The asymptotic solution of a singularly perturbed Cauchy problem for Fokker-Planck equation

The asymptotic method is a very attractive area of applied mathematics. There are many modern research directions which use a small parameter such as statistical mechanics, chemical reaction theory and so on. The application of the Fokker-Planck equation (FPE) with a small parameter is the most popular because this equation is the parabolic partial differential equations and the solutions of FPE give the probability density function. In this paper we investigate the singularly perturbed Cauchy problem for symmetric linear system of parabolic partial differential equations with a small parameter. We assume that this system is the Tikhonov non-homogeneous system with constant coefficients. The paper aims to consider this Cauchy problem, apply the asymptotic method and construct expansions of the solutions in the form of two-type decomposition. This decomposition has regular and border-layer parts. The main result of this paper is a justification of an asymptotic expansion for the solutions of this Cauchy problem. Our method can be applied in a wide variety of cases for singularly perturbed Cauchy problems of Fokker-Planck equations.Асимптотические методы - очень важная область прикладной математики. Существует множество современных направлений исследований, в которых используется малый параметр, например статистическая механика, теория химических реакций и др. Использование уравнения Фоккера-Планка с малым параметром очень востребовано, поскольку это уравнение является параболическим дифференциальным уравнением в частных производных, а решения этого уравнения дают функцию плотности вероятности. В работе исследуется сингулярно возмущённая задача Коши для симметричной линейной системы параболических дифференциальных уравнений в частных производных с малым параметром. Мы предполагаем, что эта система является неоднородной системой тихоновского типа с постоянными коэффициентами. Цель исследования - рассмотреть эту задачу Коши, применить асимптотический метод и построить асимптотические разложения решений в виде двухкомпонентного ряда. Таким образом, это разложение имеет регулярную и погранслойную части. Основным результатом данной работы является обоснование асимптотического разложения для решений этой задачи Коши. Наш метод может быть применён для широкого круга сингулярно возмущённых задач Коши для уравнений Фоккера-Планка

The process e+e−→π+π−π0e^+e^-\to\pi^+\pi^-\pi^0 in the energy range 2E_0=1.04 - 1.38 GeV

In the experiment with the SND detector at VEPP-2M e^+e^- collider the process $e^+e^-\to\pi^+\pi^-\pi^0$ was studied in the energy range 2E_0 from 1.04 to 1.38 GeV. A broad peak was observed with the visible mass $M_{vis}=1220\pm 20$ MeV and cross section in the maximum $\sigma_0\simeq 4$ nb. The peak can be interpreted as a $\omega$-like resonance $\omega (1200)$.Comment: 10 pages LATEX and 5 figure

Have mirror micrometeorites been detected?

Slow-moving ($v \sim 15$ km/s) 'dark matter particles' have allegedly been discovered in a recent experiment. We explore the possibility that these slow moving dark matter particles are small mirror matter dust particles originating from our solar system. Ways of further testing our hypothesis, including the possibility of observing these dust particles in cryogenic detectors such as NAUTILUS, are also discussed.Comment: Few changes, about 8 pages lon

Results of the BiPo-1 prototype for radiopurity measurements for the SuperNEMO double beta decay source foils

The development of BiPo detectors is dedicated to the measurement of extremely high radiopurity in $^{208}$Tl and $^{214}$Bi for the SuperNEMO double beta decay source foils. A modular prototype, called BiPo-1, with 0.8 $m^2$ of sensitive surface area, has been running in the Modane Underground Laboratory since February, 2008. The goal of BiPo-1 is to measure the different components of the background and in particular the surface radiopurity of the plastic scintillators that make up the detector. The first phase of data collection has been dedicated to the measurement of the radiopurity in $^{208}$Tl. After more than one year of background measurement, a surface activity of the scintillators of $\mathcal{A}$($^{208}$Tl) $=$ 1.5 $\mu$Bq/m$^2$ is reported here. Given this level of background, a larger BiPo detector having 12 m$^2$ of active surface area, is able to qualify the radiopurity of the SuperNEMO selenium double beta decay foils with the required sensitivity of $\mathcal{A}$($^{208}$Tl) $<$ 2 $\mu$Bq/kg (90% C.L.) with a six month measurement.Comment: 24 pages, submitted to N.I.M.

