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We simulate a relaxation process of non-brownian particles in a sheared viscous medium; the small shear strain is initially applied to a system, which then undergoes relaxation. The relaxation time and the correlation length are estimated…

Soft Condensed Matter · Physics 2009-05-05 Takahiro Hatano

We show that the twisted second moments of the Riemann zeta function averaged over the arithmetic progression $1/2 + i(an + b)$ with $a > 0$, $b$ real, exhibits a remarkable correspondance with the analogous continuous average and derive…

Number Theory · Mathematics 2012-08-14 Xiannan Li , Maksym Radziwill

We explore, employing the renormalization-group theory, the critical scaling behavior of the permutation symmetric three-vector model that obeys non-conserving dynamics and has a relevant anisotropic perturbation which drives the system…

Statistical Mechanics · Physics 2021-01-04 Rajiv G. Pereira

We prove a central limit theorem for $\log|\zeta(1/2+it)|$ with respect to the measure $|\zeta^{(m)}(1/2+it)|^{2k}dt$ ($k,m\in\mathbb N$), assuming RH and the asymptotic formula for twisted and shifted integral moments of zeta. Under the…

Number Theory · Mathematics 2021-01-21 Alessandro Fazzari

Strain correlation functions in two-dimensional isotropic elastic bodies are shown both theoretically (using the general structure of isotropic tensor fields) and numerically (using a glass-forming model system) to depend on the coordinates…

Statistical Mechanics · Physics 2023-08-17 J. P. Wittmer , A. N. Semenov , J. Baschnagel

We compute roughness exponents of elastic d-dimensional manifolds in (d+1)-dimensional embedding spaces at the depinning transition for d=1,...,4. Our numerical method is rigorously based on a Hamiltonian formulation; it allows to determine…

Disordered Systems and Neural Networks · Physics 2009-11-07 Alberto Rosso , Alexander K. Hartmann , Werner Krauth

Critical exponents are calculated exactly at the onset of an instability, using asymptotic expansiontechniques. When the unstable mode is subject to multiplicative noise whose spectrum at zero frequency vanishes, we show that the critical…

Fluid Dynamics · Physics 2015-06-03 F. Pétrélis , A. Alexakis

The motion of an elastic body over a rough surface is simulated in one dimension using Newtonian dynamics. We drive the body by prescribing a constant velocity. We extract the friction force from the work done by the applied force in order…

Condensed Matter · Physics 2008-02-03 Nathan A. Lindop , Henrik Jeldoft Jensen

We consider a specific random graph which serves as a disordered medium for a particle performing biased random walk. Take a two-sided infinite horizontal ladder and pick a random spanning tree with a certain edge weight $c$ for the…

Probability · Mathematics 2023-04-19 Nina Gantert , Achim Klenke

It will be discussed the statistics of the extreme values in time series characterized by finite-term correlations with non-exponential decay. Precisely, it will be considered the results of numerical analyses concerning the return…

Statistical Mechanics · Physics 2009-11-13 Cecilia Pennetta

We demonstrate that if the exponent $\gamma$ that measures non-smoothness of the velocity field is small then the isotropic zero modes of the scalar's triple correlation function have the scaling exponents proportional to $\sqrt{\gamma}$.…

chao-dyn · Physics 2009-10-28 E. Balkovsky , G. Falkovich , V. Lebedev

We analyze the betweenness centrality (BC) of nodes in large complex networks. In general, the BC is increasing with connectivity as a power law with an exponent $\eta$. We find that for trees or networks with a small loop density $\eta=2$…

Disordered Systems and Neural Networks · Physics 2009-11-10 Marc Barthelemy

We consider numerically the roughness of a planar crack front within the long-range elastic string model, with a tunable disorder correlation length $\xi$. The problem is shown to have two important length scales, $\xi$ and the Larkin…

Statistical Mechanics · Physics 2015-05-20 Lasse Laurson , Stefano Zapperi

The extinction transition in the presence of a localized quenched defect is studied numerically. When the bulk is at criticality, the correlation length diverges and even an infinite system cannot "decouple" from the defect. The results…

Statistical Mechanics · Physics 2010-11-16 Zvi Miller , Nadav M. Shnerb

We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity $\eta$, which implies that it diverges algebraically with a critical exponent $k\ge…

Statistical Mechanics · Physics 2013-02-26 Claas H. Köhler , Henning Löwe , Peter Müller , Annette Zippelius

The dynamics of a crack propagating in an elastic inhomogeneous material is investigated. The variations of the average crack velocity with the external loading are measured for a brittle rock and are shown to display two distinct regimes:…

Statistical Mechanics · Physics 2008-12-18 Laurent Ponson

We study elastic systems such as interfaces or lattices, pinned by quenched disorder. To escape triviality as a result of ``dimensional reduction'', we use the functional renormalization group. Difficulties arise in the calculation of the…

Condensed Matter · Physics 2009-07-10 Pierre Le Doussal , Kay Joerg Wiese , Pascal Chauve

We demonstrate the capability of Principal Component Analysis (PCA) as applied by Heyer & Schloerb (1997) to extract the statistics of turbulent interstellar velocity fields as measured by the energy spectrum, E(k)= k^-beta. Turbulent…

Astrophysics · Physics 2007-05-23 C. Brunt , M. H. Heyer

Critical properties in the dynamical charge correlation function for the one-dimensional Mott insulator are studied. By properly taking into account {\it the final-state interaction} between the charge and spin degrees of freedom, we find…

Condensed Matter · Physics 2009-10-31 T. Fujii , N. Kawakami

In this paper we first obtain the order of stress singularity for a dynamically propagating self-affine fractal crack. We then show that there is always an upper bound to roughness, i.e. a propagating fractal crack reaches a terminal…

Materials Science · Physics 2010-04-28 Arash Yavari , Hamed Khezrzadeh