On correspondence between tensors and bispinors

It is known that in the four-dimensional Riemannian space the complex bispinor generates a number of tensors: scalar, pseudo-scalar, vector, pseudo-vector, antisymmetric tensor. This paper solves the inverse problem: the above tensors are arbitrarily given, it is necessary to find a bispinor (bispinors) reproducing the tensors. The algorithm for this mapping constitutes construction of Hermitean matrix $M$ from the tensors and finding its eigenvalue spectrum. A solution to the inverse problem exists only when $M$ is nonnegatively definite. Under this condition a matrix $Z$ satisfying equation $M=ZZ^{+}$ can be found. One and the same system of tensor values can be used to construct the matrix $Z$ accurate to an arbitrary factor on the left-hand side, viz. unitary matrix $U$ in polar expansion $Z=HU$. The matrix $Z$ is shown to be expandable to a set of bispinors, for which the unitary matrix $U$ is responsible for the internal (gauge) degrees of freedom. Thus, a group of gauge transformations depends only on the Riemannian space dimension, signature, and the number field used. The constructed algorithm for mapping tensors to bispinors admits extension to Riemannian spaces of a higher dimension.Comment: 14 pages;LaTeX2e;to appear in the 9th Marcel Grossmann Meeting (MG9) Proceedings,Rome, July, 200

A Comprehensive Strategy for Longitudinal Vehicle Control with Fuzzy Supervisory Expert System

The main objectives of vehicle motion control on an automated highway system are stable and safe automatic longitudinal and/or lateral path following in a platoon of vehicles. Various controllers can be used to satisfy the same objectives, but they may require different variables to be sensed or different conditions to be met. Supervision can select a controller and switch to a different controller depending on the conditions. Specifically, a fuzzy supervisory expert system checks for various system conditions and chooses a controller from PID, PI, sliding mode and a fuzzy controller or gives a distress signal. The choice between PID and PI controllers is based on the availability of the error derivative. Robust and complex sliding mode control can counter the external disturbances which the PID and PI controllers cannot handle. The fuzzy controller is used when the sensors are not working perfectly but the sensor values are still reliable enough to define corresponding fuzzy linguistic variables

Physical Vacuum Properties and Internal Space Dimension

The paper addresses matrix spaces, whose properties and dynamics are determined by Dirac matrices in Riemannian spaces of different dimension and signature. Among all Dirac matrix systems there are such ones, which nontrivial scalar, vector or other tensors cannot be made up from. These Dirac matrix systems are associated with the vacuum state of the matrix space. The simplest vacuum system realization can be ensured using the orthonormal basis in the internal matrix space. This vacuum system realization is not however unique. The case of 7-dimensional Riemannian space of signature 7(-) is considered in detail. In this case two basically different vacuum system realizations are possible: (1) with using the orthonormal basis; (2) with using the oblique-angled basis, whose base vectors coincide with the simple roots of algebra E_{8}. Considerations are presented, from which it follows that the least-dimension space bearing on physics is the Riemannian 11-dimensional space of signature 1(-)& 10(+). The considerations consist in the condition of maximum vacuum energy density and vacuum fluctuation energy density.Comment: 19 pages, 1figure. Submitted to General Relativity and Gravitatio

Evolutionary game of coalition building under external pressure

We study the fragmentation-coagulation (or merging and splitting) evolutionary control model as introduced recently by one of the authors, where $N$ small players can form coalitions to resist to the pressure exerted by the principal. It is a Markov chain in continuous time and the players have a common reward to optimize. We study the behavior as $N$ grows and show that the problem converges to a (one player) deterministic optimization problem in continuous time, in the infinite dimensional state space

Melting Point and Lattice Parameter Shifts in Supported Metal Nanoclusters

The dependencies of the melting point and the lattice parameter of supported metal nanoclusters as functions of clusters height are theoretically investigated in the framework of the uniform approach. The vacancy mechanism describing the melting point and the lattice parameter shifts in nanoclusters with decrease of their size is proposed. It is shown that under the high vacuum conditions (p<10^-7 torr) the essential role in clusters melting point and lattice parameter shifts is played by the van der Waals forces of cluster-substrate interation. The proposed model satisfactorily accounts for the experimental data.Comment: 6 pages, 3 figures, 1 tabl

Low Energy Electron and Nuclear Recoil Thresholds in the DRIFT-II Negative Ion TPC for Dark Matter Searches

Understanding the ability to measure and discriminate particle events at the lowest possible energy is an essential requirement in developing new experiments to search for weakly interacting massive particle (WIMP) dark matter. In this paper we detail an assessment of the potential sensitivity below 10 keV in the 1 m^3 DRIFT-II directionally sensitive, low pressure, negative ion time projection chamber (NITPC), based on event-by-event track reconstruction and calorimetry in the multiwire proportional chamber (MWPC) readout. By application of a digital smoothing polynomial it is shown that the detector is sensitive to sulfur and carbon recoils down to 2.9 and 1.9 keV respectively, and 1.2 keV for electron induced events. The energy sensitivity is demonstrated through the 5.9 keV gamma spectrum of 55Fe, where the energy resolution is sufficient to identify the escape peak. The effect a lower energy sensitivity on the WIMP exclusion limit is demonstrated. In addition to recoil direction reconstruction for WIMP searches this sensitivity suggests new prospects for applications also in KK axion searches

The DRIFT Dark Matter Experiments

The current status of the DRIFT (Directional Recoil Identification From Tracks) experiment at Boulby Mine is presented, including the latest limits on the WIMP spin-dependent cross-section from 1.5 kg days of running with a mixture of CS2 and CF4. Planned upgrades to DRIFT IId are detailed, along with ongoing work towards DRIFT III, which aims to be the world's first 10 m3-scale directional Dark Matter detector.Comment: Proceedings of the 3rd International conference on Directional Detection of Dark Matter (CYGNUS 2011), Aussois, France, 8-10 June 201