Lagrange-Fedosov Nonholonomic Manifolds

We outline an unified approach to geometrization of Lagrange mechanics, Finsler geometry and geometric methods of constructing exact solutions with generic off-diagonal terms and nonholonomic variables in gravity theories. Such geometries with induced almost symplectic structure are modelled on nonholonomic manifolds provided with nonintegrable distributions defining nonlinear connections. We introduce the concept of Lagrange-Fedosov spaces and Fedosov nonholonomic manifolds provided with almost symplectic connection adapted to the nonlinear connection structure. We investigate the main properties of generalized Fedosov nonholonomic manifolds and analyze exact solutions defining almost symplectic Einstein spaces.Comment: latex2e, v3, published variant, with new S.V. affiliatio

Assessment of Mixing in Passive Microchannels with Fractal Surface Patterning

We explore numerically the feasibility of enhancing the mixing capability of microchannels by employing the Weierstrass fractal function to generate a pattern of V-shaped ridges on the channel floor. Motivated by experimental limitations such as the finite resolution (similar to 10 mu m) associated with rapid prototyping through soft lithography techniques, we study the influence on the quality of mixing of having finite width ridges. The mixing capability of the designs studied is evaluated using an entropic measure and the designs are optimized with respect to: the distances between the ridges and the position range of their tip along the width of the channels. The results are evaluated with respect to the benchmarks established by the very successful staggered herring bone (SHB) design. We find that the use of a non periodic protocol to generate the geometry of the bottom surface of the microchannels can lead to consistently larger entropic mixing indices than in cyclic structures. Furthermore, since the optimization curves (mixing index vs. geometric parameters) are broader at the maximum for fractal microchannels than for their SHB counterparts, the microchannel designs using the Weierstrass fractal function are less sensitive to experimental uncertainties

High domain wall velocities induced by current in ultrathin Pt/Co/AlOx wires with perpendicular magnetic anisotropy

Current-induced domain wall (DW) displacements in an array of ultrathin Pt/Co/AlOx wires with perpendicular magnetic anisotropy have been directly observed by wide field Kerr microscopy. DWs in all wires in the array were driven simultaneously and their displacement on the micrometer-scale was controlled by the current pulse amplitude and duration. At the lower current densities where DW displacements were observed (j less than or equal to 1.5 x 10^12 A/m^2), the DW motion obeys a creep law. At higher current density (j = 1.8 x 10^12 A/m^2), zero-field average DW velocities up to 130 +/- 10 m/s were recorded.Comment: Minor changes to Fig. 1(b) and text, correcting for the fact that domain walls were subsequently found to move counter to the electron flow. References update

Domain wall tilting in the presence of the Dzyaloshinskii-Moriya interaction in out-of-plane magnetized magnetic nanotracks

We show that the Dzyaloshinskii-Moriya interaction (DMI) can lead to a tilting of the domain wall (DW) surface in perpendicularly magnetized magnetic nanotracks when DW dynamics is driven by an easy axis magnetic field or a spin polarized current. The DW tilting affects the DW dynamics for large DMI and the tilting relaxation time can be very large as it scales with the square of the track width. The results are well explained by an analytical model based on a Lagrangian approach where the DMI and the DW tilting are included. We propose a simple way to estimate the DMI in a magnetic multilayers by measuring the dependence of the DW tilt angle on a transverse static magnetic field. Our results shed light on the current induced DW tilting observed recently in Co/Ni multilayers with inversion asymmetry, and further support the presence of DMI in these systems.Comment: 12 pages, 3 figures, 1 Supplementary Material

Electric-field control of domain wall nucleation and pinning in a metallic ferromagnet

The electric (E) field control of magnetic properties opens the prospects of an alternative to magnetic field or electric current activation to control magnetization. Multilayers with perpendicular magnetic anisotropy (PMA) have proven to be particularly sensitive to the influence of an E-field due to the interfacial origin of their anisotropy. In these systems, E-field effects have been recently applied to assist magnetization switching and control domain wall (DW) velocity. Here we report on two new applications of the E-field in a similar material : controlling DW nucleation and stopping DW propagation at the edge of the electrode

