Detection of matrix cracks in composite laminates by using the modal strain energy method

As the foremost mechanism of damage development, matrix cracking is the critical damage found in the early stage of structural failure of composites. This study aims to nondestructively detect matrix cracks in composite laminates by using an experimental modal analysis (EMA). An AS4/PEEK composite was used to fabricate cross-ply [0₂/90₁₂/0₂] and quasi-isotropic [(±45/0/90)₄] _s laminates. The damage in the form of a matrix crack in the laminates was created by using a tensile load. The EMA was conducted on the laminates to obtain the modal displacements before and after damage. The displacements were then employed to compute the modal strain energy and to define the damage index, which is used for detecting matrix cracks. Limited by the mesh points of measurements, we used the differential quadrature method to calculate the partial differentials in the strain energy formula. The results obtained were validated by using the X-ray radiography method and three-point bending tests. The experimental results showed that the damage index well identified the location of breadthwise matrix cracks inside the laminates. However, the resolution of the damage index became poor if the spans of matrix cracks were short or the matrix cracks were scattered over the laminates.     

Coarse-scale particle tracking approaches for contaminant transport in fractured rock

Random-walk particle tracking methods are frequently used for modeling contaminant transport, as relevant to radionuclide transport in fractured rock. Standard particle-tracking methods need to be modified for handling discontinuities in velocity and diffusion coefficients as at fracture–matrix interfaces, and handling these discontinuities accurately requires time steps much smaller than the diffusion time scale across narrow fracture apertures. In this work we present coarse-scale particle tracking methods that exploit the contrast in diffusivities between fracture and rock matrix to allow the use of time steps much larger than the diffusion time scale across fracture apertures. Thus, they reduce computational effort by several orders of magnitude. We develop two coarse-scale versions of the standard particle tracking method, one applicable to particles starting in the fracture, and another to particles starting in the rock matrix. The two methods can be used in combination to track particles through individual fractures, including the influence of matrix diffusion. The main advantage of our methods result from the computationally efficient treatment of (two-way) fracture–matrix particle transfer. These methods can also be combined with existing particle tracking approaches for complex advection–diffusion–dispersion in fractures to handle fracture–matrix interactions efficiently.     

An experimental study towards micro-mechanical modeling of fiber-reinforced aerogels

Fiber-reinforced aerogels are a class of reinforced aerogels characterized by very low thermal conductivity, hydrophobicity and most importantly load bearing capability. In this work, an experimental study describing the damage in these fiber-reinforced aerogels through various uniaxial compression tests is presented. While understanding the damage evolution at the micro-scale, we come across three probable sources contributing towards the damage evolution. They are: (a) matrix cracks, (b) debonding of particles due to fiber sliding, and (c) breakage of fibers. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micro-mechanical study of interactions between polymers and filler aggregates

Filled rubber-like materials exhibit a complex, history-dependent hysteretic behavior which is mostly due to damage of micro-structures inside the rubber matrix. In this paper, we study the contribution of filler aggregates inside the elastomer to this damage behavior. To this end, a recently proposed multi-scale model of single aggregates [1] is applied. The network decomposition concept adopted there is further extended here to an additional network [1] which takes into account elasticity of filler aggregates and polymer chains in their vicinity. This network is described by means of a 3D statistical volume element (SVE) obtained by homogenization over the aggregate size distribution within the rubber matrix. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Semi-infinite Asymmetric Exclusion Process: Large Deviations via Matrix Products

We study the totally asymmetric exclusion process on the positive integers with a single particle source at the origin. Liggett (Trans. Am. Math. Soc. 213, 237–261, 1975) has shown that the long term behaviour of this process has a phase transition: If the particle production rate at the source and the original density are below a critical value, the stationary measure is a product measure, otherwise the stationary measure is spatially correlated. Following the approach of Derrida et al. (J. Phys. A 26(7), 1493, 1993) it was shown by Grosskinsky (2004) that these correlations can be described by means of a matrix product representation. In this paper we derive a large deviation principle with explicit rate function for the particle density in a macroscopic box based on this representation. The novel and rigorous technique we develop for this problem combines spectral theoretical and combinatorial ideas and is potentially applicable to other models described by matrix products.     

On one mathematical model of creep in superalloys

In [Sv1] a new micromechanical approach to the prediction of creep flow in composites with perfect matrix/particle interfaces, based on the nonlinear Maxwell viscoelastic model, taking into account a finite number of discrete slip systems in the matrix, has been suggested; high-temperature creep in such composites is conditioned by the dynamic recovery of the dislocation structure due to slip/climb motion of dislocations along the matrix/particle interfaces. In this article the proper formulation of the system of PDE's generated by this model is presented, some existence results are obtained and the convergence of Rothe sequences, applied in the specialized software CDS, is studied.     

