Метод трехмерной триангуляции в задачах кластерного анализа

Представлен метод многомерного шкалирования на основе трехмерной триангуляции. Рассмотрена возможность качественного сохранения геометрической структуры множества объектов при отображении многомерного пространства в трехмерное. Приведены результаты применения метода для решения задачи кластеризации на примере периодической системы элементов Д.И. Менделеева. Экспериментально показано, что по критериям качества кластеризации предложенный метод более эффективен в сравнении с методами k-средних и нейронной сети Кохонена.Представлено метод багатовимірного шкалювання на основі тривимірної тріангуляції. Розглянуто можливість якісного збереження геометричної структури множини об’єктів при відображенні багатовимірного простору в тривимірне. Наведено результати застосування методу для вирішення задачі кластеризації на прикладі періодичної системи елементів Д.І. Менделєєва. Експериментально показано, що за критеріями якості кластеризації запропонований метод більш ефективний у порівнянні з методами k-середніх та нейронної мережі Кохонена.The method of multidimensional scaling on the basis of the 3-D triangulation is presented. The qualitative preservation possibility of geometrical structure of objects by multidimensional space mapping to three- dimensional space is considered. The results of application of the method for clustering problem of the Mendeleyev periodic table are presented. It is experimentally shown, that the presented method is more effective by criteria of clustering quality in comparison with the methods of k-averages and the Kohonen neural network

Quantum corrections to the ground state energy of a trapped Bose-Einstein condensate: A diffusion Monte Carlo calculation

The diffusion Monte Carlo method is applied to describe a trapped atomic Bose-Einstein condensate at zero temperature, fully quantum mechanically and nonperturbatively. For low densities, $n(0)a^3 \le 2 \cdot 10^{-3}$ [n(0): peak density, a: s-wave scattering length], our calculations confirm that the exact ground state energy for a sum of two-body interactions depends on only the atomic physics parameter a, and no other details of the two-body model potential. Corrections to the mean-field Gross-Pitaevskii energy range from being essentially negligible to about 20% for N=2-50 particles in the trap with positive s-wave scattering length a=100-10000 a.u.. Our numerical calculations confirm that inclusion of an additional effective potential term in the mean-field equation, which accounts for quantum fluctuations [see e.g. E. Braaten and A. Nieto, Phys. Rev. B 56}, 14745 (1997)], leads to a greatly improved description of trapped Bose gases.Comment: 7 pages, 4 figure

Synthesis and electron field emission of nanocrystalline diamond thin films grown from N2/CH4 microwave plasmas

Nanocrystalline diamond films have been synthesized by microwave plasma enhanced chemical vapor deposition using N2/CH4 as the reactant gas without additional H2. The nanocrystalline diamond phase has been identified by x-ray diffraction and transmission electron microscopy analyses. High resolution secondary ion mass spectroscopy has been employed to measure incorporated nitrogen concentrations up to 8 ×1020 atoms/cm3. Electron field emission measurements give an onset field as low as 3.2 V/μm. The effect of the incorporated nitrogen on the field emission characteristics of the nanocrystalline films is discussed

A 5D non compact and non Ricci flat Kaluza-Klein Cosmology

A model universe is proposed in the framework of 5-dimensional noncompact Kaluza-Klein cosmology which is not Ricci flat. The 4D part as the Robertson-Walker metric is coupled to conventional perfect fluid, and its extra-dimensional part is coupled to a dark pressure through a scalar field. It is shown that neither early inflation nor current acceleration of the 4D universe would happen if the non-vacuum states of the scalar field would contribute to 4D cosmology.Comment: 13 pages, major revision, published online in GR

Vortices on Higher Genus Surfaces

We consider the topological interactions of vortices on general surfaces. If the genus of the surface is greater than zero, the handles can carry magnetic flux. The classical state of the vortices and the handles can be described by a mapping from the fundamental group to the unbroken gauge group. The allowed configurations must satisfy a relation induced by the fundamental group. Upon quantization, the handles can carry ``Cheshire charge.'' The motion of the vortices can be described by the braid group of the surface. How the motion of the vortices affects the state is analyzed in detail.Comment: 28 pages with 10 figures; uses phyzzx and psfig; Caltech preprint CALT-68-187

