Search results for "vector [correlation function]"
showing 10 items of 339 documents
Normalizability, Synchronicity, and Relative Exactness for Vector Fields in C2
2004
In this paper, we study the necessary and su.cient condition under which an orbitally normalizable vector field of saddle or saddle-node type in C2 is analytically conjugate to its formal normal form (i.e., normalizable) by a transformation fixing the leaves of the foliation locally. First, we express this condition in terms of the relative exactness of a certain 1-form derived from comparing the time-form of the vector field with the time-form of the normal form. Then we show that this condition is equivalent to a synchronicity condition: the vanishing of the integral of this 1-form along certain asymptotic cycles de.ned by the vector field. This can be seen as a generalization of the clas…
The generic local structure of time-optimal synthesis with a target of codimension one in dimension greater than two
1997
In previous papers, we gave in dimension 2 and 3 a classification of generic synthesis of analytic systems\(\dot v(t) = X(v(t)) + u(t)Y(v(t))\) with a terminal submanifoldN of codimension one when the trajectories are not tangent toN. We complete here this classification in all generic cases in dimension 3, giving a topological classification and a model in each case. We prove also that in dimensionn≥3, out of a subvariety ofN of codimension there, we have described all the local synthesis.
A system-level mathematical model of Basal Ganglia motor-circuit for kinematic planning of arm movements
2017
International audience; In this paper, a novel system-level mathematical model of the Basal Ganglia (BG) for kinematic planning, is proposed. An arm composed of several segments presents a geometric redundancy. Thus, selecting one trajectory among an infinite number of possible ones requires overcoming redundancy, according to some kinds of optimization. Solving this optimization is assumed to be the function of BG in planning. In the proposed model, first, a mathematical solution of kinematic planning is proposed for movements of a redundant arm in a plane, based on minimizing energy consumption. Next, the function of each part in the model is interpreted as a possible role of a nucleus of…
Transportation-cost inequality on path spaces with uniform distance
2008
Abstract Let M be a complete Riemannian manifold and μ the distribution of the diffusion process generated by 1 2 ( Δ + Z ) where Z is a C 1 -vector field. When Ric − ∇ Z is bounded below and Z has, for instance, linear growth, the transportation-cost inequality with respect to the uniform distance is established for μ on the path space over M . A simple example is given to show the optimality of the condition.
Alignment of the ALICE Inner Tracking System with cosmic-ray tracks
2010
ALICE (A Large Ion Collider Experiment) is the LHC (Large Hadron Collider) experiment devoted to investigating the strongly interacting matter created in nucleus-nucleus collisions at the LHC energies. The ALICE ITS, Inner Tracking System, consists of six cylindrical layers of silicon detectors with three different technologies; in the outward direction: two layers of pixel detectors, two layers each of drift, and strip detectors. The number of parameters to be determined in the spatial alignment of the 2198 sensor modules of the ITS is about 13,000. The target alignment precision is well below 10 micron in some cases (pixels). The sources of alignment information include survey measurement…
Numerical evolutions of spherical Proca stars
2017
Vector boson stars, or $\textit{Proca stars}$, have been recently obtained as fully non-linear numerical solutions of the Einstein-(complex)-Proca system. These are self-gravitating, everywhere non-singular, horizonless Bose-Einstein condensates of a massive vector field, which resemble in many ways, but not all, their scalar cousins, the well-known (scalar) $\textit{boson stars}$. In this paper we report fully-non linear numerical evolutions of Proca stars, focusing on the spherically symmetric case, with the goal of assessing their stability and the end-point of the evolution of the unstable stars. Previous results from linear perturbation theory indicate the separation between stable and…
Almost-Killing conserved currents: A general mass function
2013
A new class of conserved currents, describing non-gravitational energy-momentum density, is presented. The proposed currents do not require the existence of a (timelike) Killing vector, and are not restricted to spherically symmetric spacetimes (or similar ones, in which the Kodama vector can be defined). They are based instead on almost-Killing vectors, which could in principle be defined on generic spacetimes. We provide local arguments, based on energy density profiles in highly simplified (stationary, rigidly-rotating) star models, which confirm the physical interest of these 'almost-Killing currents'. A mass function is defined in this way for the spherical case, qualitatively differen…
Understanding the global structure of two-level quantum systems with relaxation: Vector fields organized through the magic plane and the steady-state…
2013
Exercises, Hints and Selected Solutions
2016
1.1. Prove the formula (1.8a) in Sect. 1.3, $$\displaystyle{ \int \mathrm{d}^{n}x\; =\int _{ 0}^{+\infty }\!\!\!\mathrm{d}r\;r^{n-1}\int _{ 0}^{2\pi }\!\!\!\mathrm{d}\phi \prod _{ k=1}^{n-2}\int _{ 0}^{\pi }\!\!\!\mathrm{d}\theta _{ k}\sin ^{k}(\theta _{ k}) }$$ (1.1) by means of induction.
Asymptotic Behaviour and Qualitative Properties of Solutions
2004
The purpose of this chapter is to give some qualitative properties of the flow $$ frac{{\partial u}}{{\partial t}} = div\left( {\frac{{Du}}{{\left| {Du} \right|}}} \right) in\;]0,\infty [ \times {\mathbb{R}^N} $$ (4.1) .