On the stability of the solutions to an integral evolution equation of the non linear particle transport theory

Summary In this paper we study the stability, with respect to the initial data, of the solutions to a non linear integral equation arising in particles transport theory.

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Sommario In questo lavoro si prova la stabilità, rispetto ai dati iniziali, delle soluzioni di un'equazione integrale non lineare che si incontra in teoria del trasporto di particelle.

     

Effect of particle number density in in-line digital holographic particle velocimetry

A digital in-line holographic particle tracking velocimetry (HPTV) system was developed to measure 3D (three-dimensional) velocity fields of turbulent flows. The digital HPTV (DHPTV) procedure consists of four steps: recording, numerical reconstruction, particle extraction and velocity extraction. In the recording step, a digital CCD camera was used as a recording device. Holograms contained many unwanted images or noise. To get clean holograms, digital image processing techniques were adopted. In the velocity extraction routine, we improved the HPTV algorithm to extract 3D displacement information of tracer particles. In general, the results obtained using HPTV were not fully acceptable due to technical limitations such as low spatial resolution, small volume size, and low numerical aperture (NA). The problems of spatial resolution and NA are closely related with a recording device. As one experimental parameter that can be optimized, we focused on the particle number density. Variation of the reconstruction efficiency and recovery ratio were compared quantitatively with varying particle number density to check performance of the developed in-line DHPTV system. The reconstruction efficiency represented the particle number distribution acquired through the numerical reconstruction procedure. In addition the recovery ratio showed the performance of 3D PTV algorithm employed for DHPTV measurements. The particle number density in the range of C _o = 13–17 particles/mm³ was found to be optimum for the DHPTV system tested in this study.     

L1 -stability of the solutions to an integral evolution equation of the non-linear particle transport theory

Summary The problem of L ¹-stability of the solutions to a non linear integral equation arising in particles transport theory is studied. This equation can represent the standard spatially homogeneous Boltzmann equation in the case of Maxwellium particles with cut off.

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Sommario Si studia la stabilita non lineare nella norma di L ¹ delle soluzioni di un'equazione integrale non lineare della teoria del trasporto di particelle, cui si riduce l'usuale equazione di Boltzmann nel caso spazialmente omogeneo e per particelle Maxwelliane con cut-off.

     

Discrete particle simulation of mixed sand transport

An Eulerian/Lagrangian numerical simulation is performed on mixed sand transport. Volume averaged Navier–Stokes equations are solved to calculate gas motion, and particle motion is calculated using Newton's equation, involving a hard sphere model to describe particle-to-particle and particle-to-wall collisions. The influence of wall characteristics, size distribution of sand particles and boundary layer depth on vertical distribution of sand mass flux and particle mean horizontal velocity is analyzed, suggesting that all these three factors affect sand transport at different levels. In all cases, for small size groups, sand mass flux first increases with height and then decreases while for large size groups, it decreases exponentially with height and for middle size groups the behavior is in-between. The mean horizontal velocity for all size groups well fits experimental data, that is, increasing logarithmically with height in the middle height region. Wall characteristics greatly affects particle to wall collision and makes the flat bed similar to a Gobi surface and the rough bed similar to a sandy surface. Particle size distribution largely affects the sand mass flux and the highest heights they can reach especially for larger particles.     

Compatibility conditions in the linear micropolar theory

Various representations of compatibility (continuity) conditions are obtained in terms of strain and bending-torsion tensors as well as in terms of stress and couple-stress tensors.     

The linear growth of the density wave in galaxies

The aim of this article is to study the linear growth of the density wave in galaxies by means of numerically resolving unsteady, two-dimensional hydrodynamic equations coupled with Poisson equation under the condition that the local asymptotic solution of linear density wave is given.as an initial value. The results show that the perturbed peak density of linear density wave grows to the same order as the basic state density during merely tens of million years,the spiral pattern emerging which has barred structure in its inner region. The angular velocity of the spiral pattern and the growth rate of perturbed density vary gradually with changes in spatial place and time. The approximate property of quasistationary spiral structure hypothesis is discussed in this paper.     

Applications of energy density theory in cyclic plasticity

This paper discusses the application of energy density theory to a variety of problems associated with cyclic plasticity. Attention is focused on problems related to fatigue life enhancement procedures, and on understanding the mechanism which govern failure.     

