Stochastic Approach to Flat Direction during Inflation

We revisit the time evolution of a flat and non-flat direction system during inflation. In order to take into account quantum noises in the analysis, we base on stochastic formalism and solve coupled Langevin equations numerically. We focus on a class of models in which tree-level Hubble-induced mass is not generated. Although the non-flat directions can block the growth of the flat direction's variance in principle, the blocking effects are suppressed by the effective masses of the non-flat directions. We find that the fate of the flat direction during inflation is determined by one-loop radiative corrections and non-renormalizable terms as usually considered, if we remove the zero-point fluctuation from the noise terms.Comment: 17 pages, 4 figures, v2: minor corrections made, published in JCA

Transference of fractional Laplacian regularity

In this note we show how to obtain regularity estimates for the fractional Laplacian on the multidimensional torus $\mathbb{T}^n$ from the fractional Laplacian on $\mathbb{R}^n$. Though at first glance this may seem quite natural, it must be carefully precised. A reason for that is the simple fact that $L^2$ functions on the torus can not be identified with $L^2$ functions on $\mathbb{R}^n$. The transference is achieved through a formula that holds in the distributional sense. Such an identity allows us to transfer Harnack inequalities, to relate the extension problems, and to obtain pointwise formulas and H\"older regularity estimates.Comment: 7 pages. To appear in Special Functions, Partial Differential Equations and Harmonic Analysis. Proceedings of the conference in honor of Calixto P. Calder\'on, Roosevelt University at Chicago, November 16-18, 2012. C. Georgakis, A. Stokolos and W. Urbina (eds

Reversible reorganization of the chlorophyll-protein complexes of photosystem II in cyanobacterium cells in the dark ag

AbstractA new emission band at 673 nm was detected in the low-temperature fluorescence spectrum of dark-adapted cyanobacteria Gloeotrichia raciborski. The excitation spectrum of this band was close to the absorbance of the isolated reaction centre of photosystem II. The relative intensities of the bands of chlorophyll and pheophytin in this spectrum showed the relative concentrations of these pigments to be about 3:1. The intensity of the band increased with darkness (half-time about 2 h). Under illumination the band rapidly disappeared (half-time about 60 s). The appearance of a 673 nm band in the dark and its disappearance in the light were accompanied by a decrease, and, respectively, an increase in the fluorescence of the PS II band at 697 nm

Composition of processes and related partial differential equations

In this paper different types of compositions involving independent fractional Brownian motions B^j_{H_j}(t), t>0, j=1,$ are examined. The partial differential equations governing the distributions of I_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|), t>0 and J_F(t)=B^1_{H_1}(|B^2_{H_2}(t)|^{1/H_1}), t>0 are derived by different methods and compared with those existing in the literature and with those related to B^1(|B^2_{H_2}(t)|), t>0. The process of iterated Brownian motion I^n_F(t), t>0 is examined in detail and its moments are calculated. Furthermore for J^{n-1}_F(t)=B^1_{H}(|B^2_H(...|B^n_H(t)|^{1/H}...)|^{1/H}), t>0 the following factorization is proved J^{n-1}_F(t)=\prod_{j=1}^{n} B^j_{\frac{H}{n}}(t), t>0. A series of compositions involving Cauchy processes and fractional Brownian motions are also studied and the corresponding non-homogeneous wave equations are derived.Comment: 32 page

Global well-posedness for a nonlocal Gross-Pitaevskii equation with non-zero condition at infinity

We study the Gross-Pitaevskii equation involving a nonlocal interaction potential. Our aim is to give sufficient conditions that cover a variety of nonlocal interactions such that the associated Cauchy problem is globally well-posed with non-zero boundary condition at infinity, in any dimension. We focus on even potentials that are positive definite or positive tempered distributions.Comment: Communications in Partial Differential Equations (2010

