Terms Of Exponents Research Articles

Effects of geometric array and size of internal voids on tensile ductility of AZ31 magnesium alloy sheets

This study aims to investigate the contributions of the geometric array and size distribution of perforated cylindrical voids to the tensile strain of a metallic sheet through the numerical correction of the plastic constraint factor with regard to the geometric array of internal voids. In AZ31 alloy sheets fabricated via strip casting, internal voids were formed via mechanical drilling in the form of perforated cylindrical holes. The tensile strain decreased significantly (from 0.18 to 0.01) as the void area fraction increased to 40%, and its nominal value decreased with an increase in the void size, even when the geometric array (ratio of void size to ligament distance between voids, a/l) was maintained. A plastic constraint factor describing the geometric array and size distribution of perforated cylindrical voids was proposed through the modification of an original form for isolated spherical voids, and the theoretical prediction using a modified constitutive model agreed well with the experimental results. The tensile ductility of a metallic sheet with perforated cylindrical voids depends more sensitively than isolated spherical voids on the variation in the void area fraction, because the effective void area fraction is overestimated by the exclusion of the strain-hardening exponent term in the modified plastic constraint factor. Additionally, increases in the void size and void area fraction at a fixed a/l ratio lead to a reduction in the tensile strain, by the increase of the plastic zone and the intensification of stress concentration around a void.

At the end of the world: Local Dynamical Cobordism

The Cobordism Conjecture states that any Quantum Gravity configuration admits, at topological level, a boundary ending spacetime. We study the dynamical realization of cobordism, as spacetime dependent solutions of Einstein gravity coupled to scalars containing such end-of-the-world ‘branes’. The latter appear in effective theory as a singularity at finite spacetime distance at which scalars go off to infinite field space distance. We provide a local description near the end-of-the-world branes, in which the solutions simplify dramatically and are characterized in terms of a critical exponent, which controls the asymptotic profiles of fields and the universal scaling relations among the spacetime distance to the singularity, the field space distance, and the spacetime curvature. The analysis does not rely on supersymmetry. We study many explicit examples of such Local Dynamical Cobordisms in string theory, including 10d massive IIA, the 10d non-supersymmetric USp(32) theory, Bubbles of Nothing, 4d \U0001d4a9 = 1 cosmic string solutions, the Klebanov-Strassler throat, Dp-brane solutions, brane configurations related to the D1/D5 systems, and small black holes. Our framework encompasses diverse recent setups in which scalars diverge at the core of defects, by regarding them as suitable end-of-the-world branes. We explore the interplay of Local Dynamical Cobordisms with the Distance Conjecture and other swampland constraints.

Decision making for large-scale multi-armed bandit problems using bias control of chaotic temporal waveforms in semiconductor lasers

Decision making using photonic technologies has been intensively researched for solving the multi-armed bandit problem, which is fundamental to reinforcement learning. However, these technologies are yet to be extended to large-scale multi-armed bandit problems. In this study, we conduct a numerical investigation of decision making to solve large-scale multi-armed bandit problems by controlling the biases of chaotic temporal waveforms generated in semiconductor lasers with optical feedback. We generate chaotic temporal waveforms using the semiconductor lasers, and each waveform is assigned to a slot machine (or choice) in the multi-armed bandit problem. The biases in the amplitudes of the chaotic waveforms are adjusted based on rewards using the tug-of-war method. Subsequently, the slot machine that yields the maximum-amplitude chaotic temporal waveform with bias is selected. The scaling properties of the correct decision-making process are examined by increasing the number of slot machines to 1024, and the scaling exponent of the power-law distribution is 0.97. We demonstrate that the proposed method outperforms existing software algorithms in terms of the scaling exponent. This result paves the way for photonic decision making in large-scale multi-armed bandit problems using photonic accelerators.

(p(x),q(x))-Kirchhoff-Type Problems Involving Logarithmic Nonlinearity with Variable Exponent and Convection Term

In the present article, we study a class of Kirchhoff-type equations driven by the (p(x),q(x))-Laplacian. Due to the lack of a variational structure, ellipticity, and monotonicity, the well-known variational methods are not applicable. With the help of the Galerkin method and Brezis theorem, we obtain the existence of finite-dimensional approximate solutions and weak solutions. One of the main difficulties and innovations of the present article is that we consider competing (p(x),q(x))-Laplacian, convective terms, and logarithmic nonlinearity with variable exponents, another one is the weaker assumptions on nonlocal term Mυ(x) and nonlinear term g.