Application of the lent particle method to Poisson-driven SDEs

We apply the Dirichlet form theory to stochastic differential equations with jumps as extension of Malliavin calculus reasoning. As in the continuous case, this weakens significantly the assumptions on the coefficients of the SDE. Thanks to the flexibility of the Dirichlet forms language, this approach brings also an important simplification which was neither available nor visible previously: an explicit formula giving the carré du champ matrix, i.e., the Malliavin matrix. Following this formula a new procedure appears, called the lent particle method which shortens the computations both theoretically and in concrete examples. In this paper which uses the construction done in Bouleau and Denis (J. Funct. Analysis 257:1144?C1174, 2009) we restrict ourselves to the existence of densities; smoothness will be studied separately.     

A decoupled finite particle method for modeling incompressible flows with free surfaces

Smoothed particle hydrodynamics (SPH) is a meshfree Lagrangian particle method, and it has been applied to different areas in engineering and sciences. One concern of the conventional SPH is its low accuracy due to particle inconsistency, which hinders the further methodology development. The finite particle method (FPM) restores the particle consistency in the conventional SPH and thus significantly improves the computational accuracy. However, as pointwise corrective matrix inversion is necessary, FPM may encounter instability problems for highly disordered particle distribution. In this paper, through Taylor series analyses with integration approximation and assuming diagonal dominance of the resultant corrective matrix, a new meshfree particle approximation method, decoupled FPM (DFPM), is developed. DFPM is a corrective SPH method, and is flexible, cost-effective and easy in coding with better computational accuracy. It is very attractive for modeling problems with extremely disordered particle distribution as no matrix inversion is required. One- and two-dimensional numerical tests with different kernel functions, smoothing lengths and particle distributions are conducted. It is demonstrated that DFPM has much better accuracy than conventional SPH, while particle distribution and the selection of smoothing function and smoothing length have little influence on DFPM simulation results. DFPM is further applied to model incompressible flows including Poiseuille flow, Couette flow, shear cavity and liquid sloshing. It is shown that DFPM is as accurate as FPM while as flexible as SPH, and it is very attractive in modeling incompressible flows with possible free surfaces.     

Deterministic particle method approximation of a contact inhibition cross-diffusion problem

We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations.According to the values of the diffusion parameters related to the intra- and inter-population repulsion intensities, the system may be classified in terms of an associated matrix. When the matrix is definite positive, the problem is well posed and the finite element approximation produces convergent approximations to the exact solution.A particularly important case arises when the matrix is only positive semi-definite and the initial data are segregated: the contact inhibition problem. In this case, the solutions may be discontinuous and hence the (conforming) finite element approximation may exhibit instabilities in the neighborhood of the discontinuity.In this article we deduce the particle method approximation to the general cross-diffusion problem and apply it to the contact inhibition problem. We then provide some numerical experiments comparing the results produced by the finite element and the particle method discretizations.     

The SU(v) Calogero spin system

A one-dimensional quantum particle system in which particles with su(v) spins interact through inverse square interactions is introduced. We refer to it as the SU(v) Calogero spin system. Using the quantum inverse scattering method, we reveal algebraic structures of the system: hidden symmetry is the U(v) − SU(v) U(1) current algebra. This is consistent with the fact that the ground-state wave function is a solution of the Knizhnik-Zamolodchikov equation. Furthermore we show that the system has a higher symmetry, known as the w_{1 + ∞}-algebra. With this W-algebra we have a unified viewpoint on the integrable quantum particle systems with long-range interactions such as the Calogero type (1/x²-interactions) and Sutherland type (1/sin²x-interactions). The Yangian symmetry is briefly discussed.     

Gravitational instanton in Hilbert space and the mass of high energy elementary particles

While the theory of relativity was formulated in real spacetime geometry, the exact formulation of quantum mechanics is in a mathematical construction called Hilbert space. For this reason transferring a solution of Einstein’s field equation to a quantum gravity Hilbert space is far of being a trivial problem.

On the other hand ^(∞) spacetime which is assumed to be real is applicable to both, relativity theory and quantum mechanics. Consequently, one may expect that a solution of Einstein’s equation could be interpreted more smoothly at the quantum resolution using the Cantorian ^(∞) theory.

In the present paper we will attempt to implement the above strategy to study the Eguchi–Hanson gravitational instanton solution and its interpretation by ‘t Hooft in the context of quantum gravity Hilbert space as an event and a possible solitonic “extended” particle. Subsequently we do not only reproduce the result of ‘t Hooft but also find the mass of a fundamental “exotic” symplictic-transfinite particle m1.8 MeV as well as the mass M_x and M (Planck) which are believed to determine the GUT and the total unification of all fundamental interactions respectively. This may be seen as a further confirmation to an argument which we put forward in various previous publications in favour of an alternative mass acquisition mechanism based on unification and duality considerations. Thus even in case that we never find the Higgs particle experimentally, the standard model would remain substantially intact as we can appeal to tunnelling and unification arguments to explain the mass. In fact a minority opinion at present is that finding the Higgs particle is not a final conclusive argument since one could ask further how the Higgs particle came to its mass which necessitates a second Higgs field. By contrast the present argument could be viewed as an ultimate theory based on the existence of a “super” force, beyond which nothing else exists.     

