On the many-time formulation of classical particle dynamics

Starting from the standard one-time dynamics of n nonrelativistic particles, the n-time equations of motion are inferred, and a variational principle is formulated. A suitable generalization of the classical LieKnig theorem is demonstrated, which allows the determination of all the associated presymplectic structures. The conditions under which the action of an invariance group is canonical are studied, and a corresponding Noether theorem is deduced. A formulation of the theory in terms of n first-class constraints is recovered by means of coisotropic imbeddings. The proposed approach also provides for a better understanding of the relativistic particle dynamics, since it shows that the different roles of the physical positions and the canonical variables is not peculiar to special relativity, but rather to any n-time approach: indeed a nonrelativistic no-interaction theorem is deduced.

Higher order Lagrangian systems: Geometric structures, Dynamics, and Constraints

In order to study the connections between Lagrangian and Hamiltonian formalisms constructed from aperhaps singularhigher-order Lagrangian, some geometric structures are constructed. Intermediate spaces between those of Lagrangian and Hamiltonian formalisms, partial Ostrogradskiis transformations and unambiguous evolution operators connecting these spaces are intrinsically defined, and some of their properties studied. Equations of motion, constraints, and arbitrary functions of Lagrangian and Hamiltonian formalisms are thoroughly studied. In particular, all the Lagrangian constraints are obtained from the Hamiltonian ones. Once the gauge transformations are taken into account, the true number of degrees of freedom is obtained, both in the Lagrangian and Hamiltonian formalisms, and also in all the intermediate formalisms herein defined.

Front dynamics in turbulent media

A study of a stable front propagating in a turbulent medium is presented. The front is generated through a reaction-diffusion equation, and the turbulent medium is statistically modeled using a Langevin equation. Numerical simulations indicate the presence of two different dynamical regimes. These regimes appear when the turbulent flow either wrinkles a still rather sharp propagating interfase or broadens it. Specific dependences of the propagating velocities on stirring intensities appropriate to each case are found and fitted when possible according to theoretically predicted laws. Different turbulent spectra are considered.

Dynamics of driven three-dimensional thin films: from hdrophilic to superhydrophobic substrates

We study the forced displacement of a thin film of fluid in contact with vertical and inclined substrates of different wetting properties, that range from hydrophilic to hydrophobic, using the lattice-Boltzmann method. We study the stability and pattern formation of the contact line in the hydrophilic and superhydrophobic regimes, which correspond to wedge-shaped and nose-shaped fronts, respectively. We find that contact lines are considerably more stable for hydrophilic substrates and small inclination angles. The qualitative behavior of the front in the linear regime remains independent of the wetting properties of the substrate as a single dispersion relation describes the stability of both wedges and noses. Nonlinear patterns show a clear dependence on wetting properties and substrate inclination angle. The effect is quantified in terms of the pattern growth rate, which vanishes for the sawtooth pattern and is finite for the finger pattern. Sawtooth shaped patterns are observed for hydrophilic substrates and low inclination angles, while finger-shaped patterns arise for hydrophobic substrates and large inclination angles. Finger dynamics show a transient in which neighboring fingers interact, followed by a steady state where each finger grows independently.

Influence of the dipolar interactions in the magnetization reversal asymmetry of hard-soft magnetic ribbons

Partial crystallization of the metallic glass Co66Si16B12Fe4Mo2 was performed by annealing at temperatures between 500 and 540°C for 10-20 min, resulting in crystallite volume fractions of (0.7-5)×10¿3 and sizes of 50-100 nm. This two-phase alloy presents a remarkable feature: a hysteresis loop shift that can be tailored by simply premagnetizing the sample in the adequate magnetic field. Shifts as large as five times the coercive field have been obtained which make them interesting for application as magnetic cores in dc pulse transformers. The asymetrical magnetic reversal is explained in terms of the magnetic dipolar field interaction and the observed hysteresis loops have been satisfactorily simulated by a modification of Stoner-Wohlfarth¿s model of coherent rotations.

Statistical dynamics of dislocation systems: The influence of dislocation-dislocation correlations.

During plastic deformation of crystalline materials, the collective dynamics of interacting dislocations gives rise to various patterning phenomena. A crucial and still open question is whether the long range dislocation-dislocation interactions which do not have an intrinsic range can lead to spatial patterns which may exhibit well-defined characteristic scales. It is demonstrated for a general model of two-dimensional dislocation systems that spontaneously emerging dislocation pair correlations introduce a length scale which is proportional to the mean dislocation spacing. General properties of the pair correlation functions are derived, and explicit calculations are performed for a simple special case, viz pair correlations in single-glide dislocation dynamics. It is shown that in this case the dislocation system exhibits a patterning instability leading to the formation of walls normal to the glide plane. The results are discussed in terms of their general implications for dislocation patterning.

