Quasi-brittle fracture as failure of hierarchical structure

The paper proposes a quasi-brittle fracture model based on the kinetic approach and empirical regularities such as the concentration criterion and Zhurkov’s formula for a material in the form of a nested self-similar hierarchical structure. The concentration criterion is reformulated as a failure probability condition for structural levels. The hierarchy scheme takes into account critical values of the concentration parameter. The failure probabilities of hierarchy levels are calculated as functions of time, temperature, material parameters, and loading condition. Knowing the failure probabilities of hierarchy levels allows one to evaluate the stress dynamics in a material, average failure volume, elastic energy and inelastic strain release, etc. Experimental and calculated dependences are compared.     

Collective properties of defects,multiscale plasticity,and shock induced phenomena in solids

A statistically based approach is developed for the construction of constitutive equations that provides linkages between defect-induced mechanisms of structural relaxation, thermally activated plastic flow, and material response to extreme loading conditions. The collective properties of defects have been studied to establish the interaction of multiscale defect dynamics and plastic flow, and to explain the mechanisms leading to the universal self-similar structure of shock wave fronts. Pn explanation for structural universality of the steady-state plastic shock front (the four power law) and the self-similarity of shock wave profiles under reloading (unloading) is proposed. Structural characterization under transition from thermally activated dislocation glide to nonlinear dislocation drag effects is developed in terms of scaling invariants (effective temperatures) related to mesodefect induced morphology formed during the different stages of plastic deformation.     

Multiscale structural relaxation and adiabatic shear failure mechanisms

Stages of plastic shear instability and adiabatic shear failure are associated with the initiation of collective modes of defect ensembles that have a self-similar nature of autosoliton and "blow-up" structures. Experimental and structural studies have confirmed simulation results for the stages of plastic strain localization and adiabatic shear failure based on the constitutive equations that relate structural relaxation and failure mechanisms to the formation of multiscale collective modes in defect ensembles.     

Nanoporous gold: 3D structural analyses of representative volumes and their implications on scaling relations of mechanical behaviour

We present a quantitative study of the salient structural parameters identified from so-called ‘representative volumes’ of the bicontinuous nanoporous gold (NPG) network, and examine the validity of self-similarity in describing its evolution. The approach is based on 3D-focused ion beam tomography applied to as-dealloyed and isothermally annealed NPG samples. After identifying sufficiently large representative volumes, we show that the ligament width distributions coarsen in a sufficiently self-similar, time-invariant manner, while the scaled connectivity density shows a self-similar ligament network topology. Using these critical parameters, namely mean ligament diameter and connectivity density, the Gibson–Ashby scaling laws for the mechanical response of cellular materials are revisited. The inappropriateness of directly applying the Gibson–Ashby model to NPG is demonstrated by comparing finite element method compression simulations of both the NPG reconstruction and that of the Gibson–Ashby solid model; rather than the solid volume fraction, we show that an effective load-bearing ring structure governs mechanical behaviour.     

Substantiation of the Possibility of Predicting Behavior of Solids under Extreme Conditions at Various High-Intensity Impacts

The paper is devoted to the data analysis on the amplitude-time regularities of the dynamic failure process of solids under various types of high-intensity impact in the ranges of nonequilibrium states from 3 × 10^?10 to 10^?5 s and establishing general regularities of behavior of unstudied materials under extreme conditions. We have analyzed the process of dynamic destruction of solids of different nature using the method of magnetic-pulse loading in the microsecond range of nonequilibrium states, as well as the dynamic failure process for a number of metals in the mode of pulsed volume heating under the action of pulsed relativistic electron beams in the nanosecond and subnanosecond range of nonequilibrium states. It has been shown that, upon using different methods of pulsed loading in the dynamic longevity range, the failure time as a function of amplitude of applied load has an exponential form for various solid materials. This indicates the scaling nature of the destruction process. The foregoing determines the possibility of predicting the behavior of unstudied solid bodies in the dynamic range of nonequilibrium states.     

Resistance Scaling and the Number of Spanning Trees in Self-Similar Lattices

We consider the problem of enumerating spanning trees in self-similar lattices, motivated by recent work of Chang, Chen and Yang, who determined explicit formulae in the case of Sierpiński graphs and some of their generalizations. The aim of this note is to show that their results hold in more generality and that there is a strong relation between this enumeration problem and resistance scaling on self-similar lattices.     

