Creep rupture due to thermally induced cracking

2013 ◽  
Vol 1535 ◽  
Author(s):  
Naoki Yoshioka ◽  
Ferenc Kun ◽  
Nobuyasu Ito
Keyword(s):  
Power Law ◽  
Crack Nucleation ◽  
Waiting Times ◽  
System Size ◽  
Thermal Fluctuations ◽  
Average Lifetime ◽  
Thermally Induced ◽  
Thermally Activated ◽  
Structural Entropy ◽  
Stochastic Time Series

ABSTRACTWe study sub-critical fracture driven by thermally activated crack nucleation in the framework of a fiber bundle model. Based on analytic calculations and computer simulations we show that in the presence of stress inhomogeneities, thermally activated cracking results in an anomalous size effect, i.e. the average lifetime of the system decreases as a power law of the system size, where the exponent depends on the external load and on the temperature. We propose a modified form of the Arrhenius law which provides a comprehensive description of the load, temperature, and size dependence of the lifetime of the system. On the micro-level, thermal fluctuations trigger bursts of breaking events which form a stochastic time series as the system evolves towards failure. Numerical and analytical calculations revealed that both the size of bursts and the waiting times between consecutive events have power law distributions, however, the exponents depend on the load and temperature. Analyzing the structural entropy and the location of consecutive bursts we show that in the presence of stress concentration the acceleration of the rupture process close to failure is the consequence of damage localization.

scholarly journals Clustered continuous-time random walks: diffusion and relaxation consequences

2012 ◽  
Vol 468 (2142) ◽  
pp. 1615-1628 ◽  
Author(s):  
Karina Weron ◽  
Aleksander Stanislavsky ◽  
Agnieszka Jurlewicz ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Walks ◽  
Power Law ◽  
Continuous Time ◽  
Waiting Times ◽  
Scaling Limit ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
The Novel ◽  
Fractional Diffusion Equations ◽  
Continuous Time Random Walks

We present a class of continuous-time random walks (CTRWs), in which random jumps are separated by random waiting times. The novel feature of these CTRWs is that the jumps are clustered. This introduces a coupled effect, with longer waiting times separating larger jump clusters. We show that the CTRW scaling limits are time-changed processes. Their densities solve two different fractional diffusion equations, depending on whether the waiting time is coupled to the preceding jump, or the following one. These fractional diffusion equations can be used to model all types of experimentally observed two power-law relaxation patterns. The parameters of the scaling limit process determine the power-law exponents and loss peak frequencies.

Thermally Induced Pain, the Dol Scale, and the Psychophysical Power Law

1968 ◽  
Vol 81 (2) ◽  
pp. 147 ◽  
Author(s):  
Eleanor R. Adair ◽  
Joseph C. Stevens ◽  
Lawrence E. Marks
Keyword(s):  
Power Law ◽  
Thermally Induced

scholarly journals Large Hall and Nernst responses from thermally induced spin chirality in a spin-trimer ferromagnet

2021 ◽  
Vol 118 (33) ◽  
pp. e2023588118
Author(s):  
Kamil K. Kolincio ◽  
Max Hirschberger ◽  
Jan Masell ◽  
Shang Gao ◽  
Akiko Kikkawa ◽  
...  
Keyword(s):  
Hall Effect ◽  
Thermal Fluctuations ◽  
Hall Conductivity ◽  
Strong Response ◽  
Thermally Induced ◽  
Conduction Electrons ◽  
Lattice State ◽  
Ferromagnetic Ordering ◽  
Ordering Transition ◽  
Fundamental Units

The long-range order of noncoplanar magnetic textures with scalar spin chirality (SSC) can couple to conduction electrons to produce an additional (termed geometrical or topological) Hall effect. One such example is the Hall effect in the skyrmion lattice state with quantized SSC. An alternative route to attain a finite SSC is via the spin canting caused by thermal fluctuations in the vicinity of the ferromagnetic ordering transition. Here, we report that for a highly conducting ferromagnet with a two-dimensional array of spin trimers, the thermally generated SSC can give rise to a gigantic geometrical Hall conductivity even larger than the intrinsic anomalous Hall conductivity of the ground state. We also demonstrate that the SSC induced by thermal fluctuations leads to a strong response in the Nernst effect. A comparison of the sign and magnitude of fluctuation–Nernst and Hall responses in fundamental units indicates the need for a momentum–space picture to model these thermally induced signals.

Thermally Induced Superlow Friction of DLC Films in Ambient Air

2018 ◽  
Vol 37 (8) ◽  
pp. 725-731 ◽  
Author(s):  
Qunfeng Zeng
Keyword(s):  
Photoelectron Spectroscopy ◽  
Ambient Air ◽  
Friction Model ◽  
Repulsive Force ◽  
Hydroxyl Group ◽  
Thermally Induced ◽  
X Ray ◽  
Thermally Activated ◽  
Charged Interface ◽  
Positively Charged

AbstractThermally induced superlow friction (0.008) of diamond-like carbon (DLC) films was achieved in ambient air in the present work. Raman and XPS (X-ray Photoelectron Spectroscopy) measurements and analyses show that superlow friction of the annealed DLC films is involved in the transformation of sp3 to sp2 hybridized carbon during annealing and the tribochemical reactions during sliding. The thermally activated graphitization and oxidation of the annealed DLC films in ambient air is beneficial to form the positively charged interface and achieve the stable superlow friction. A friction model was developed and applied to explain superlow friction, which is attributed to Van de Waals force between graphite layers and the repulsive force between hydroxyl group of graphite oxide and hydrogen terminated DLC films surface.

