Fatigue in metallic alloys containing non-metallic particles

This paper examines the effects of non-metallic particles on fatigue performance and, in particular, their influence on fatigue crack propagation at high ΔK (Kmax) levels. The nature and properties of a number of common non-metallic particles found in Fe- and Al- based alloys are described, and consideration is given to the consequences of mismatch of physical and chemical properties between particle and matrix. Effects of particles on fatigue in conventional alloys are illustrated and compared with the behaviour of Al/SiCp MMC. The problems associated with developing particulate reinforced MMC with adequate fatigue crack growth resistance and toughness for structural applications are discussed. © 1991.

Spectral asymptotic properties of semi-regular non-commutative harmonic oscillators

The study carried out in this thesis is devoted to spectral analysis of systems of PDEs related also with quantum physics models. Namely, the research deals with classes of systems that contain certain quantum optics models such as Jaynes-Cummings, Rabi and their generalizations that describe light-matter interaction. First we investigate the spectral Weyl asymptotics for a class of semiregular systems, extending to the vector-valued case results of Helffer and Robert, and more recently of Doll, Gannot and Wunsch. Actually, the asymptotics by Doll, Gannot and Wunsch is more precise (that is why we call it refined) than the classical result by Helffer and Robert, but deals with a less general class of systems, since the authors make an hypothesis on the measure of the subset of the unit sphere on which the tangential derivatives of the X-Ray transform of the semiprincipal symbol vanish to infinity order. Abstract Next, we give a meromorphic continuation of the spectral zeta function for semiregular differential systems with polynomial coefficients, generalizing the results by Ichinose and Wakayama and Parmeggiani. Finally, we state and prove a quasi-clustering result for a class of systems including the aforementioned quantum optics models and we conclude the thesis by showing a Weyl law result for the Rabi model and its generalizations.

Bifurcations in the non-dissipative dynamics of ultra cold atoms

We present the first experimental observation of several bifurcations in a controllable non-linear Hamiltonian system. Dynamics of cold atoms are used to test predictions of non-linear, non-dissipative Hamiltonian dynamics.

Strong shift equivalence, algebraic K-theory, and isolating zero-dimensional dynamics on manifolds

We study the relations of shift equivalence and strong shift equivalence for matrices over a ring $\mathcal{R}$, and establish a connection between these relations and algebraic K-theory. We utilize this connection to obtain results in two areas where the shift and strong shift equivalence relations play an important role: the study of finite group extensions of shifts of finite type, and the Generalized Spectral Conjectures of Boyle and Handelman for nonnegative matrices over subrings of the real numbers. We show the refinement of the shift equivalence class of a matrix $A$ over a ring $\mathcal{R}$ by strong shift equivalence classes over the ring is classified by a quotient $NK_{1}(\mathcal{R}) / E(A,\mathcal{R})$ of the algebraic K-group $NK_{1}(\calR)$. We use the K-theory of non-commutative localizations to show that in certain cases the subgroup $E(A,\mathcal{R})$ must vanish, including the case $A$ is invertible over $\mathcal{R}$. We use the K-theory connection to clarify the structure of algebraic invariants for finite group extensions of shifts of finite type. In particular, we give a strong negative answer to a question of Parry, who asked whether the dynamical zeta function determines up to finitely many topological conjugacy classes the extensions by $G$ of a fixed mixing shift of finite type. We apply the K-theory connection to prove the equivalence of a strong and weak form of the Generalized Spectral Conjecture of Boyle and Handelman for primitive matrices over subrings of $\mathbb{R}$. We construct explicit matrices whose class in the algebraic K-group $NK_{1}(\mathcal{R})$ is non-zero for certain rings $\mathcal{R}$ motivated by applications. We study the possible dynamics of the restriction of a homeomorphism of a compact manifold to an isolated zero-dimensional set. We prove that for $n \ge 3$ every compact zero-dimensional system can arise as an isolated invariant set for a homeomorphism of a compact $n$-manifold. In dimension two, we provide obstructions and examples.