Polarized Fluorescence in Tryptophan Excited by Two-Photon Femtosecond Laser Pulses

The shape of an optical self-similar pulse that propagates in a medium of finite length with noninstantaneous nonlinear absorption is found analytically. The pulse has an asymmetric shape and, in addition, frequency modulation, which confirms that it belongs to a new type of self-similar propagation modes of laser radiation—chirped pulses with a self-similar shape. The existence of pulses of this kind is also confirmed by results of computer simulation.     

On the random cascading model study of anomalous scaling in multiparticle production with continuously diminishing scale

The anomalous scaling of factorial moments with continuously diminishing scale is studied using a random cascading model. It is shown that the model currently used have the property of anomalous scaling only for descrete values of elementary cell size. A revised model is proposed which can give good scaling property also for continuously varying scale. It turns out that the strip integral has good scaling property provided the integral regions are chosen correctly, and that this property is insensitive to the concrete way of self-similar subdivision of phase space in the models.     

Self-similar radiation from numerical Rosenau–Hyman compactons

The numerical simulation of compactons, solitary waves with compact support, is characterized by the presence of spurious phenomena, as numerically induced radiation, which is illustrated here using four numerical methods applied to the Rosenau–Hyman K(p, p) equation. Both forward and backward radiations are emitted from the compacton presenting a self-similar shape which has been illustrated graphically by the proper scaling. A grid refinement study shows that the amplitude of the radiations decreases as the grid size does, confirming its numerical origin. The front velocity and the amplitude of both radiations have been studied as a function of both the compacton and the numerical parameters. The amplitude of the radiations decreases exponentially in time, being characterized by a nearly constant scaling exponent. An ansatz for both the backward and forward radiations corresponding to a self-similar function characterized by the scaling exponent is suggested by the present numerical results.     

Self-similar scaling of density in complex real-world networks

Despite their diverse origin, networks of large real-world systems reveal a number of common properties including small-world phenomena, scale-free degree distributions and modularity. Recently, network self-similarity as a natural outcome of the evolution of real-world systems has also attracted much attention within the physics literature. Here we investigate the scaling of density in complex networks under two classical box-covering renormalizations–network coarse-graining–and also different community-based renormalizations. The analysis on over 50 real-world networks reveals a power-law scaling of network density and size under adequate renormalization technique, yet irrespective of network type and origin. The results thus advance a recent discovery of a universal scaling of density among different real-world networks [P.J. Laurienti, K.E. Joyce, Q.K. Telesford, J.H. Burdette, S. Hayasaka, Universal fractal scaling of self-organized networks, Physica A 390 (20) (2011) 3608–3613] and imply an existence of a scale-free density also within–among different self-similar scales of–complex real-world networks. The latter further improves the comprehension of self-similar structure in large real-world networks with several possible applications.     

Self-Similar Cosmological model: Introduction and empirical tests

After calling attention to the empirical and theoretical motivations for considering the hypothesis of a self-similar cosmos, the basic concepts and scaling rules of the Self-Similar Cosmological Model are presented. The results of a diverse set of 20 falsification tests are then shown to provide strong quantitative support for the uniqueness and broad applicability of the self-similar scale transformation equations, which successfully correlate physical parameters of atomic, stellar, and galactic scale systems. Possible implications of these results are discussed.     

Duffing方程的分叉结构及其标度特性

对称三次幂的Duffing方程经标度变换可化为三参数方程。在小周期强迫力的条件下,负线性项的Duffing方程具有封闭的分叉结构,且分叉区域随着线性系数的增大而缩小。在大周期强迫力的条件下,方程具有一系列自相似分叉结构,并呈现标度特性,利用一维映射对此标度特性进行了讨论、理论结果与计算机结果符合很好。 关键词：     

Delocalization transition of a rough adsorption-reaction interface

We introduce a kinetic interface model suitable for simulating adsorption-reaction processes which take place preferentially at surface defects such as steps and vacancies. As the average interface velocity is taken to zero, the self-affine interface with Kardar-Parisi-Zhang-like scaling behavior undergoes a delocalization transition with critical exponents that fall into a different universality class. As the critical point is approached, the interface becomes a multivalued, multiply connected self-similar fractal set. The scaling behavior and critical exponents of the relevant correlation functions are determined from Monte Carlo simulations and scaling arguments.     