scholarly journals Micromagnetic Simulation of Thermal Effects in Magnetic Nanostructures

2002 ◽  
Vol 746 ◽  
Author(s):  
Rok Dittrich ◽  
Thomas Schrefl ◽  
Vassilios Tsiantos ◽  
Hermann Forster ◽  
Dieter Suess ◽  
...  
Keyword(s):  
Minimum Energy ◽  
Saddle Points ◽  
Time Integration ◽  
Magnetic Nanostructures ◽  
Integration Scheme ◽  
Thermally Induced ◽  
Thermally Activated ◽  
Time Integration Scheme ◽  
Stochastic Time ◽  
Finding Method

ABSTRACTA path finding method and a stochastic time integration scheme for the simulation of thermally activated magnetization processes are introduced. The minimum energy path and the saddle points for the thermally induced transitions between the ground states of NiFe magnetic nano-elements are calculated.

scholarly journals Space–Time Duality for Fractional Diffusion

2009 ◽  
Vol 46 (4) ◽  
pp. 1100-1115 ◽  
Author(s):  
Boris Baeumer ◽  
Mark M. Meerschaert ◽  
Erkan Nane
Keyword(s):  
Contaminant Transport ◽  
Power Law ◽  
Fractional Derivatives ◽  
Waiting Times ◽  
Stable Process ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equations ◽  
Lévy Motion ◽  
Current Controversy ◽  
A Current

Zolotarev (1961) proved a duality result that relates stable densities with different indices. In this paper we show how Zolotarev's duality leads to some interesting results on fractional diffusion. Fractional diffusion equations employ fractional derivatives in place of the usual integer-order derivatives. They govern scaling limits of random walk models, with power-law jumps leading to fractional derivatives in space, and power-law waiting times between the jumps leading to fractional derivatives in time. The limit process is a stable Lévy motion that models the jumps, subordinated to an inverse stable process that models the waiting times. Using duality, we relate the density of a spectrally negative stable process with index 1<α<2 to the density of the hitting time of a stable subordinator with index 1/α, and thereby unify some recent results in the literature. These results provide a concrete interpretation of Zolotarev's duality in terms of the fractional diffusion model. They also illuminate a current controversy in hydrology, regarding the appropriate use of space- and time-fractional derivatives to model contaminant transport in river flows.

scholarly journals Generalized Diffusion Equation Associated with a Power-Law Correlated Continuous Time Random Walk

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Long Shi
Keyword(s):  
Random Walk ◽  
Diffusion Equation ◽  
Power Law ◽  
Continuous Time ◽  
Continuum Limit ◽  
Waiting Times ◽  
Mean Square Displacement ◽  
Continuous Time Random Walk ◽  
Mean Square ◽  
The Mean

In this work, a generalization of continuous time random walk is considered, where the waiting times among the subsequent jumps are power-law correlated with kernel function M(t)=tρ(ρ>-1). In a continuum limit, the correlated continuous time random walk converges in distribution a subordinated process. The mean square displacement of the proposed process is computed, which is of the form 〈x2(t)〉∝tH=t1/(1+ρ+1/α). The anomy exponent H varies from α to α/(1+α) when -1<ρ<0 and from α/(1+α) to 0 when ρ>0. The generalized diffusion equation of the process is also derived, which has a unified form for the above two cases.

Macroscopic Magnetic Properties of High Temperature Superconductors: Effect of a Pinning Barrier Distribution

1988 ◽  
Vol 02 (05) ◽  
pp. 1293-1303 ◽  
Author(s):  
A. P. Malozemoff ◽  
T. K. Worthington ◽  
R. M. Yandrofski ◽  
Y. Yeshurun
Keyword(s):  
Magnetic Properties ◽  
Critical Current ◽  
Power Law ◽  
High Temperature Superconductors ◽  
Time Derivative ◽  
Magnetic Data ◽  
Power Law Distribution ◽  
Thermally Activated ◽  
Barrier Distribution ◽  
Activated Flux

The magnetic properties of YBaCuO crystals are strongly affected by thermally activated flux creep over pinning barriers. Here the effect of a power-law distribution of pinning barriers is explored. The critical current density is predicted to have a power-law dependence on the reduced temperature difference approaching the transition temperature T c and a logarithmic dependence on the timescale of the measurement. The dependence of the critical current on the measurement time provides a possible explanation of the disparity between the critical current measured in thin film transport experiments and J c obtained from magnetic data. Also, in contrast to some earlier theory, the normalized logarithmic time derivative of the remanent magnetization is shown to not diverge near T c , irrespective of the pinning barrier distribution.

scholarly journals MECHANISM FOR POWERLAWS WITHOUT SELF-ORGANIZATION

2002 ◽  
Vol 13 (02) ◽  
pp. 133-136 ◽  
Author(s):  
DIDIER SORNETTE
Keyword(s):  
Power Law ◽  
Waiting Times ◽  
Self Regulation ◽  
Waiting Lists ◽  
Self Organization ◽  
Recent Claim

A recent claim has been made that there must be a self-regulation in the waiting times to see hospital consultants on the ground that the relative changes in the size of waiting lists follow a power law.4 In agreement with simulations of Frecketon and Sutherland, we explain the general nonself-regulating mechanism underlying this result and derive the exponent value -2 exactly. In addition, we provide links with related phenomena encountered in many other fields.

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