Hadronic final states in deep-inelastic scattering with Sherpa

We extend the multi-purpose Monte-Carlo event generator Sherpa to include processes in deeply inelastic lepton-nucleon scattering. Hadronic final states in this kinematical setting are characterised by the presence of multiple kinematical scales, which were up to now accounted for only by specific resummations in individual kinematical regions. Using an extension of the recently introduced method for merging truncated parton showers with higher-order tree-level matrix elements, it is possible to obtain predictions which are reliable in all kinematical limits. Different hadronic final states, defined by jets or individual hadrons, in deep-inelastic scattering are analysed and the corresponding results are compared to HERA data. The various sources of theoretical uncertainties of the approach are discussed and quantified. The extension to deeply inelastic processes provides the opportunity to validate the merging of matrix elements and parton showers in multi-scale kinematics inaccessible in other collider environments. It also allows to use HERA data on hadronic final states in the tuning of hadronisation models.Comment: 32 pages, 22 figure

Cosmology at the Millennium

One hundred years ago we did not know how stars generate energy, the age of the Universe was thought to be only millions of years, and our Milky Way galaxy was the only galaxy known. Today, we know that we live in an evolving and expanding Universe comprising billions of galaxies, all held together by dark matter. With the hot big-bang model, we can trace the evolution of the Universe from the hot soup of quarks and leptons that existed a fraction of a second after the beginning to the formation of galaxies a few billion years later, and finally to the Universe we see today 13 billion years after the big bang, with its clusters of galaxies, superclusters, voids, and great walls. The attractive force of gravity acting on tiny primeval inhomogeneities in the distribution of matter gave rise to all the structure seen today. A paradigm based upon deep connections between cosmology and elementary particle physics -- inflation + cold dark matter -- holds the promise of extending our understanding to an even more fundamental level and much earlier times, as well as shedding light on the unification of the forces and particles of nature. As we enter the 21st century, a flood of observations is testing this paradigm.Comment: 44 pages LaTeX with 14 eps figures. To be published in the Centennial Volume of Reviews of Modern Physic

Possible Origin of Antimatter Regions in the Baryon Dominated Universe

We discuss the evolution of U(1) symmetric scalar field at the inflation epoch with a pseudo Nambu-Goldstone tilt revealing after the end of exponential expansion of the Universe. The U(1) symmetry is supposed to be associated with baryon charge. It is shown that quantum fluctuations lead in natural way to baryon dominated Universe with antibaryon excess regions. The range of parameters is calculated at which the fraction of Universe occupied by antimatter and the size of antimatter regions satisfy the observational constraints, survive to the modern time and lead to effects, accessible to experimental search for antimatter.Comment: 10 pages, 1 figur

Super AutoDipole

The publicly available package for an automated dipole subtraction, AutoDipole, is extended to include the SUSY dipoles in the MSSM. All fields in the SM and the MSSM are available. The code is checked against the analytical expressions for a simple process. The extended package makes it possible to compute the QCD NLO corrections to SUSY multi-parton processes like the stop pair production plus jets at the LHC.Comment: 16 pages, 1 figure, v2: a few typos to match the published version in Eur. Phys. J.

Recent Advances in Understanding Particle Acceleration Processes in Solar Flares

We review basic theoretical concepts in particle acceleration, with particular emphasis on processes likely to occur in regions of magnetic reconnection. Several new developments are discussed, including detailed studies of reconnection in three-dimensional magnetic field configurations (e.g., current sheets, collapsing traps, separatrix regions) and stochastic acceleration in a turbulent environment. Fluid, test-particle, and particle-in-cell approaches are used and results compared. While these studies show considerable promise in accounting for the various observational manifestations of solar flares, they are limited by a number of factors, mostly relating to available computational power. Not the least of these issues is the need to explicitly incorporate the electrodynamic feedback of the accelerated particles themselves on the environment in which they are accelerated. A brief prognosis for future advancement is offered.Comment: This is a chapter in a monograph on the physics of solar flares, inspired by RHESSI observations. The individual articles are to appear in Space Science Reviews (2011