Nanoelectromechanics of Piezoresponse Force Microscopy

To achieve quantitative interpretation of Piezoresponse Force Microscopy (PFM), including resolution limits, tip bias- and strain-induced phenomena and spectroscopy, analytical representations for tip-induced electroelastic fields inside the material are derived for the cases of weak and strong indentation. In the weak indentation case, electrostatic field distribution is calculated using image charge model. In the strong indentation case, the solution of the coupled electroelastic problem for piezoelectric indentation is used to obtain the electric field and strain distribution in the ferroelectric material. This establishes a complete continuum mechanics description of the PFM contact mechanics and imaging mechanism. The electroelastic field distribution allows signal generation volume in PFM to be determined. These rigorous solutions are compared with the electrostatic point charge and sphere-plane models, and the applicability limits for asymptotic point charge and point force models are established. The implications of these results for ferroelectric polarization switching processes are analyzed.Comment: 81 pages, 19 figures, to be published in Phys. Rev.

Exact Analytic Solution for the Rotation of a Rigid Body having Spherical Ellipsoid of Inertia and Subjected to a Constant Torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" In particular: typos present in Eq. 28 of the Journal version are HERE correcte

Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque

New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes' theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a "virtual" spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this "virtual" body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The following typos present in the Journal version are HERE corrected: 1) Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3) Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6

Plasma-surface interaction and mechanisms of dust production in ITER ELM simulation experiments with QSPA Kh-50

Experimental simulations of ITER transient events with relevant surface heat load parameters (energy density and the pulse duration) were carried out with a quasi-stationary plasma accelerator QSPA Kh-50. The several mechanisms of dust generation from tungsten surfaces were identified. The major cracks development and it bifurcation led to generation dust particles with sizes up to tens μm. Melting of surface and development of fine meshes of cracks along the grain boundaries are accompanied by resolidified bridges formation through the fine cracks. Such bridges produce nm-size dust. Appearance of sub-micron and nanometer-size cellular structures under plasma irradiation can leads to the intensification of the dust formation.Экспериментальное моделирование ИТЭР переходных явлений с соответствующими параметрами тепловых нагрузок на поверхность (плотности энергии и длительности импульса) выполнены в квазистационарном плазменном ускорителе КСПУ Х-50. Были идентифицированы несколько механизмов генерации пыли с поверхности вольфрама. Развитие макротрещин и их бифуркация привели к генерации частиц пыли размером до десятков микрометров. Плавление поверхности и развитие сетки мелких трещин по границам зерен, сопровождаются образованием перезатвердевших мостов через мелкие трещины. Такие мосты создают наноразмерную пыль. Появление субмикронных и наноразмерных ячеистых структур при облучении плазмой может интенсифицировать образование пыли.Експериментальне моделювання ІТЕР перехідних явищ з відповідними параметрами теплових навантажень на поверхню (густини енергії і тривалості імпульсу) виконані в квазістаціонарному плазмовому прискорювачі КСПП Х-50. Були ідентифіковані декілька механізмів генерації пилу з поверхні вольфраму. Розвиток макротріщин і їх біфуркація привели до генерації частинок пилу розміром до десятків мікрометрів. Плавлення поверхні і розвиток сітки дрібних тріщин по границях зерен супроводжуються утворенням перезатверділих мостів через дрібні тріщини. Такі мости створюють нанорозмірний пил. Поява субмікронних і нанорозмірних стільникових структур під час опромінення плазмою може інтенсифікувати утворення пилу

Vibrations and fractional vibrations of rods, plates and Fresnel pseudo-processes

Different initial and boundary value problems for the equation of vibrations of rods (also called Fresnel equation) are solved by exploiting the connection with Brownian motion and the heat equation. The analysis of the fractional version (of order $\nu$) of the Fresnel equation is also performed and, in detail, some specific cases, like $\nu=1/2$, 1/3, 2/3, are analyzed. By means of the fundamental solution of the Fresnel equation, a pseudo-process $F(t)$, $t>0$ with real sign-varying density is constructed and some of its properties examined. The equation of vibrations of plates is considered and the case of circular vibrating disks $C_R$ is investigated by applying the methods of planar orthogonally reflecting Brownian motion within $C_R$. The composition of F with reflecting Brownian motion $B$ yields the law of biquadratic heat equation while the composition of $F$ with the first passage time $T_t$ of $B$ produces a genuine probability law strictly connected with the Cauchy process.Comment: 33 pages,8 figure