Microwave absorption and magnetization tunneling in Mn12-acetate molecular clusters

In this paper we study the effect of microwave absorption on the quantum relaxation rate of Mn12 molecular clusters. We have determined first the resonant frequencies of a microwave resonator containing a single crystal of Mn12-Acetate and measured initial isothermal magnetization curves while microwave power was put into the resonator. We have found that the tunneling rate changes one order of magnitude for certain frequencies. This suggests that the microwave shaking of the nuclear spin and molecular vibrational degrees of freedom is responsible for the huge increasing of the tunneling rate.

Loop bifurcation and magnetization rotation in exchange-biased Ni/FeF2

Exchange-biased Ni/FeF2 films have been investigated using vector coil vibrating-sample magnetometry as a function of the cooling field strength HFC . In films with epitaxial FeF2 , a loop bifurcation develops with increasing HFC as it divides into two sub-loops shifted oppositely from zero field by the same amount. The positively biased sub-loop grows in size with HFC until only a single positively shifted loop is found. Throughout this process, the negative and positive (sub)loop shifts maintain the same discrete value. This is in sharp contrast to films with twinned FeF2 where the exchange field gradually changes with increasing HFC . The transverse magnetization shows clear correlations with the longitudinal subloops. Interestingly, over 85% of the Ni reverses its magnetization by rotation, either in one step or through two successive rotations. These results are due to the single-crystal nature of the antiferromagnetic FeF2 , which breaks down into two opposite regions of large domains.

Pulsed-field studies of the magnetization reversal in molecular nanomagnets

We report experimental studies of crystals of Mn12 molecular magnetic clusters in pulsed magnetic fields with sweep rates up to 410^3 T/s . The steps in the magnetization curve are observed at fields that are shifted with respect to the resonant field values. The shift systematically increases as the rate of the field sweep goes up. These data are consistent with the theory of the collective dipolar relaxation in molecular magnets.

Cation distribution and high field magnetization studies on SrFe12-xCrxO19

With the aim of a better understanding of both cationic distribution and magnetic properties of the uniaxial SrFe12-xCrxO19hexagonal ferrites, Mössbauer spectroscopy, neutron diffraction and high field magnetization measurements have been carried out. The Cr3+ions occupy the octahedral sites of the M structure with a preference hierarchy within them. The magnetic measurements, together with the deduced cationic distribution, indicate that some sublattices have a random spin canting around the c-axis.

Solvable dynamics in a system of interacting random tops

A new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops or magnetic moments with random precession frequencies. The model allows for an explicit study of orientational effects in synchronization phenomena as well as nonlinear processes in resonance phenomena in strongly coupled magnetic systems. A stability analysis of the incoherent solution is performed for different types of orientational disorder. A system with orientational disorder always synchronizes in the absence of noise.

Exactly solvable phase oscillator models with syncrhonization dynamics

Populations of phase oscillators interacting globally through a general coupling function f(x) have been considered. We analyze the conditions required to ensure the existence of a Lyapunov functional giving close expressions for it in terms of a generating function. We have also proposed a family of exactly solvable models with singular couplings showing that it is possible to map the synchronization phenomenon into other physical problems. In particular, the stationary solutions of the least singular coupling considered, f(x) = sgn(x), have been found analytically in terms of elliptic functions. This last case is one of the few nontrivial models for synchronization dynamics which can be analytically solved.

Comment on "Neutron brillouin scattering study of collective dynamics in a dense He-Ne gaseous mixture"

A Comment on the Letter by Ubaldo Bafile, et al., Phys. Rev. Lett. 86, 1019 (2001). The authors of the Letter offer a Reply.

Critical clusters and efficient dynamics for frustrated spin models

A general method to find, in a systematic way, efficient Monte Carlo cluster dynamics among the avast class of dynamics introduced by Kandel et al. [Phys. Rev. Lett. 65, 941 (1990)] is proposed. The method is successfully applied to a class of frustrated two-dimensional Ising systems. In the case of the fully frustrated model, we also find the intriguing result that critical clusters consist of self-avoiding walk at the theta point.