Magnetic domain wall motion in a nanowire: depinning and creep

The domain wall motion in a magnetic nanowire is examined theoretically in the regime where the domain wall driving force is weak and its competition against disorders is assisted by thermal agitations. Two types of driving forces are considered; magnetic field and current. While the field induces the domain wall motion through the Zeeman energy, the current induces the domain wall motion by generating the spin transfer torque, of which effects in this regime remain controversial. The spin transfer torque has two mutually orthogonal vector components, the adiabatic spin transfer torque and the nonadiabatic spin transfer torque. We investigate separate effects of the two components on the domain wall depinning rate in one-dimensional systems and on the domain wall creep velocity in two-dimensional systems, both below the Walker breakdown threshold. In addition to the leading order contribution coming from the field and/or the nonadiabatic spin transfer torque, we find that the adiabatic spin transfer torque generates corrections, which can be of relevance for an unambiguous analysis of experimental results. For instance, it is demonstrated that the neglect of the corrections in experimental analysis may lead to incorrect evaluation of the nonadiabaticity parameter. Effects of the Rashba spin-orbit coupling on the domain wall motion are also analyzed.Comment: 14 pages, 3 figure

Finsler Branes and Quantum Gravity Phenomenology with Lorentz Symmetry Violations

A consistent theory of quantum gravity (QG) at Planck scale almost sure contains manifestations of Lorentz local symmetry violations (LV) which may be detected at observable scales. This can be effectively described and classified by models with nonlinear dispersions and related Finsler metrics and fundamental geometric objects (nonlinear and linear connections) depending on velocity/ momentum variables. We prove that the trapping brane mechanism provides an accurate description of gravitational and matter field phenomena with LV over a wide range of distance scales and recovering in a systematic way the general relativity (GR) and local Lorentz symmetries. In contrast to the models with extra spacetime dimensions, the Einstein-Finsler type gravity theories are positively with nontrivial nonlinear connection structure, nonholonomic constraints and torsion induced by generic off-diagonal coefficients of metrics, and determined by fundamental QG and/or LV effects.Comment: latex2e, 11pt, 34 pages, the version accepted to Class. Quant. Gra

On General Solutions for Field Equations in Einstein and Higher Dimension Gravity

We prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing exact solutions in gravity. The main idea of this method is to introduce on (pseudo) Riemannian manifolds an alternative (to the Levi-Civita connection) metric compatible linear connection which is also completely defined by the same metric structure. Such a canonically distinguished connection is with nontrivial torsion which is induced by some nonholonomy frame coefficients and generic off-diagonal terms of metrics. It is possible to define certain classes of adapted frames of reference when the Einstein equations for such an alternative connection transform into a system of partial differential equations which can be integrated in very general forms. Imposing nonholonomic constraints on generalized metrics and connections and adapted frames (selecting Levi-Civita configurations), we generate exact solutions in Einstein gravity and extra dimension generalizations.Comment: latex 2e, 11pt, 40 pages; it is a generalizaton with modified title, including proofs and additional results for higher dimensional gravity of the letter v1, on 14 pages; v4, with new abstract, modified title and up-dated references is accepted by Int. J. Theor. Phy

On Finslerized Absolute Parallelism spaces

The aim of the present paper is to construct and investigate a Finsler structure within the framework of a Generalized Absolute Parallelism space (GAP-space). The Finsler structure is obtained from the vector fields forming the parallelization of the GAP-space. The resulting space, which we refer to as a Finslerized Parallelizable space, combines within its geometric structure the simplicity of GAP-geometry and the richness of Finsler geometry, hence is potentially more suitable for applications and especially for describing physical phenomena. A study of the geometry of the two structures and their interrelation is carried out. Five connections are introduced and their torsion and curvature tensors derived. Some special Finslerized Parallelizable spaces are singled out. One of the main reasons to introduce this new space is that both Absolute Parallelism and Finsler geometries have proved effective in the formulation of physical theories, so it is worthy to try to build a more general geometric structure that would share the benefits of both geometries.Comment: Some references added and others removed, PACS2010, Typos corrected, Amendemrnts and revisions performe