Scaling dynamics for a particle in a time-dependent potential well

Some dynamical properties for a classical particle confined in an infinitely deep box of potential containing a periodically oscillating square well are studied. The dynamics of the system is described by using a two-dimensional non-linear area-preserving map for the variables energy and time. The phase space is mixed and the chaotic sea is described using scaling arguments. Scaling exponents are obtained as a function of all the control parameters, extending the previous results obtained in the literature. (c) 2012 Elsevier B.V. All rights reserved.

Boundary crisis and suppression of Fermi acceleration in a dissipative two-dimensional non-integrable time-dependent billiard

Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non-dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time-dependent billiards. (C) 2010 Elsevier B.V. All rights reserved.

Fermi acceleration and its suppression in a time-dependent Lorentz gas

Some dynamical properties for a Lorentz gas were studied considering both static and time-dependent boundaries. For the static case, it was confirmed that the system has a chaotic component characterized with a positive Lyapunov exponent. For the time-dependent perturbation, the model was described using a four-dimensional nonlinear map. The behaviour of the average velocity is considered in two different situations: (i) non-dissipative and (ii) dissipative dynamics. Our results confirm that unlimited energy growth is observed for the non-dissipative case. However, and totally new for this model, when dissipation via inelastic collisions is introduced, the scenario changes and the unlimited energy growth is suppressed, thus leading to a phase transition from unlimited to limited energy growth. The behaviour of the average velocity is described using scaling arguments. (C) 2010 Elsevier B.V. All rights reserved.

A peculiar Maxwell's Demon observed in a time-dependent stadium-like billiard

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

CRITICAL EXPONENTS and SCALING PROPERTIES FOR THE CHAOTIC DYNAMICS of A PARTICLE IN A TIME-DEPENDENT POTENTIAL BARRIER

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

Time-dependent non-Hermitian Hamiltonians with real energies

In this work we intend to study a class of time-dependent quantum systems with non-Hermitian Hamiltonians, particularly those whose Hermitian counterparts are important for the comprehension of posed problems in quantum optics and quantum chemistry. They consist of an oscillator with time-dependent mass and frequency under the action of a time-dependent imaginary potential. The wave functions are used to obtain the expectation value of the Hamiltonian. Although it is neither Hermitian nor PT symmetric, the Hamiltonian under study exhibits real values of energy.

Phagocytosis of PLGA microparticles in rat peritoneal exudate cells: A time-dependent study

With the purpose of enhancing the efficacy of microparticle-encapsulated therapeutic agents, in this study we evaluated the phagocytic ability of rat peritoneal exudate cells and the preferential location of poly(D,L-lactide-co-glycolic acid) (PLGA) microparticles inside these cells. The microparticles used were produced by a solvent evaporation method and were characterized by dynamic light scattering (DLS), transmission electron microscopy (TEM), and scanning electron microscopy (SEM). Size distribution analysis using DLS and SEM showed that the particles were spherical, with diameters falling between 0.5 and 1.5 mu m. Results from cell adhesion by SEM assay, indicated that the PLGA microparticles are not toxic to cells and do not cause any distinct damage to them as confirmed by the MTT (3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl tetrazolium bromide) assay. Among the large variety of cell populations found in the peritoneal exudates (neutrophils, eosinophils, monocytes, and macrophages), TEM showed that only the latter phagocytosed PLGA microparticles, in a time-dependent manner. The results obtained indicate that the microparticles studied show merits as possible carriers of drugs for intracellular delivery.

Exact boundary control for the wave equation in a polyhedral time-dependent domain

We establish exact boundary controllability for the wave equation in a polyhedral domain where a part of the boundary moves slowly with constant speed in a small interval of time. The control on the moving part of the boundary is given by the conormal derivative associated with the wave operator while in the fixed part the control is of Neuman type. For initial state H-1 x L-2 we obtain controls in L-2. (C) 1999 Elsevier B.V. Ltd. All rights reserved.

Separation of particles in time-dependent focusing billiards

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

Purification of a PHA-Like chitin-binding protein from Acacia farnesiana seeds: A time-dependent oligomerization protein

A lectin-like protein from the seeds of Acacia farnesiana was isolated from the albumin fraction, characterized, and sequenced by tandem mass spectrometry. The albumin fraction was extracted with 0.5 M NaCl, and the lectin-like protein of A. farnesiana (AFAL) was purified by ion-exchange chromatography (Mono-Q) followed by chromatofocusing. AFAL agglutinated rabbit erythrocytes and did not agglutinate human ABO erythrocytes either native or treated with proteolytic enzymes. In sodium dodecyl sulfate gel electrophoresis under reducing and nonreducing conditions, AFAL separated into two bands with a subunit molecular mass of 35 and 50 kDa. The homogeneity of purified protein was confirmed by chromatofocusing with a pI=4.0+/-0.5. Molecular exclusion chromatography confirmed time-dependent oligomerization in AFAL, in accordance with mass spectrometry analysis, which confers an alteration in AFAL affinity for chitin. The protein sequence was obtained by a liquid chromatography quadrupole time-of-flight experiment and showed that AFAL has 68% and 63% sequence similarity with lectins of Phaseolus vulgaris and Dolichos biflorus, respectively.

Comment on Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential [J. Math. Phys. 48, 073515 (2007)]

It is shown that the paper Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential by Merad and Bensaid [J. Math. Phys. 48, 073515 (2007)] is not correct in using inadvertently a non-Hermitian Hamiltonian in a formalism that does require Hermitian Hamiltonians.

Fermi acceleration and scaling properties of a time dependent oval billiard

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Escape of particles in a time-dependent potential well

We investigate the escape of an ensemble of noninteracting particles inside an infinite potential box that contains a time-dependent potential well. The dynamics of each particle is described by a two-dimensional nonlinear area-preserving mapping for the variables energy and time, leading to a mixed phase space. The chaotic sea in the phase space surrounds periodic islands and is limited by a set of invariant spanning curves. When a hole is introduced in the energy axis, the histogram of frequency for the escape of particles, which we observe to be scaling invariant, grows rapidly until it reaches a maximum and then decreases toward zero at sufficiently long times. A plot of the survival probability of a particle in the dynamics as function of time is observed to be exponential for short times, reaching a crossover time and turning to a slower-decay regime, due to sticky regions observed in the phase space.