Gauge Equivalence among Quantum Nonlinear Many Body Systems

Transformations performing on the dependent and/or the independent variables are an useful method used to classify PDE in class of equivalence. In this paper we consider a large class of U(1)-invariant nonlinear Schrödinger equations containing complex nonlinearities. The U(1) symmetry implies the existence of a continuity equation for the particle density ρ≡|ψ|² where the current j _ψ has, in general, a nonlinear structure. We introduce a nonlinear gauge transformation on the dependent variables ρ and j _ψ which changes the evolution equation in another one containing only a real nonlinearity and transforms the particle current j _ψ in the standard bilinear form. We extend the method to U(1)-invariant coupled nonlinear Schrödinger equations where the most general nonlinearity is taken into account through the sum of an Hermitian matrix and an anti-Hermitian matrix. By means of the nonlinear gauge transformation we change the nonlinear system in another one containing only a purely Hermitian nonlinearity. Finally, we consider nonlinear Schrödinger equations minimally coupled with an Abelian gauge field whose dynamics is governed, in the most general fashion, through the Maxwell-Chern-Simons equation. It is shown that the nonlinear transformation we are introducing can be applied, in this case, separately to the gauge field or to the matter field with the same final result. In conclusion, some relevant examples are presented to show the applicability of the method.     

Neutrino processes in an external magnetic field in the density matrix formalism

In the matrix density formalism for a charged spinor particle located in a constant uniform magnetic field, we develop a technique for calculating the reaction rate and the four-momentum carried away from a plasma by a neutrino in one-vertex neutrino processes. Using this technique, we reproduce results for the luminosity in processes of neutrino synchrotron emission by electrons (positrons) and of electron-positron annihilation producing the neutrino pair.     

A solvable mixed charge ensemble on the line: global results

We consider an ensemble of interacting charged particles on the line consisting of two species of particles with charge ratio 2:1 in the presence of an external field. With the total charge fixed and the system held at temperature corresponding to β = 1, it is proved that the particles form a Pfaffian point process. When the external field is quadratic (the harmonic oscillator potential), we produce the explicit family of skew-orthogonal polynomials necessary to simplify the related matrix kernels. In this setting a variety of limit theorems are proved on the distribution of the number as well as the spatial density of each species of particle as the total charge increases to infinity. Connections to Ginibre’s real ensemble of random matrix theory are highlighted throughout.     

One-particle density matrix of liquid 4He

Using the expression for the total density matrix for a system of N interacting Bose particles found in our previous papers, we calculate the one-particle density matrix in the coordinate representation. At low temperatures, the leading approximation of this matrix reproduces the results of the Bogoliubov theory. In the classical limit, the proposed theory reproduces the results of the theory of the classical liquid in the approximation of chaotic phases. From the one-particle density matrix, we find the particle momentum distribution function and the mean kinetic energy of the Bose liquid and investigate the phenomenon of Bose-Einstein condensation. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 9–30, January, 2008.     

Complementarity forms of theorems of Lyapunov and Stein, and related results

The well-known Lyapunov's theorem in matrix theory / continuous dynamical systems asserts that a (complex) square matrix A is positive stable (i.e., all eigenvalues lie in the open right-half plane) if and only if there exists a positive definite matrix X such that AX+XA^* is positive definite. In this paper, we prove a complementarity form of this theorem: A is positive stable if and only if for any Hermitian matrix Q, there exists a positive semidefinite matrix X such that AX+XA^*+Q is positive semidefinite and X[AX+XA^*+Q]=0. By considering cone complementarity problems corresponding to linear transformations of the form I−S, we show that a (complex) matrix A has all eigenvalues in the open unit disk of the complex plane if and only if for every Hermitian matrix Q, there exists a positive semidefinite matrix X such that X−AXA^*+Q is positive semidefinite and X[X−AXA^*+Q]=0. By specializing Q (to −I), we deduce the well known Stein's theorem in discrete linear dynamical systems: A has all eigenvalues in the open unit disk if and only if there exists a positive definite matrix X such that X−AXA^* is positive definite.     

Steady and oscillatory analysis of porous catalysts in fluidized beds

In this paper, we consider the steady /oscillatory flow field within a porous particle contained in a fixed or fluidized bed, in which the spherical porous particle is placed in a spherical envelope of fluid. Stokes equations are employed inside the fluid envelope and Brinkman/Darcy equations are used inside the porous region. We compute drag force acting on the particle and hence the overall bed permeability of the bed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

环境激励下基于柔度矩阵分解的损伤诊断

为了解决环境激励作用下结构自由度不完备对损伤诊断的影响,提出了一种基于自由度缩聚的比例柔度矩阵分解损伤诊断法.利用附加质量法求解出环境激励作用下振型关于质量归一化因子.进而根据质量归一化因子和比例柔度矩阵系数之间的关系,构建出其比例柔度矩阵,再通过使用QR矩阵分解法对构建出的比例柔度矩阵进行分解.以分解后得到的三角矩阵...