Unifying scaling theory for vortex dynamics in two-dimensional turbulence

We present a scaling theory for unforced inviscid two-dimensional turbulence. Our model unifies existing spatial and temporal scaling theories. The theory is based on a self-similar distribution of vortices of different sizes A. Our model uniquely determines the spatial and temporal scaling of the associated vortex number density which allows the determination of the energy spectra and the vortex distributions. We find that the vortex number density scales as n(A,t)-t(-2/3)/A, which implies an energy spectrum E-k(-5), significantly steeper than the classical Batchelor-Kraichnan scaling. High-resolution numerical simulations corroborate the model.     

Multifractal properties of self-similar stress distributions

We consider highly heterogeneous materials with multiscale microstructures, such as, for instance, the Earth's crust, and focus on the case when the microstructure could be considered self-similar, at least in a range of scales. The paper develops a conceptual framework to treat such materials within the paradigm of continuum mechanics. We represent the material, within its range of self-similarity, by a self-similar sequence of what we call H-continua. Each H-continuum replaces the original materials with all structural elements of sizes smaller than H, such that the average (over the volume elements of size H) response of the continuum is similar to the original material. In each continuum, stress, strain and displacement fields are defined as usual. We then continue this sequence in a self-similar manner to the limits H?→ 0 and H?→ ∞, such that a truly self-similar system is obtained. The intersection of these continua (generally a fractal F) consists of points where all fields scale according to power laws. In this system, the equations of equilibrium are determined using the H-derivative, which is a difference quotient with the increment equal to H. Multifractal formalism is developed for non-uniform stress scaling and applied to the growth of a crack in a continuous material with fractal distribution of body forces. Fractal dimension of the future fracture surface is determined and the conditions of stable and unstable crack growth are formulated based on the multifractal spectrum.     

Spectral self-similarity in fractal one-dimensional photonic structures

Transmission spectra of one-dimensional fractal multilayer structures are found to exhibit self-similar properties. Self-similarity manifests itself in the shape of a transmission envelope (map of transmission dips) rather than in the map of resonance transmission peaks, as is commonly the case with spectra of quasiperiodic systems. To observe the self-similarity, one needs to apply a power transformation to the transmittance in addition to the usual frequency scaling. The values of this power as well as the scaling factor have been calculated analytically and found to depend on the geometrical parameters of the structure.     

Superconducting transition temperatures of amorphous binary alloy systems based on Bi,Pb, Ga and Be

Quench condensed binary alloy films are produced by evaporation from two separated furnaces. The films contain the whole composition range of the respective alloy system in well defined arrangement.T _c is measured as a function of concentration. Eight predominantly amorphous alloy systems are studied: Bi—Ga, Pb—Ga, Pb—Bi, Be—Bi, Be—Pb, Be—Ga, Be—Al, Be—Li. In Bi—Ga and Pb—GaT _c is a linear function of concentration in the amorphous composition range. In Pb—BiT _c has a maximum. All Be-alloys show lower transition temperatures than pure quench condensed Be. Except for Be—Li all systems have aT _c minimum. The experiments are compared to aT _c calculation using tunelling spectroscopy data. Except for the Be-alloys the agreement is satisfying.     

Self-similar behavior and chemistry tabulation of burnt-gas diluted premixed flamelets including heat-loss

In many combustion systems, the reactive gases feeding the reaction zones are diluted by burnt products, to favor flame stabilization, homogenize the temperature distribution and reduce pollutant emission. The objective of this paper is to discuss a premixed flamelet detailed chemistry tabulation strategy for vitiated and non-adiabatic combustion. Dilution by burnt products is parameterized here with two controlling quantities: the amplitude of the heat-loss in the burnt gases, for instance at walls, and the level of reactant vitiation. The chemical response of premixed flames to variations of these parameters is studied and it is shown that most chemical properties of burnt-gas diluted flames feature self-similar behavior, which can be used to dramatically downsize chemical tables based on canonical flamelets. The self-similar behavior of the flamelets is studied for both molecular diffusion and chemical source budgets in a progress variable composition space. It is found that two different scaling relations are needed to ensure self-similar behavior of both major and radical species.