On More General Distributions of Random Binning for Slepian–Wolf Encoding

Traditionally, ensembles of Slepian-Wolf (SW) codes are defined such that every bin of each $n$-vector of each source is randomly drawn under the uniform distribution across the sets $\{0,1,\ldots,2^{nR_X}-1\}$ and $\{0,1,\ldots,2^{nR_Y}-1\}$, where $R_X$ and $R_Y$ are the coding rates of the two sources, $X$ and $Y$, respectively. In a few more recent works, where only one source, say, $X$, is compressed and the other one, $Y$, serves as side information available at the decoder, the scope is extended to variable-rate S-W (VRSW) codes, where the rate is allowed to depend on the type class of the source string, but still, the random-binning distribution is assumed uniform within the corresponding, type-dependent, bin index set. In this expository work, we investigate the role of the uniformity of the random binning distribution from the perspective of the trade-off between the reliability (defined in terms of the error exponent) and the compression performance (measured from the viewpoint of the source coding exponent). To this end, we study a much wider class of random-binning distributions, which includes the ensemble of VRSW codes as a special case, but it also goes considerably beyond. We first show that, with the exception of some pathological cases, the smaller ensemble, of VRSW codes, is as good as the larger ensemble in terms the trade-off between the error exponent and the source coding exponent. Notwithstanding this finding, the wider class of ensembles proposed is motivated in two ways. The first is that it outperforms VRSW codes in the above-mentioned pathological cases, and the second is that it allows robustness: in the event of a system failure that causes unavailability of the compressed bit-stream from one of the sources, it still allows reconstruction of the other source within some controllable distortion.

Scaling relations reveal global and regional differences in morphometry of reservoirs and natural lakes

Water bodies provide essential ecosystem services linked to morphometric features that might differ between natural lakes and reservoirs. We use the HydroLAKES global dataset to quantitatively compare large (area > 1 km2) reservoirs and natural lakes in terms of scaling exponents between morphometric measures (volume, area, shore length). These exponents are further compared to those expected from geometrical assumptions and constraints. Lakes cover a larger range of volumes for the same range of surface areas than reservoirs, and have a larger volume-area scaling exponent. The volume-area scaling exponent for reservoirs (but not natural lakes) and the area-shore length exponent for all water bodies follow the predictions for self-affine surfaces. Land cover and terrain influence the scaling relations more for lakes than for reservoirs. These morphometric differences may be used to model the impact of reservoirs and lakes on hydrological processes and associated ecosystem services at regional to global scales.

Spectral crossovers and universality in quantum spin chains coupled to random fields

We study the spectral properties of and spectral crossovers between different random matrix ensembles [Poissonian, Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE)] in correlated spin-chain systems, in the presence of random magnetic fields, and the scalar spin-chirality term, competing with the usual isotropic and time-reversal invariant Heisenberg term. We have investigated these crossovers in the context of the level-spacing distribution and the level-spacing ratio distribution. We use random matrix theory (RMT) analytical results to fit the observed Poissonian-to-GOE and GOE-to-GUE crossovers, and examine the relationship between the RMT crossover parameter $\ensuremath{\lambda}$ and scaled physical parameters of the spin-chain systems in terms of a scaling exponent. We find that the crossover behavior exhibits universality, in the sense that, it becomes independent of lattice size in the large Hamiltonian matrix dimension limit. Moreover, the scaling exponent obtained from such a finite size scaling analysis, seems to be quite robust and independent of the type of crossover considered or the specific spectral correlation measure used.

Some existence results for a fractional problem involving Hardy potential and variable exponent singular term

Some existence results for a fractional problem involving Hardy potential and variable exponent singular term

Bottom of the $$L^2$$ spectrum of the Laplacian on locally symmetric spaces

We estimate the bottom of the \(L^2\) spectrum of the Laplacian on locally symmetric spaces in terms of the critical exponents of appropriate Poincaré series. Our main result is the higher rank analog of a characterization due to Elstrodt, Patterson, Sullivan and Corlette in rank one. It improves upon previous results obtained by Leuzinger and Weber in higher rank.

