54 research outputs found
Deterministic growth model of Laplacian charged particle aggregates
The results of the computer simulation of the aggregates growth of the
similarly charged particles in the framework of deterministic Laplacian growth
model on a square lattice are presented. Cluster growth is controlled by three
parameters , where - Laplacian growth parameter, -
energy of a particle sticking to a cluster, - the screening length of
electrostatic interactions. The phase diagram of cluster growth is built in the
co-ordinates . The zones of different cluster morphology are
selected: I-the zone of finite X-like structures,II-the zone of infinite
ramified structures, controlled by electrostatic interactions, III-the zone of
infinite structures with electrostatic interactions effectively switched off.
Simple electrostatic estimations of the locations of the zone boundaries are
presented. It is shown that in general case within the zone II the continuous
change of , controlled by parameters , takes place. In the
degeneration limit when the given model transforms into deterministic version
of the Eden model (at ), the crossover from linear to compact
structures is observed when passing through the boundary between the
zones I and II.Comment: REVTEX, 3 pages with 4 postscript figure
Complex Kerr Geometry, Twistors and the Dirac Electron
The Kerr-Newman spinning particle displays some remarkable relations to the
Dirac electron and has a reach spinor structure which is based on a twistorial
description of the Kerr congruence determined by the Kerr theorem. We consider
the relation between this spinor-twistorial structure and spinors of the Dirac
equation, and show that the Dirac equation may naturally be incorporated into
Kerr-Schild formalism as a master equation controlling the twistorial structure
of Kerr geometry. As a result, the Dirac electron acquires an extended
space-time structure having clear coordinate description with natural
incorporation of a gravitational field. The relation between the Dirac wave
function and Kerr geometry is realized via a chain of links: {\it Dirac wave
function Complex Kerr-Newman Source Kerr
Theorem Real Kerr geometry.} As a result, the wave function
acquires the role of an ``order parameter'' which controls spin, dynamics, and
twistorial polarization of Kerr-Newman space-time.Comment: 12 pages, 3 figs. Talk at the conference QFEXT'0
SOME PROPERTIES OF THE KERR SOLUTION TO LOW ENERGY STRING THEORY
The Kerr solution to axidilaton gravity is analyzed in the
Debney--Kerr--Schild formalism. It is shown that the Kerr principal null
congruence retains its property to be geodesic and shear free, however, the
axidilatonic Kerr solution is not algebraically special. A limiting form of
this solution is considered near the ring-like Kerr singularity. This limiting
solution coincides with the field around a fundamental heterotic string
obtained by Sen.Comment: 14 pages., LaTe
Structure of Spinning Particle Suggested by Gravity, Supergravity and Low Energy String Theory
The structure of spinning particle suggested by the rotating Kerr-Newman
(black hole) solution, super-Kerr-Newman solution and the Kerr-Sen solution to
low energy string theory is considered. Main peculiarities of the Kerr spinning
particle are discussed: a vortex of twisting principal null congruence,
singular ring and the Kerr source representing a rotating relativistic disk of
the Compton size. A few stringy structures can be found in the real and complex
Kerr geometry.
Low-energy string theory predicts the existence of a heterotic string placed
on the sharp boundary of this disk. The obtained recently supergeneralization
of the Kerr-Newman solution suggests the existence of extra axial singular line
and fermionic traveling waves concentrating near these singularities.
We discuss briefly a possibility of experimental test of these predictions.Comment: Latex, 8 pages, talk at the International Workshop Spin'99, Prague,
5-11 September, 199
Rotating Black Hole, Twistor-String and Spinning Particle
We discuss basic features of the model of spinning particle based on the Kerr
solution. It contains a very nontrivial {\it real} stringy structure consisting
of the Kerr circular string and an axial stringy system.
We consider also the complex and twistorial structures of the Kerr geometry
and show that there is a {\it complex} twistor-string built of the complex N=2
chiral string with a twistorial structure. By imbedding into the
real Minkowski , the N=2 supersymmetry is partially broken and string
acquires the open ends. Orientifolding this string, we identify the chiral and
antichiral structures. Target space of this string is equivalent to the
Witten's `diagonal' of the Comment: 19 p. 4 figures, extended version of hep-th/0412065, based on the
talk given at the Conference `Symmetries and Spin'(SPIN-Praha-2004) July 200
Nuclear matter at high density: Phase transitions, multiquark states, and supernova outbursts
Phase transition from hadronic matter to quark-gluon matter is discussed for
various regimes of temperature and baryon number density. For small and medium
densities, the phase transition is accurately described in the framework of the
Field Correlation Method, whereas at high density predictions are less certain
and leave room for the phenomenological models. We study formation of
multiquark states (MQS) at zero temperature and high density. Relevant MQS
components of the nuclear matter can be described using a previously developed
formalism of the quark compound bags (QCB).
