Some theoretical and experimental aspects of the tachyon problem

In this paper, the hypothetical existence of tachyons is re-examined. It has previously been doubted whether tachyons would exist, for it can be shown with the space-time diagram used in the Special Theory of Relativity that they are moving backward in time for some moving systems, and this would contradict the principle of causality. Some scientists tried to save the tachyon theory by using the so-called reinterpretation principle, but it is considered that this can be easily refuted. This paper shows that it can be concluded from the Einstein-Planck frequency relation and the de Broglie wave equation that the absolute value of the mass of the tachyons must be much lower than the rest mass of the electrons-nearly zero. But that means that they do not have any measurable energy if they move with a finite value aboutc. But if tachyons withv>c cannot be measured they cannot cause causality paradoxes. The low mass of the tachyons has also consequences for experimental search, and it will be shown that the previous search was doomed to failure. The limits of the photo-production cross-section for tachyons in lead can be given as 1.5·10^?32?σ<7·10^?31 cm². Further, it can be shown that the kinetic energy of the tachyons is identical to their total energy. We see that tachyons cannot be regarded as ‘faster than light particles’ — they are more a new kind of luxons. If they were to be uncharged it would be nearly impossible to distinguish them from this class of particles.     

Some theoretical aspects of the presence of spin in proton proton elastic scattering

Some theoretical aspects on the problem of spin in proton proton elastic scattering in the range of energy starting from few GeV/c up to ISR energies are discussed.Presented at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.I thank A.Martin and J.Soffer for their help in preparing this talk.     

Some theoretical aspects of elastic wave modeling with a recently developed spectral element method

A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media, based on the Galerkin approach applied to a partition, in small subdomains, of the original physical domain. In this work, some mathematical aspects of the method and the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobatto collocation points are introduced. The related integration formulas are obtained. The standard error estimations and expansion convergence are discussed. An element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence, neither the global matrices nor the effective force vector is assembled. When analytical formulas are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without losing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes this method much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The first part mainly focuses on theoretical studies with a simple numerical result for the Che-byshev spectral element, and the second part, mainly with the Legendre spectral element, will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the detailed modeling example comparisons of the proposed spectral element method with a pseudo-spectral method, which will be seen in another work by Lin, Wang and Zhang.     

Some aspects of thermal self-focusing

The factors influencing the intensity at the focal point of a steady thermally self-focused beam are considered in detail and it is shown that in this case the beam will not split into filaments. The self-focusing of short pulses is considered and is shown that the shape of the focus depends on the time constant associated with the change of refractive index.     

Some formal aspects of subdynamics

The theory of subdynamics is formulated assuming the existence of a spectral representation of the collision operator. This approach avoids perturbation schemes; however the presentation is formal. It may be used to develop further the theory as well as a starting point for a rigorous mathematical discussion. The construction of the operators introduced in the theory of subdynamics is presented in detail. Some questions related to the transformation theory leading to the so-called “physical representation” are briefly discussed.     

Some aspects of Kaluza-Klein cosmology

This article contains a brief account of Kaluza-Klein theory and its applications in cosmology from the very beginning.     

Some stochastic aspects of quantization

From the advent of quantum mechanics, various types of stochastic-dynamical approach to quantum mechanics have been tried. We discuss how to utilize Nelson’s stochastic quantum mechanics to analyze the tunneling phenomena, how to derive relativistic field equations via the Poisson process and how to describe a quantum dynamics of open systems by the use of quantum state diffusion, or the stochastic Schrödinger equation.     

Some aspects of positronium physics

Some aspects of both theoretical and experimental study of the positronium system to probe physics beyond the Standard Model are reviewed. In particular, new experiments to search for the invisible decay of orthopositronium (o-Ps) with the sensitivity in the branching ratio Br(o-Ps → invisible) ≃ 10⁻⁸–10⁻⁷ are discussed. The experimental technique involves a specially designed high-efficiency pulsed slow positron beam, which is also applicable for other experiments with o-Ps in vacuum. Details of the beam design, as well as the first measurements results are presented. Possible applications of the slow-pulsed positron beam for materials research are discussed. The text was submitted by the authors in English.     

Some geometric aspects of maps

In this talk we introduce a Weierstrass-like system of equations corresponding to CP N -1 fields in two dimensions. Then using this representation we introduce a vector in R N 2-1 and treating this vector as the radius vector of a surface immersed in R N 2-1 we discuss to what extent the associated metric describes the geometry of the CP N -1 maps. We show that for the holomorphic maps - the correspondence is exact; while for the more general fields we have to go beyond the Weierstrass system and add extra terms. Received 1st August 2001 / Received in final form 18 October 2001 Published online 2 October 2002 RID="a" ID="a"Work done in collaboration with M. Grundland e-mail: w.j.zakrzewski@durham.ac.uk     

Some aspects of single-grain luminescence dating

Single-grain methods of luminescence dating have been developed in order to circumvent problems of variability among aliquots of the sample being dated. Sufficient single grains must be separated in order to make an appropriate interpretation of the variability among such grains. We describe an automated apparatus for sorting grains for routine age determinations by green light stimulation. The sorted grains are then available for study of their collective luminescence physics characteristics. Examples are given of statistical frequency functions of grain brightness obtained with the apparatus and their interpretation. These frequency functions are lognormal or similar, covering up to four orders of magnitude, with consequent implications for luminescence dating application.     