Robust uniform persistence for structured models of delay differential equations

<p style='text-indent:20px;'>We consider a general class of delay differential equations systems, typically used to model the dynamics of structured biological populations, and establish necessary conditions for the part of the attractor contained in the boundary of the state space to repel the complementary dynamics contained in the interior of the state space. The conditions are formulated in terms of Lyapunov exponents and invariant probability measures and we use them to prove a robust uniform persistence result.</p>

POSITIVE SOLUTIONS FOR A NONLOCAL PROBLEM WITH CRITICAL SOBOLEV EXPONENT IN HIGHER DIMENSIONS

This paper is devoted to a nonlocal problem involving critical Sobolev exponent and negative nonlocal term. By virtue of a cut-off technique and the concentration compactness principle, we prove the existence and asymptotic behavior of positive solutions for the considered problem. In particular, our results generalize the existence results of positive solutions to higher dimensions <i>N</i> ≥ 5.

Thermophoresis and Brownian Effect for Chemically Reacting Magneto-Hydrodynamic Nanofluid Flow across an Exponentially Stretching Sheet

This comparative research investigates the influence of a flexible magnetic flux and a chemical change on the freely fluid motion of a (MHD) magneto hydrodynamic boundary layer incompressible nanofluid across an exponentially expanding sheet. Water and ethanol are used for this analysis. The temperature transmission improvement of fluids is described using the Buongiorno model, which includes Brownian movement and thermophoretic distribution. The nonlinear partial differential equalities governing the boundary layer were changed to a set of standard nonlinear differential equalities utilizing certain appropriate similarity transformations. The bvp4c algorithm is then used to tackle the transformed equations numerically. Fluid motion is slowed by the magnetic field, but it is sped up by thermal and mass buoyancy forces and thermophoretic distribution increases non-dimensional fluid temperature resulting in higher temperature and thicker boundary layers. Temperature and concentration, on the other hand, have the same trend in terms of the concentration exponent, Brownian motion constraint, and chemical reaction constraint. Furthermore, The occurrence of a magnetic field, which is aided by thermal and mass buoyancies, assists in the enhancement of heat transmission and wall shear stress, whereas a smaller concentration boundary layer is produced by a first-order chemical reaction and a lower Schmidt number.

New 4D chaotic system with hidden attractors and self-excited attractors and its application in image encryption based on RNG

A new 4D chaotic system with self-excited attractors or hidden attractors is designed and the generation of self-excited attractors and hidden attractors depends on the parameters of the new 4D chaotic system. The detailed dynamical properties of the designed new 4D chaotic system have been vividly demonstrated in terms of phase portraits, bifurcation diagrams, and Lyapunov exponents. When fixing the system parameters and changing the initial value, different kinds of coexisting asymmetric attractors are discovered in the new 4D chaotic system. Besides, the corresponding analog electronic circuit of the 4D chaotic system is designed and implemented to verify its feasibility, concurrently the random number generator and an image encryption algorithm based on the designed new 4D chaotic system are provided. Then the effectiveness of the image encryption system is verified by some basic security analysis.

A fractal scaling analysis of the SARS-CoV-2 genome sequence

An approach based on fractal scaling analysis to characterize the organization of the SARS-CoV-2 genome sequence was used. The method is based on the detrended fluctuation analysis (DFA) implemented on a sliding window scheme to detect variations of long-range correlations over the genome sequence regions. The nucleotides sequence is mapped in a numerical sequence by using four different assignation rules: amino-keto, purine-pyrimidine, hydrogen-bond and hydrophobicity patterns. The originally reported sequence from Wuhan isolates (Wuhan Hu-1) was considered as a reference to contrast the structure of the 2002–2004 SARS-CoV-1 strain. Long-range correlations, quantified in terms of a scaling exponent, depended on both the mapping rule and the sequence region. Deviations from randomness were attributed to serial correlations or anti-correlations, which can be ascribed to ordered regions of the genome sequence. It was found that the Wuhan Hu-1 sequence was more random than the SARS-CoV-1 sequence, which suggests that the SARS-CoV-2 possesses a more efficient genomic structure for replication and infection. In general, the virus isolated in the early 2020 months showed slight correlation differences with the Wuhan Hu-1 sequence. However, early isolates from India and Italy presented visible differences that led to a more ordered sequence organization. It is apparent that the increased sequence order, particularly in the spike region, endowed some early variants with a more efficient mechanism to spreading, replicating and infecting. Overall, the results showed that the DFA provides a suitable framework to assess long-term correlations hidden in the internal organization of the SARS-CoV-2 genome sequence.

Relative Gol’dberg Order and Type of Multiple Entire Dirichlet Series in Terms of Coefficients and Exponents

This paper aims to define and characterize the relative Gol'dberg order and type of a multiple entire Dirichlet series with respect to another multiple entire Dirichlet series in terms of their coefficients and exponents. By using the definition, we study the growth properties of the Hadamard product between two such series.