Strongly non-degenerate Lie algebras

Let A be a semiprime 2 and 3-torsion free non-commutative associative algebra. We show that the Lie algebra Der(A) of(associative) derivations of A is strongly non-degenerate, which is a strong form of semiprimeness for Lie algebras, under some additional restrictions on the center of A. This result follows from a description of the quadratic annihilator of a general Lie algebra inside appropriate Lie overalgebras. Similar results are obtained for an associative algebra A with involution and the Lie algebra SDer(A) of involution preserving derivations of A

Influence of hydrodynamic interactions on the adsoption process of large particles

We have studied the adsorption process of non-Brownian particles on a line. Our work differs from previously proposed models in that we have incorporated hydrodynamic interactions between the incoming particles and the preadsorbed particles as well as the surface. We then numerically analyze the effect of these interactions on quantities related to the adsorption process. Comparing our model to the ballistic deposition model (BM) shows a significant discrepancy in the pair correlation function. These results can explain some differences between recent experiments and BM predictions. Finally, the limitations of the applicability of BM are addressed.

Non-thermal emission from microquasar/ISM interaction

Context. The interaction of microquasar jets with their environment can produce non-thermal radiation as in the case of extragalactic outflows impacting on their surroundings. Significant observational evidence of jet/medium interaction in galactic microquasars has been collected in the past few years, although little theoretical work has been done regarding the resulting non-thermal emission. Aims. In this work, we investigate the non-thermal emission produced in the interaction between microquasar jets and their environment, and the physical conditions for its production. Methods. We developed an analytical model based on those successfully applied to extragalactic sources. The jet is taken to be a supersonic and mildly relativistic hydrodynamical outflow. We focus on the jet/shocked medium structure in its adiabatic phase, and assume that it grows in a self-similar way. We calculate the fluxes and spectra of the radiation produced via synchrotron, inverse Compton, and relativistic bremsstrahlung processes by electrons accelerated in strong shocks. A hydrodynamical simulation is also performed to investigate further the jet interaction with the environment and check the physical parameters used in the analytical model. Results. For reasonable values of the magnetic field, and using typical values of the external matter density, the non-thermal particles could produce significant amounts of radiation at different wavelengths, although they do not cool primarily radiatively, but by adiabatic losses. The physical conditions of the analytical jet/medium interaction model are consistent with those found in the hydrodynamical simulation. Conclusions. Microquasar jet termination regions could be detectable at radio wavelengths for current instruments sensitive to ~arcminute scales. At X-ray energies, the expected luminosities are moderate, although the emitter is more compact than the radio one. The source may be detectable by XMM-Newton or Chandra, with 1-10 arcsec of angular resolution. The radiation at gamma-ray energies may be within the detection limits of the next generation of satellite and ground-based instruments.

Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

In-flight and collisional dissipation as a mechanism to suppress Fermi acceleration in a breathing Lorentz gas

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Periodic compression of an adiabatic gas: Intermittency-enhanced Fermi acceleration

A gas of non-interacting particles diffuses in a lattice of pulsating scatterers. In the finite-horizon case with bounded distance between collisions and strongly chaotic dynamics, the velocity growth (Fermi acceleration) is well described by a master equation, leading to an asymptotic universal non-Maxwellian velocity distribution scaling as v∼t. The infinite-horizon case has intermittent dynamics which enhances the acceleration, leading to v∼t ln t and a non-universal distribution. © Copyright EPLA, 2013.

Aceleração de Fermi em bilhares com fronteiras dependentes do tempo descritas por osciladores não lineares: caso conservativo e dissipativo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Thermodynamics of a bouncer model: A simplified one-dimensional gas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the statistical and transport properties of a non-dissipative Fermi-Ulam model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Estudo do fenômeno de decaimento de energia média do Bilhar Stadium dependente do tempo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Decay of energy and suppression of Fermi acceleration in a dissipative driven stadium-like billiard

The behavior of the average energy for an ensemble of non-interacting particles is studied using scaling arguments in a dissipative time-dependent stadium-like billiard. The dynamics of the system is described by a four dimensional nonlinear mapping. The dissipation is introduced via inelastic collisions between the particles and the moving boundary. For different combinations of initial velocities and damping coefficients, the long time dynamics of the particles leads them to reach different states of final energy and to visit different attractors, which change as the dissipation is varied. The decay of the average energy of the particles, which is observed for a large range of restitution coefficients and different initial velocities, is described using scaling arguments. Since this system exhibits unlimited energy growth in the absence of dissipation, our results for the dissipative case give support to the principle that Fermi acceleration seems not to be a robust phenomenon. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3699465]