Some new aspects of dendrimer applications

Dendrimers are characterized by special features that make them promising candidates for many applications. Here we focus on two such applications: dendrimers as light harvesting antennae, and dendrimers as molecular amplifiers, which may serve as novel platforms for drug delivery. Both applications stem from the unique structure of dendrimers. We present a theoretical framework based on the master equation within which we describe these applications. The quantities of interest are the first passage time (FPT), probability density function (PDF) and its moments. We examine how the FPT PDF and its characteristics depend on the geometric and energetic structures of the dendrimeric system. In particular, we investigate the dependence of the FPT properties on the number of generations (dendrimer size) and the system bias. We present analytical expressions for the FPT PDF for very efficient dendrimeric antennae and for dendrimeric amplifiers. For these cases the mean FPT scales linearly with the system length, and fluctuations around the mean FPT are negligible for large systems. Relationships of the FPT to light harvesting process for other types of system-bias are discussed.     

Some aspects of laser-metal vapour interaction

The vapour beam interaction plays an important role in laser machining process, since the vapour generated on the workpiece surface absorbs some fraction of the incident beam and heats the workpiece surface. Consequently, a study of this interaction mechanism is essential. For this purpose, a computer program was developed to investigate the interaction interaction, it provides a foundation to do further studies. It was found that the vapour locally high pressure gradients. Although the analysis presents a simplified picture of the interaction, it provides a foundation to do further studies. It was found that the vapour temperature reaches 5000 K after 10⁻⁶ s for a laser pulse of 10¹¹ W/m² power intensity. The leading edge of the vapour velocity had a velocity of the order of 4000–7000 m/s.     

Some aspects of gravitational quantum mechanics

String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle. Such a modified Heisenberg uncertainty principle is referred as gravitational uncertainty principle(GUP) in literatures. This proposal has some novel implications on various domains of theoretical physics. Here, we study some consequences of GUP in the spirit of Quantum mechanics. We consider two problem: a particle in an one-dimensional box and free particle wave function. In each case we will solve corresponding perturbational equations and compare the results with ordinary solutions.     

Some aspects of R-parity violating supersymmetry

I briefly review a scenario where R-parity is explicitly broken through a term bilinear in the lepton and Higgs superfields in the superpotential. An immediate consequence of the presence of this term is the generation of a massive neutrino at the tree level. Constraints on the parameter space are discussed in the context of recent super-Kamiokande results on atmospheric neutrinos. The testability of such models is emphasized through the observation of comparable numbers of muons and taus, produced together with the H⁻-boson, in decays of the lightest neutralino. Some other phenomenological implications of such a scenario are also discussed.     

Some aspects of negative ion chemistry

In a classic early review on ion-molecule reactions, a table of negative ion-neutral reactions for which quantitative data were available had 9 entries. In a recent review on negative ion-neutral reactions alone, tables of negative ion-neutral reaction rate constants included 174 reactions, reflecting the increase in knowledge in this field in a little over one decade. In this paper some of the negative ion-neutral reaction studies done at Boulder in a flowing afterglow system are discussed. Some of the current research on both positive and negative ions in the recently developed Flow-Drift Tube are discussed, including both mobility and reaction rate constant measurements.     

Some aspects of scanning electron microscopy

The main components of the SEM are the signal generation and the signal detection and display systems. A finely focussed electron beam scans the specimen surface. Due to the interaction between electrons and solid, signals such as secondary emission, light, X-radiation and currents are generated. Depending on the selected detection system the displayed images provide a variety of information, such as topography, element distribution, surface voltage, luminescence, conductivity, etc. The useful application of the SEM ranges from surface study to bulk analysis to device fabrication.     

Some aspects of virtual black holes

We first consider consistently third-quantize modified gravity. We then analyze certain aspects of virtual black holes in this third-quantized modified gravity. We see how a statistical mechanical origin for the Bekenstein-Hawking entropy naturally arises in this model. Furthermore, the area and hence the entropy of a real macroscopic black hole is quantized in this model. Virtual black holes cause a loss of quantum coherence, which gives an intrinsic entropy to all physical systems that can be used to define a direction of time and hence provide a solution to the problem of time.