Search results for "classical"
showing 10 items of 2294 documents
Geometric versus numerical optimal control of a dissipative spin-12particle
2010
We analyze the saturation of a nuclear magnetic resonance (NMR) signal using optimal magnetic fields. We consider both the problems of minimizing the duration of the control and its energy for a fixed duration. We solve the optimal control problems by using geometric methods and a purely numerical approach, the grape algorithm, the two methods being based on the application of the Pontryagin maximum principle. A very good agreement is obtained between the two results. The optimal solutions for the energy-minimization problem are finally implemented experimentally with available NMR techniques.
Central role of the observable electric potential in transport equations.
2001
Nonequilibrium systems are usually studied in the framework of transport equations that involve the true electric potential (TEP), a nonobservable variable. Nevertheless another electric potential, the observable electric potential (OEP), may be defined to construct a useful set of transport equations. In this paper several basic characteristics of the OEP are deduced and emphasized: (i) the OEP distribution depends on thermodynamic state of the solution, (ii) the observable equations have a reference value for all other transport equations, (iii) the bridge that connects the OEP with a certain TEP is usually defined by the ion activity coefficient, (iv) the electric charge density is a non…
General-relativistic approach to the nonlinear evolution of collisionless matter.
1993
A new general-relativistic algorithm is developed to study the nonlinear evolution of scalar (density) perturbations of an irrotational collisionless fluid up to shell crossing, under the approximation of neglecting the interaction with tensor (gravitational-wave) perturbations. The dynamics of each fluid element is separately followed in its own inertial rest frame by a system of twelve coupled first-order ordinary differential equations, which can be further reduced to six under very general conditions. Initial conditions are obtained in a cosmological framework, from linear theory, in terms of a single gauge-invariant potential. Physical observables, which are expressed in the Lagrangian…
Spin-up instability of electromagnetically levitated spherical bodies
2000
Stability of a solid sphere in both uniform and linear alternating magnetic fields is considered with respect to virtual rotations. When the frequency of the alternating magnetic field exceeds a certain critical threshold depending on the configuration of the field, the sphere is found to spin up around a horizontal axis. The physical mechanism of this instability is the same as that of operation of a single-phase induction motor. Sufficiently small rotational disturbances can be completely suppressed by imposing an axial steady magnetic field of strength comparable to that of the alternating field. Nonlinear stability analysis shows that for sufficiently high frequencies, spin-up can be ca…
Bidirectional random motion driven by globally coupled noisy active elements in an electric field
2004
The assembly of the insulating Brownian particles globally coupled due to the macroscopic flow of the liquid with low conductivity has transitions between the states of random motion and random bidirectional and unidirectional motion. The threshold values of the parameters for the transition to random bidirectional motion is found by the effective field method and correspond to those found by Brownian dynamics. The behavior of the assembly is similar to the behavior of different active multistable systems.
Scattering and Localization of Classical Waves Along a Wave Guide with Disorder and Dissipation
1993
The problem of localization of classical waves has recently attracted consider-able attention.1,2 Classical waves have, of course, been the subject of extensive research already in the last century, as emphasized by Landauer in his historical sketch.3 A variety of interesting phenomena is associated with classical waves like seismic waves, tidal waves, acoustic as well as optical waves. A major topic is the transport of energy or information by these waves. The current interest in classical waves is stimulated by the development of microelectronics with its very small structures, in particular very thin wires (as connections between the components of integrated circuits) which may (or may n…
Stability and Chaos
2010
In this chapter we study a larger class of dynamical systems that include but go beyond Hamiltonian systems. We are interested, on the one hand, in dissipative systems, i.e. systems that lose energy through frictional forces or into which energy is fed from exterior sources, and, on the other hand, in discrete, or discretized, systems such as those generated by studying flows by means of the Poincare mapping. The occurence of dissipation implies that the system is coupled to other, external systems, in a controllable manner. The strength of such couplings appears in the set of solutions, usually in the form of parameters. If these parameters are varied it may happen that the flow undergoes …
Pattern formation through phase bistability in oscillatory systems with space-modulated forcing.
2010
We propose a novel forcing technique of spatially extended self-oscillatory systems able to excite phase bistability and the dissipative structures associated with it. The forcing is time periodic at a frequency close to the oscillators' frequency and is spatially modulated. The effects of this type of forcing are demonstrated analytically and numerically in a directly driven complex Ginzburg-Landau equation. Both spatially periodic and spatially random drives prove to be effective.
NEW DEVELOPMENTS ON INVERSE POLYGON MAPPING TO CALCULATE GRAVITATIONAL LENSING MAGNIFICATION MAPS: OPTIMIZED COMPUTATIONS
2011
We derive an exact solution (in the form of a series expansion) to compute gravitational lensing magnification maps. It is based on the backward gravitational lens mapping of a partition of the image plane in polygonal cells (inverse polygon mapping, IPM), not including critical points (except perhaps at the cell boundaries). The zeroth-order term of the series expansion leads to the method described by Mediavilla et al. The first-order term is used to study the error induced by the truncation of the series at zeroth order, explaining the high accuracy of the IPM even at this low order of approximation. Interpreting the Inverse Ray Shooting (IRS) method in terms of IPM, we explain the previ…
Current-Induced Dynamics of Chiral Magnetic Structures: Creation, Motion, and Applications
2021
Magnetic textures can be manipulated by electric currents via the mechanisms of spin-transfer and spin-orbit-torques. We review how these torques can be exploited to create chiral magnetic textures in magnets with broken inversion symmetries, including domain walls and skyrmions. These chiral textures can also be moved by (electric) currents and obey very rich dynamics. For example, magnetic domain walls feature the famous Walker breakdown, and magnetic whirls are subject to the skyrmion Hall effect, which is rooted in their real-space topology. These properties led to a variety of potential novel applications which we briefly overview.