Galerkin finite element approximation for semilinear stochastic time-tempered fractional wave equations with multiplicative white noise and fractional Gaussian noise

**power**-

**law**attenuation, it is needed to use the fractional

**powers**of symmetric coercive elliptic operators in space and the Caputo tempered fractional derivative in time. Expand abstract.

**power**-

**law**attenuation, it is needed to use the fractional

**powers**of symmetric coercive elliptic operators in space and the Caputo tempered fractional derivative in time. The model studied in this paper is semilinear stochastic space-time fractional wave equations driven by infinite dimensional multiplicative white noise and fractional Gaussian noise, because of the potential fluctuations of the external sources. The purpose of this work is to discuss the Galerkin finite element approximation for the semilinear stochastic fractional wave equation. We first provide a complete solution theory, e.g., existence, uniqueness, and regularity. Then the space-time multiplicative white noise and fractional Gaussian noise are discretized, which results in a regularized stochastic fractional wave equation while introducing a modeling error in the mean-square sense. We further present a complete regularity theory for the regularized equation. A standard finite element approximation is used for the spatial operator, and the mean-square priori estimates for the modeling error and for the approximation error to the solution of the regularized problem are established.

4/10 relevant

arXiv

Avalanches on the Complex Network of Rigan Earthquake, Virtual Seismometer Technique, Criticality and Seismic Cycle

**power**-

**law**degree distribution with the exponent $\gamma=2.3\pm 0.2$. Our findings show that the seismic activity is strongly intermittent, and have a \textit{cyclic shape} as is seen in the natural situations, which is main finding of this study. The branching ratio inside and between avalanches reveal that the system is at (or more precisely close to) the critical point with

**power**-

**law**behavior for the distribution function of the size and the mass and the duration of the avalanches, and with some scaling relations between these quantities. The critical exponent of the size of avalanches is $\tau_S=1.45\pm 0.02$. We find a considerable correlation between the dynamical Green function and the nodes centralities.

5/10 relevant

arXiv

On the Strong Attraction Limit for a Class of Nonlocal Interaction Energies

**power**

**law**potentials with attractive

**powers**$\alpha\in(0,\infty)$ and repulsive

**powers**associated with Riesz potentials. The strong attraction limit $\alpha\rightarrow\infty$ is addressed via Gamma-convergence, and minimizers of the limit are characterized in terms of an isodiametric capacity problem.

4/10 relevant

arXiv

Engel's **law** in the commodity composition of exports

**power**-

**law**with the exponents characterizing the GDP-elasticity of their export shares. Expand abstract.

**law**for the household expenditure and the shift from primary to manufacturing and service sector in the three sector model. Searching for large-scale quantitative evidence of such correlation, we analyze the gross-domestic product (GDP) and international trade data based on the standard international trade classification (SITC) in the period 1962 to 2000. Three categories, among ten in the SITC, are found to have their export shares significantly correlated with the GDP over countries and time; The machinery category has positive and food and crude materials have negative correlations. The export shares of commodity categories of a country are related to its GDP by a

**power**-

**law**with the exponents characterizing the GDP-elasticity of their export shares. The distance between two countries in terms of their export portfolios is measured to identify several clusters of countries sharing similar portfolios in 1962 and 2000. We show that the countries whose GDP is increased significantly in the period are likely to transit to the clusters displaying large share of the machinery category.

4/10 relevant

arXiv

Universal **power** **law** decay in the dynamic hysteresis of an optical cavity
with non-instantaneous photon-photon interactions

**powers**, and at room temperature. Expand abstract.

**power**

**law**with exponent -1. The exponent of this

**power**

**law**is independent of the system parameters. To reveal this universal scaling behavior theoretically, we introduce a memory kernel for the interaction term in the standard driven-dissipative Kerr model. Our results offer new perspectives for exploring non-Markovian dynamics of light using arrays of bistable cavities with low quality factors, driven by low laser powers, and at room temperature.