Dynamic load balance applied to particle transport in fluids

This work presents a parallel numerical strategy to transport Lagrangian particles in a fluid using a dynamic load balance strategy. Both fluid and particle solvers are parallel, with two levels of parallelism. The first level is based on a substructuring technique and uses message passing interface (MPI) as the communication library; the second level consists of OpenMP pragmas for loop parallelisation at the node level. When dealing with transient flows, there exist two main alternatives to address the coupling of these solvers. On the one hand, a single-code approach consists in solving the particle equations once the fluid solution has been obtained at the end of a time step, using the same instance of the same code. On the other hand, a multi-code approach enables one to overlap the transport of the particles with the next time-step solution of the fluid equations, and thus obtain asynchronism. In this case, different codes or two instances of the same code can be used. Both approaches will be presented. In addition, a dynamic load balancing library is used on the top of OpenMP pragmas in order to continuously exploit all the resources available at the node level, thus increasing the load balance and the efficiency of the parallelisation and uses the MPI.     

Functional methods in three-dimensional neutron transport theory

Summary In this work, we are concerned with the stationary neutron transport Boltzmann equation (in its integral form) in a parallelepiped. Functional methods allow us to prove that the integral transport operator, which is defined in L² space, has eigenvalues depending continuously and monotonically on geometrical and physical parameters. We show that the eigenfunctions are continuous with respect to set of the spatial variables and the optical parameters. Finally, we remark that the same results are valid if the study is carried out in the Banach space C.

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Sommario In questo lavoro consideriamo l'equazione stazionaria di Boltzmann (nella forma integrale) per neutroni monoenergetici nel caso di un sistema tridimensionale a forma di parallelepipedo. L'uso di alcuni metodi dell'analisi funzionale ci permette di provare che l'operatore integrale del trasporto, definito nello spazio L², ha autovalori che dipendono continuamente dai parametri geometrici e fisici. Si prova che le autofunzioni sono continue rispetto all'insieme delle variabili spaziali e dei parametri ottici. Infine, si osserva che gli stessi risultati sono validi se l'operatore del trasporto agisce nello spazio di Banach C.

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Work performed under contract C.N.R. (Gruppo Nazionale per la Fisica Matematica).     

Strict solution of a nonlinear particle transport problem

Summary We show that an evolution problem arising from particle transport with quadratic nonlinearities has a unique positive strict solution in the Banach space UCB.

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Sommario Facendo uso della teoria dei semigruppi si prova che un problema di trasporto di particelle con non-linearità quadratiche ha un'unica soluzione forte nello spazio di Banach UCB.

     

Transients and Evolution in NiTi

Many of the applications that seek to utilize shape memory alloys for their unique set of properties inevitably must deal, on some level, with the dimensional instability that is inherent to these materials under cyclic thermomechanical loading conditions. As a result, a better understanding of the transient and evolutionary behavior of a shape memory alloy is critical to both the successful design of useful actuation systems and development of accurate material models that can adequately capture the types of dimensional instability that can arise during component design. To this end, a set of experiments were conducted wherein the temperature cycling excursion was held fixed while the applied stress was varied. The results indicated that the extent of strain evolution produced under the initially applied stress has a significant impact on both the amount of transient that is observed as well as the rate of evolution observed under subsequent stress levels. In particular, lowering the applied stress to 50 MPa after cycling under an initial stress of 75 MPa did not stabilize the strain. However, lowering the applied stress to 50 MPa after cycling under an initial stress of 150 MPa produced a nearly saturated strain/temperature response. The thermomechanical observations are discussed in terms of the nature of strain evolution and its connection to the concept of a local/global minimization of the energy of the system, however, the exact mechanisms associated with these strain evolutions were not determined.     

A linear theory of straight elastic rods

This paper is based on the work of Green & Laws who have given a general thermodynamical theory of rods which is valid for any material. Here, starting with the general non-linear theory of elastic rods, we derive a linear theory allowing for thermal effects. The resulting free energy as a quadratic function of kinematic variables is restricted by certain symmetry conditions. The basic equations then separate into four groups, two for flexure, one for torsion and one for extension of the rod with temperature effects occurring only in the latter group. Wave propagation along an infinite rod is considered. There are two wave speeds for each type of flexure, two for torsion and three for isothermal extension and all wave speeds depend on the wave length.     

A generalized theory of linear micropolar thermoelasticity

Summary The linear theory of thermoelasticity established by Green and Lindsay with the help of an entropy production inequality proposed by Green and Laws is generalized to the case of a homogeneous micropolar continuum. The basic equations are derived using invariance conditions under superposed rigid body motions.

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Sommario La teoria lineare della termoelasticità stabilita da Green e Lindsay sulla base della disuguaglianza della produzione dell'entropia proposta da Green e Laws è generalizzata al caso di un continuo micropolare omogeneo. Le equazioni fondamentali vengono derivate usando condizioni di invarianza rispetto a moti rigidi sovrapposti.

     

Minimum principles in the linear dynamic theory of viscoelasticity

This paper establishes three minimum principles and transformed minimum principles concerning Laplace transformation in the linear dynamic theory of viscoelasticity.