurate Quantum States for a 2D-Dipole.

Edge dislocations are crucial in understanding both mechanical and electrical transport in solid and are modeled as line distributions of dipole moments. The calculation of the electronic spectrum for the two dimensional dipole, represented by the potential energy V(r,θ)=pcosθ/r, has been the topic of several studies that show significant difficulties in obtaining accurate results. In this work, we demonstrate that the source of these difficulties is a logarithmic contribution to the behavior of the wave function at the origin that was neglected by previous authors. By taking into account this non-analytic deviation of the solution of Schrödinger's equation, superior results, with the expected rate of convergence, are obtained. This goal is accomplished by "adapting" general algorithms for solving partial derivative differential equations to include the desired asymptotic behavior. We illustrate this principle for the variational principle and finite difference methods. Accurate energies and wave functions are obtained not only for the ground state but also for the first eleven excited states and are useful for designing nanoelectronic devices. This paper demonstrates that augmentary knowledge about analytic properties of the solutions leads to the improved convergence and stability of numerical methods.

Exploring wormhole solutions in curvature–matter coupling gravity supported by noncommutative geometry and conformal symmetry

This article explores new physically viable wormhole solutions within the framework of f(R,ℒm) gravity theory, incorporating noncommutative backgrounds and conformal symmetries. The study investigates the impact of model parameters on the existence and properties of wormholes. The derived shape function is found to obey all the required criteria. Specific attention is given to traceless wormholes with Gaussian and Lorentzian distributions, investigating the behavior of the shape functions and energy conditions. In both cases, the presence of exotic fluid is confirmed.

Almost Everywhere Behavior of Functions According to Partition Measures

Almost Everywhere Behavior of Functions According to Partition Measures

Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. I

The model of the impurity diffusion process in the layer where a system of random point mass sources acts, is proposed. Mass sources of various power are uniformly distributed in a certain internal interval of the body. Statistics of random sources are given. The solution of the initial-boundary value problem is constructed as a sum of the homogeneous problem solution and the convolution of the Green's function and the system of the random point mass sources. The solution is averaged over both certain internal subinterval and the entire body region. Simulation units are designed for modeling of the behavior of the averaged concentration function with acting system of point mass sources of various power. On this basis, the averaged concentration field is investigated depending on the internal interval length, power and number of sources in the system as well as the concentration values at the layer boundaries.

Directional dependence of the electronic and transport properties of biphenylene under strain conditions.

In this study, we investigated the electronic and electronic transport properties of biphenylene (BPN) using first-principles density functional theory (DFT) calculations combined with the non-equilibrium Green's function (NEGF) formalism. We have focused on understanding the electronic properties of BPN, and the anisotropic behavior of electronic transport upon external strain. We found the emergence of electronic stripes (ESs) on the BPN surface and the formation of type-II Dirac cone near the Fermi level. In the sequence, the electronic transport results reveal that such ESs dictate the anisotropic behavior of the transmission function. Finally, we show that the tuning of the (anisotropic) electronic current, mediated by external mechanical strain, is ruled by the energy position of the lowest unoccupied states with wave-vectors perpedicular to the ESs. This control could be advantageous for applications in nanoelectronic devices that require precise control of current direction.