Partial-wave analysis of nucleon-nucleon scattering indicates the existence
of 6QS which manifest themselves as poles of -matrix. In the framework of
the QCB model, we formulate a self-consistent system of coupled equations for
the nucleon and 6QS propagators in nuclear matter and the G-matrix. The
approach provides a link between high-density nuclear matter with the MQS
components and the cumulative effect observed in reactions on the nuclei, which
requires the admixture of MQS in the wave functions of nuclei kinematically.
6QS determine the natural scale of the density for a possible phase
transition into the MQS phase of nuclear matter. Such a phase transition can
lead to dynamic instability of newly born protoneutron stars and dramatically
affect the dynamics of supernovae. Numerical simulations show that the phase
transition may be a good remedy for the triggering supernova explosions in the
spherically symmetric supernova models. A specific signature of the phase
transition is an additional neutrino peak in the neutrino light curve. For a
Galactic core-collapse supernova, such a peak could be resolved by the present
neutrino detectors. The possibility of extracting the parameters of the phase
of transition from observation of the neutrino signal is discussed also.Comment: 57 pages, 22 figures, 7 tables; RevTeX 4; submitted to Phys. Atom.
Nuc
A cyclic universe with colour fields
The topology of the universe is discussed in relation to the singularity
problem. We explore the possibility that the initial state of the universe
might have had a structure with 3-Klein bottle topology, which would lead to a
model of a nonsingular oscillating (cyclic) universe with a well-defined
boundary condition. The same topology is assumed to be intrinsic to the nature
of the hypothetical primitive constituents of matter (usually called preons)
giving rise to the observed variety of elementary particles. Some
phenomenological implications of this approach are also discussed.Comment: 21 pages, 9 figures; v.4: final versio
Невизначеність та відсутність арбітражної можливості
A new classification of the decision-making situations is proposed. It is based on the notion of uncertainty in matrix scheme of the situation. Such an approach to the classification of the decision-making situations differs from known approach, according to which the situations with risk and uncertainty are distinguished depending on the presence of probability distribution on the values of an unknown parameter. The necessary and sufficient conditions for existence of uncertainty in matrix scheme are established. The proposed notion of uncertainty is applied to the analysis of the financial markets. It is shown that the absence of an arbitrage opportunity on the financial market in the Arrow–Debreu model with a riskless asset is a particular case of the existence of uncertainty in the decision-making situation. This result gives an opportunity to view the no–arbitrage pricing theory for financial instruments as a branch of the general decision theory.Предложена новая классификация ситуаций принятия решений, в основе которой лежит понятие неопределенности в матричной схеме ситуации. Такой подход к классификации ситуаций принятия решений отличается от известного, согласно которому разделяют ситуации с риском и неопределенностью в зависимости от наличия распределения вероятностей на множестве значений неизвестного параметра. Установлены необходимые и достаточные условия существования неопределенности в матричной схеме. Предложенная классификация применена в анализе финансовых рынков. Показано, что отсутствие арбитражной возможности на финансовом рынке в модели Эрроу-Дебре с безрисковым активом есть частным случаем существования неопределенности в матричной схеме ситуации принятия решений. Этот результат даёт возможность рассматривать теорию безарбитражного оценивания финансовых инструментов как ветвь общей теории решений.Запропоновано нову класифікацію ситуацій прийняття рішень, в основі якої знаходиться поняття невизначеності в матричній схемі ситуації. Такий підхід до класифікації ситуацій прийняття рішень відрізняється від відомого, згідно з яким розрізняють ситуації з ризиком та невизначеністю в залежності від наявності розподілу ймовірностей на множині значень невідомого параметра. Встановлено необхідні й достатні умови існування невизначеності в матричній схемі. Запропоновану класифікацію застосовано в аналізі фінансових ринків. Показано, що відсутність арбітражної можливості на фінансовому ринку в моделі Ерроу-Дебре з безризиковим активом є частковим випадком існування невизначеності в матричній схемі ситуації прийняття рішень. Цей результат дає можливість розглядати теорію безарбітражного оцінювання фінансових інструментів як галузь загальної теорії рішень
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