Designing 1D Chaotic Maps for Fast Chaotic Image Encryption

Chaotic maps that can provide highly secure key sequences and ease of structure implementation are predominant requirements in image encryption systems. One Dimensional (1D) chaotic maps have the advantage of a simple structure and can be easily implemented by software and hardware. However, key sequences produced by 1D chaotic maps are not adequately secure. Therefore, to improve the 1D chaotic maps sequence security, we propose two chaotic maps: 1D Improved Logistic Map (1D-ILM) and 1D Improved Quadratic Map (1D-IQM). The proposed maps have shown higher efficiency than existing maps in terms of Lyapunov exponent, complexity, wider chaotic range, and higher sensitivity. Additionally, we present an efficient and fast encryption method based on 1D-ILM and 1D-IQM to enhance image encryption system performance. This paper also introduces a key expansion method to reduce the number of chaotic map iteration needs, thereby decreasing encryption time. The security analyses and experimental results are confirmed that 2D Correlation Coefficient (CC) Information Entropy (IE), Number of Pixels Change Rate (NPCR), Unified Average Changing Intensity (UACI), Mean Absolute Error (MAE), and decryption quality are able to meet the encryption security demands (CC = −0.00139, IE = 7.9990, NPCR = 99.6114%, UACI = 33.46952% and MAE = 85.3473). Furthermore, the proposed keyspace reaches 10240, and the encryption time is 0.025s for an image with a size of 256 × 256. The proposed system can yield efficacious security results compared to obtained results from other encryption systems.

Analysis of the Dynamic Stiffness, Hysteresis Resonances and Complex Responses for Nonlinear Spring Systems in Power-Form Order

Power-form nonlinear contact force models are widely adopted in relatively moving parts of macro (e.g., rolling bearings considering Hertzian contact restoring force between rolling elements and bearing raceways) or micro (e.g., the micro cantilever probe system of atomic force microscopy) scale mechanical systems, and contact resonance could cause serious problems of wear, contact fatigue, vibration, and noise, which has attracted widespread attention. In the present paper, the softening/hardening stiffness characteristics of continuous and one-sided contact power-form nonlinear spring models are addressed, respectively, by the analysis of the monotone features of resonant frequency-response skeleton lines. Herein, the period-n solution branch and its stability characteristics are obtained by the harmonic balance and alternating frequency/time domain (HB–AFT) method and Floquet theory. Compared with previous studies, this paper will furtherly clarify the influences of externally normal load, the power form exponent term, and excitation amplitude on the softening/hardening stiffness characteristics of general power-form spring systems. In addition, for a power-form system with a one-sided contact, the phenomena of primary and super/sub-harmonic hysteretic resonances inducing period-doubling, folding bifurcation, the coexistence of multiple solutions are demonstrated. Besides, it gives the evolution mechanism of two types of intermittency chaos in a one-sided contact system. The overall results may have certain basic theoretical significance and engineering values for the control of vibration and noise in contact mechanical systems.

Continuity of delta invariants and twisted Kähler–Einstein metrics

We show that delta invariant is a continuous function on the big cone. We will also introduce an analytic delta invariant in terms of the optimal exponent in the Moser–Trudinger inequality and prove that it varies continuously in the Kähler cone, from which we will deduce the continuity of the greatest Ricci lower bound. Then building on the work Berman–Boucksom–Jonsson, we obtain a uniform Yau–Tian–Donaldson theorem for twisted Kähler–Einstein metrics in transcendental cohomology classes.

A branching process model for dormancy and seed banks in randomly fluctuating environments

The goal of this article is to contribute towards the conceptual and quantitative understanding of the evolutionary benefits for (microbial) populations to maintain a seed bank consisting of dormant individuals when facing fluctuating environmental conditions. To this end, we discuss a class of ‘2-type’ branching processes describing populations of individuals that may switch between ‘active’ and ‘dormant’ states in a random environment oscillating between a ‘healthy’ and a ‘harsh’ state. We incorporate different switching strategies and suggest a method of ‘fair comparison’ to incorporate potentially varying reproductive costs. We then use this concept to compare the fitness of the different strategies in terms of maximal Lyapunov exponents. This gives rise to a ‘fitness map’ depicting the environmental regimes where certain switching strategies are uniquely supercritical.

Energy uniform decay rates for the semilinear wave equation with nonlinear localized damping and source terms of critical variable exponent

Energy uniform decay rates for the semilinear wave equation with nonlinear localized damping and source terms of critical variable exponent