Measurement of the Lambda^0_b lifetime in the decay Lambda^0_b -> J/psi Lambda^0 with the D0 Detector

We present measurements of the Lambda^0_b lifetime in the exclusive decay channel Lambda^0_{b}->J/psi Lambda^0, with J/psi to mu+ mu- and Lambda^0 to p pi-, the B^0 lifetime in the decay B^0 -> J/psi K^0_S with J/psi to mu+ mu- and K^0_S to pi+ pi-, and the ratio of these lifetimes. The analysis is based on approximately 250 pb^{-1} of data recorded with the D0 detector in pp(bar) collisions at sqrt{s}=1.96 TeV. The Lambda^0_b lifetime is determined to be tau(Lambda^0_b) = 1.22 +0.22/-0.18 (stat) +/- 0.04 (syst) ps, the B^0 lifetime tau(B^0) = 1.40 +0.11/-0.10 (stat) +/- 0.03 (syst) ps, and the ratio tau(Lambda^0_b)/tau(B^0) = 0.87 +0.17/-0.14 (stat) +/- 0.03 (syst). In contrast with previous measurements using semileptonic decays, this is the first determination of the Lambda^0_b lifetime based on a fully reconstructed decay channel.Comment: 7 pages, 4 figures, Submitted to Physical Review Letters, v2: Added FNAL Pub-numbe

The Majorana Demonstrator: A Search for Neutrinoless Double-beta Decay of 76Ge

Neutrinoless double-beta (0νββ) decay is a hypothesized process where in some even-even nuclei it might be possible for two neutrons to simultaneously decay into two protons and two electrons without emitting neutrinos. This is possible only if neutrinos are Majorana particles, i.e. fermions that are their own antiparticles. Neutrinos being Majorana particles would explicitly violate lepton number conservation, and might play a role in the matter-antimatter asymmetry in the universe. The observation of neutrinoless double-beta decay would also provide complementary information related to neutrino masses. The Majorana Collaboration is constructing the MAJORANA DEMONSTRATOR, with a total of 40-kg Germanium detectors, to search for the 0νββ decay of 76Ge and to demonstrate a background rate at or below 3 counts/(ROI•t•y) in the 4 keV region of interest (ROI) around the 2039 keV Q-value for 76Ge 0νββ decay. In this paper, we discuss the physics of neutrinoless double beta decay and then focus on the MAJORANA DEMONSTRATOR, including its design and approach to achieve ultra-low backgrounds and the status of the experiment

The MAJORANA DEMONSTRATOR for 0νββ: Current Status and Future Plans

The MAJORANA DEMONSTRATOR will search for neutrinoless-double-beta decay (0νββ) in 76Ge, while establishing the feasibility of a future tonne-scale germanium-based 0νββ experiment, and performing searches for new physics beyond the Standard Model. The experiment, currently under construction at the Sanford Underground Research Facility in Lead, SD, will consist of a pair of modular high-purity germanium detector arrays housed inside of a compact copper, lead, and polyethylene shield. Through a combination of strict materials qualifications and assay, low-background design, and powerful background rejection techniques, the Demonstrator aims to achieve a background rate in the 0νββ region of interest (ROI) of no more than 3 counts in the 0νββ-decay ROI per tonne of target isotope per year (cnts/(ROI-t-y)). The current status of the Demonstrator is discussed, as are plans for its completion

A Dark Matter Search with MALBEK

The Majorana Demonstrator is an array of natural and enriched high purity germanium detectors that will search for the neutrinoless double-beta decay of 76Ge and perform a search for weakly interacting massive particles (WIMPs) with masses below 10 GeV. As part of the Majorana research and development efforts, we have deployed a modified, low-background broad energy germanium detector at the Kimballton Underground Research Facility. With its sub-keV energy threshold, this detector is sensitive to potential non-Standard Model physics, including interactions with WIMPs. We discuss the backgrounds present in the WIMP region of interest and explore the impact of slow surface event contamination when searching for a WIMP signal

Search for Neutrinoless Double- β Decay in Ge 76 with the Majorana Demonstrator

The Majorana Collaboration is operating an array of high purity Ge detectors to search for neutrinoless double-β decay in Ge76. The Majorana Demonstrator comprises 44.1 kg of Ge detectors (29.7 kg enriched in Ge76) split between two modules contained in a low background shield at the Sanford Underground Research Facility in Lead, South Dakota. Here we present results from data taken during construction, commissioning, and the start of full operations. We achieve unprecedented energy resolution of 2.5 keV FWHM at Qββ and a very low background with no observed candidate events in 9.95 kg yr of enriched Ge exposure, resulting in a lower limit on the half-life of 1.9×1025 yr (90% C.L.). This result constrains the effective Majorana neutrino mass to below 240-520 meV, depending on the matrix elements used. In our experimental configuration with the lowest background, the background is 4.0-2.5+3.1 counts/(FWHM t yr)