Search results for "scaling law"

Health and Disease Imprinted in the Time Variability of the Human Microbiome

2017

The human microbiota correlates closely with the health status of its host. This article analyzes the microbial composition of several subjects under different conditions over time spans that ranged from days to months. Using the Langevin equation as the basis of our mathematical framework to evaluate microbial temporal stability, we proved that stable microbiotas can be distinguished from unstable microbiotas. This initial step will help us to determine how temporal microbiota stability is related to a subject’s health status and to develop a more comprehensive framework that will provide greater insight into this complex system.

Crack bifurcations in a strained lattice

1996

Dynamic crack propagation in a strained, granular, and brittle material is investigated by modeling the material as a lattice network of elastic beams. By tuning the strain and the ratio of axial to bending stiffness of the beams, a crack propagates either straight, or it branches, or it bifurcates. The crack tip velocity is calculated approximately for cracks that propagate straight. In a bifurcated crack the number of broken beams follows a scaling law. The shape of the branches is found to be the same as in recent experiments.

Observation of the Kibble-Zurek scaling law for defect formation in ion crystals

2013

Traversal of a symmetry-breaking phase transition at finite rates can lead to causally separated regions with incompatible symmetries and the formation of defects at their boundaries, which has a crucial role in quantum and statistical mechanics, cosmology and condensed matter physics. This mechanism is conjectured to follow universal scaling laws prescribed by the Kibble-Zurek mechanism. Here we determine the scaling law for defect formation in a crystal of 16 laser-cooled trapped ions, which are conducive to the precise control of structural phases and the detection of defects. The experiment reveals an exponential scaling of defect formation γ(β), where γ is the rate of traversal of the …

1986

An osmotic pressure equation proposed over 50 years ago is found to be consistent with the des Cloizeaux scaling relation for semi-dilute polymer solutions in good solvents. With a physically plausible modification, the equation can also give a satisfactory representation of dilute solutions and of the cross-over to the semi-dilute regime.

Glass transitions and scaling laws within an alternative mode-coupling theory

2015

Idealized glass transitions are discussed within an alternative mode-coupling theory (TMCT) proposed by Tokuyama [Physica A 395, 31 (2014)]. This is done in order to identify common ground with and differences from the conventional mode-coupling theory (MCT). It is proven that both theories imply the same scaling laws for the transition dynamics, which are characterized by two power-law decay functions and two diverging power-law time scales. However, the values for the corresponding anomalous exponents calculated within both theories differ from each other. It is proven that the TMCT, contrary to the MCT, does not describe transitions with continuously vanishing arrested parts of the corre…

Switching times in long-overlap Josephson junctions subject to thermal fluctuations and non-Gaussian noise sources

2014

We investigate the superconducting lifetime of long current-biased Josephson junctions, in the presence of Gaussian and non-Gaussian noise sources. In particular, we analyze the dynamics of a Josephson junction as a function of the noise signal intensity, for different values of the parameters of the system and external driving currents. We find that the mean lifetime of the superconductive state is characterized by nonmonotonic behavior as a function of noise intensity, driving frequency and junction length. We observe that these nonmonotonic behaviours are connected with the dynamics of the junction phase string during the switching towards the resistive state. An important role is played…

Effects of partial self-ordering of Si dots formed by chemical vapor deposition on the threshold voltage window distribution of Si nanocrystal memori…

2006

We study the role that the denuded zone around Si nanocrystals obtained by chemical vapor deposition plays on the fluctuations of the dot surface coverage. In fact, the capture mechanism of the silicon adatoms in the proximity of existing dots restricts the number of possible nucleation sites, the final dot size, and the dot position, thus driving the process toward partial self-order. We numerically evaluate the relative dispersion of surface coverage for several gate areas and compare the results to the fully random case. The coverage dispersion is related to the fluctuations from bit to bit of the threshold voltage window (Δ Vth) distribution of nanocrystal memories. The evaluations, com…

Mott transitions in the half-filled SU(2M) symmetric Hubbard model

2012

The Hubbard model with large orbital degeneracy has recently gained relevance in the context of ultracold earth alkali like atoms. We compute its static properties in the SU(2M) symmetric limit for up to M=8 bands at half filling within dynamical mean-field theory, using the numerically exact multigrid Hirsch-Fye quantum Monte Carlo approach. Based on this unbiased data, we establish scaling laws which predict the phase boundaries of the paramagnetic Mott metal-insulator transition at arbitrary orbital degeneracy M with high accuracy.

Effective temperature and scaling laws of polarized quantum vortex bundles

2011

Abstract An effective non-equilibrium temperature is defined for (locally) polarized and dense turbulent superfluid vortex bundles, related to the average energy of the excitations (Kelvin waves) of vortex lines. In the quadratic approximation of the excitation energy in terms of the wave amplitude A, a previously known scaling relation between amplitude and wavelength k of Kelvin waves in polarized bundles, namely A ∝ k − 1 / 2 , follows from the homogeneity of the effective temperature. This result is analogous to that of the well-known equipartition result in equilibrium systems.

Dynamic fragmentation of a two-dimensional brittle material with quenched disorder

1997

Fragmentation of a two-dimensional brittle material caused by a rapid impact has been analyzed. Computer simulations together with simple arguments are used to obtain a qualitative understanding of crack formation, which is then used to derive an exponential fragment size distribution valid in the large fragment size limit. In the limit of small fragments this distribution is solved numerically, and it is found to obey a scaling law with the exponent {minus}1.5. These results suggest that two different mechanisms are operative in the fragmentation process: branching of propagating cracks determines the small fragment size limit, and merging of the nucleated cracks determines the large size …