10/10 relevant

arXiv

Non-standard anomalous heat conduction in harmonic chains with correlated isotopic disorder

**power**spectrum $W$ (of the fluctuations of the random masses around their common mean value) scales as $W(\mu)\sim \mu^\beta$, the asymptotic thermal conductivity $\kappa$ scales with the system size $N$ as $\kappa \sim N^{(1+\beta)/(2+\beta)}$ for free boundary conditions, whereas for fixed boundary conditions $\kappa \sim N^{(\beta-1)/(2+\beta)}$; where $\beta>-1$, which is the usual

**power**

**law**scaling for one dimensional systems. Nevertheless, if $W$ does not scale as a

**power**

**law**in the low wavelength limit, the thermal conductivity may not scale in its usual form $\kappa\sim N^{\alpha}$, where the value of $\alpha$ depends on the particular one dimensional model. As an example of the latter statement, if $W(\mu)\sim \exp(-1/\mu)/\mu^2$, $\kappa \sim N/(\log N)^3$ for fixed boundary conditions and $\kappa \sim N/\log(N)$ for free boundary conditions, which represent non-standard scalings of the thermal conductivity.

5/10 relevant

arXiv

Generating large scale-free networks with the Chung-Lu random graph model

**power**-

**law**degree profile by means of the Chung-Lu model. In particular, we are concerned with the fulfillment of a fundamental hypothesis that must be placed on the model parameters, without which the generated graphs loose all the theoretical properties of the model, notably, the controllability of the expected node degrees and the absence of correlations between the degrees of two nodes joined by an edge. We provide explicit formulas for the model parameters in order to generate random graphs which fulfil a number of requirements on the behavior of the smallest, largest, and average expected degrees and have several desirable properties, including a

**power**-

**law**degree distribution with any prescribed exponent larger than $2$, the presence of a giant component and no potentially isolated nodes.

5/10 relevant

arXiv

Out-of-equilibrium phase diagram of long-range superconductors

**power**-

**law**hopping and pairing, and provide analytic and numerical evidence showing a direct connection between nonanalyticities of the return rate and zero crossings of the string order parameter. Expand abstract.

**power**-

**law**interactions exhibit rich well-understood critical behavior in equilibrium, but the out-of-equilibrium picture has remained incomplete, despite recent experimental progress. We construct the rich dynamical phase diagram of free-fermionic chains with

**power**-

**law**hopping and pairing, and provide analytic and numerical evidence showing a direct connection between nonanalyticities of the return rate and zero crossings of the string order parameter. Our results may explain the experimental observation of so-called \textit{accidental} dynamical vortices, which appear for quenches within the same topological phase of the Haldane model, as reported in [Fl\"aschner \textit{et al.}, Nature Physics \textbf{14}, 265 (2018)]. Our work is readily applicable to modern ultracold-atom experiments, not least because state-of-the-art quantum gas microscopes can now reliably measure the string order parameter, which, as we show, can serve as an indicator of dynamical criticality.

5/10 relevant

arXiv

Renormalization group approach to **power**-**law** modeling of complex
metabolic networks

**power**-

**laws**are the critical solutions of the renormalization group transformation, namely power-

**law**rate-laws are the renormalization group invariant solutions. Expand abstract.

**power**-

**law**models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully understood at present. In order to provide additional insight in this sense, this article is devoted to the renormalization group analysis of reactions in fractal or self-similar media. In particular, the renormalization group methodology is applied to the investigation of how rate-

**laws**describing such reactions are transformed when the geometric scale is changed. The precise purpose of such analysis is to investigate whether or not

**power**-

**law**rate-

**laws**present some remarkable features accounting for the successes of

**power**-

**law**modeling. As we shall see, according to the renormalization group point of view the answer is positive, as far as

**power**-

**laws**are the critical solutions of the renormalization group transformation, namely

**power**-

**law**rate-

**laws**are the renormalization group invariant solutions. Moreover, it is shown that these results also imply invariance under the group of concentration scalings, thus accounting for the reported

**power**-

**law**model accuracy over several orders of magnitude in metabolite concentrations.

10/10 relevant

arXiv

Power-**Law** Dynamics in Cortical Excitability as probed by Early Somatosensory Evoked Responses

**power**-

**laws**may originate from neuronal networks poised close to a critical state, representing a parsimonious organizing principle of... Expand abstract.

**power**-

**law**across trials. As these dynamics covaried with pre-stimulus alpha oscillations, we establish a functional link between ongoing and evoked activity and argue that the co-emergence of similar temporal

**power**-

**laws**may originate from neuronal networks poised close to a critical state, representing a parsimonious organizing principle of neural variability.

10/10 relevant

bioRxiv