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In this paper, we study a class of stochastic nonlinear wave equation with memory driven by Lévy noise. We first show the existence and uniqueness of global mild solutions using a suitable energy function. Second, under some additional assumptions we prove the exponential stability of the solutions.
For UCP Si, randomly selected wafers and wafers cut from two specific ingots were studied. For the randomly selected wafers, a moderate gettering diffusion had little effect. Moreover, an efficiency up to 14% AMI was achieved with advanced processes. For the two specific UCP ingots, ingot #5848-13C displayed severe impurity effects as shown by lower 3sc in the middle of the ingot and low CFF in the top of the ingot. Also the middle portions of this ingot responded to a series of progressively more severe gettering diffusion. Unexplained was the fact that severely gettered samples of this ingot displayed a negative light biased effect on the minority carrier diffusion length while the nongettered or moderately gettered ones had the more conventional positive light biased effect on diffusion length. On the other hand, ingot C-4-21A did not have the problem of ingot 5848-13C and behaved like to the randomly selected wafers. The top half of the ingot was shown to be slightly superior to the bottom half, but moderate gettering helped to narrow the gap.
During the formation of the solar system the variation of the gravitational field produced by removal of a nebula with its moderately massive accretion disk led to sweeping of the Jovian commensurability resonances through the asteroid zone. This process produced increased eccentricities and random velocities of the early planetesimals which resulted in collisional comminution rather than accretion. The existence of the asteroids, their low mass density, and their high relative velocities are interpreted as due to disruption of the accretion processes of the terrestrial planets by the influences of Jupiter.
Many mathematical, man-made and natural systems exhibit a leading-digit bias, where a first digit (base 10) of 1 occurs not 11% of the time, as one would expect if all digits were equally likely, but rather 30%. This phenomenon is known as Benford’s Law. Analyzing which datasets adhere to Benford’s Law and how quickly Benford behavior sets in are the two most important problems in the field. Most previous work studied systems of independent random variables, and relied on the independence in their analyses. Inspired by natural processes such as particle decay, we study the dependent random variables that emerge from models of decomposition of conserved quantities. We prove that in many instances the distribution of lengths of the resulting pieces converges to Benford behavior as the number of divisions grow, and give several conjectures for other fragmentation processes. The main difficulty is that the resulting random variables are dependent. We handle this by using tools from Fourier analysis and irrationality exponents to obtain quantified convergence rates as well as introducing and developing techniques to measure and control the dependencies. The construction of these tools is one of the major motivations of this work, as our approach can be applied to many other dependent systems. As an example, we show that the n! entries in the determinant expansions of n×n matrices with entries independently drawn from nice random variables converges to Benford’s Law.
In the present paper we continue the investigation of solutions to higher-order heat-type equations with random initial conditions, which play the important role in many applied areas. We consider the random initial conditions given by harmonizable φ-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema over bounded and unbounded domains for solutions of such equations. The results obtained in the paper hold, in particular, for the case of Gaussian initial condition.
Random sequential adsorption (RSA) is a time-dependent packing process, in which particles of certain shapes are randomly and sequentially placed into an empty space without overlap. In the infinite-time limit, the density approaches a "saturation'' limit. Although this limit has attracted particular research interest, the majority of past studies could only probe this limit by extrapolation. We have previously found an algorithm to reach this limit using finite computational time for spherical particles, and could thus determine the saturation density of spheres with high accuracy. Here in this paper, we generalize this algorithm to generate saturated RSA packings of two-dimensional polygons. We also calculate the saturation density for regular polygons of three to ten sides, and obtain results that are consistent with previous, extrapolation-based studies.
Let P{sub n} and Q{sub n} be two probability measures representing two different probabilistic models of some system (e.g., an n-particle equilibrium system, a set of random graphs with n vertices, or a stochastic process evolving over a time n) and let M{sub n} be a random variable representing a “macrostate” or “global observable” of that system. We provide sufficient conditions, based on the Radon–Nikodym derivative of P{sub n} and Q{sub n}, for the set of typical values of M{sub n} obtained relative to P{sub n} to be the same as the set of typical values obtained relative to Q{sub n} in the limit n→∞. This extends to general probability measures and stochastic processes the well-known thermodynamic-limit equivalence of the microcanonical and canonical ensembles, related mathematically to the asymptotic equivalence of conditional and exponentially-tilted measures. In this more general sense, two probability measures that are asymptotically equivalent predict the same typical or macroscopic properties of the system they are meant to model.
This paper presents recent results in an ongoing effort to understand and develop techniques to process launch vehicle data, which is extremely challenging for modal parameter identification. The primary source of difficulty is due to the nonstationary nature of the situation. The system is changing, the environment is not steady, and there is an active control system operating. Hence, the primary tool for producing clean operational results (significant data lengths and data averaging) is not available to the user. This work reported herein uses a correlation-based two step operational modal analysis approach to process the relevant data sets for understanding and development of processes. A significant drawback for such processing of short time histories is a series of beating phenomena due to the inability to average out random modal excitations. A recursive correlation process coupled to a new convergence metric (designed to mitigate the beating phenomena) is the object of this study. It has been found in limited studies that this process creates clean modal frequency estimates but numerically alters the damping.
Stochastic approximation methods have found extensive and diversified applications. Recent emergence of networked systems and cyber-physical systems has generated renewed interest in advancing stochastic approximation into a general framework to support algorithm development for information processing and decisions in such systems. This paper presents a survey on some recent developments in stochastic approximation methods and their applications. Using connected vehicles in platoon formation and coordination as a platform, we highlight some traditional and new methodologies of stochastic approximation algorithms and explain how they can be used to capture essential features in networked systems. Distinct features of networked systems with randomly switching topologies, dynamically evolving parameters, and unknown delays are presented, and control strategies are provided.
This paper is devoted to the study of the solvability of random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability. The notions of random fuzzy variables and fuzzy stochastic processes are developed for multivariable functions. The existence and uniqueness of two types of integral solutions generated from Darboux problem for nonlinear wave equations are proved using the successive approximations method and Gronwall’s inequality for stochastic processes. The continuous dependence on the data, the boundedness, and the stability with probability one of integral solutions are established to confirm the well posedness of our model. Some computational examples are presented to illustrate the theoretical results.
A scientific program of beta-decay spectroscopy relevant to r-process nucleosynthesis has been started using high intensity U-beam at the RIBF. The first results of {beta}-decay half-lives of very neutron-rich Kr to Tc nuclides, all of which lie close to the r-process path, suggest a systematic enhancement of the the {beta}-decay rates of the Zr and Nb isotopes around A110 with respect to the predictions of the deformed quasiparticle-random-phase-approximation model (FRDM + QRPA). An impact of the results on the astrophysical r-process is discussed together with the future perspective of the {beta}-decay spectroscopy with the EURICA.
The Laser Interferometer Space Antenna Pathfinder (LPF) main observable, labelled∆g, is the differential force per unit mass acting on the two test masses in free fall condition, after the contribution of all non-gravitational forces have been compensated. At low frequencies the differential force is compensated by an applied electrostatic actuation force,which then must be subtracted from the measured acceleration to obtain∆g. Any inaccuracy in the actuation force contaminates the residual acceleration. This study investigates the accuracy of the electrostatic actuation system and its impact on the LPF main observable. It is shown that the inaccuracy is mainly caused by the rounding errors in the waveform processing and also by the random error caused by the analog to digital converter (ADC) random noise in the control loop. Both errors are one order of magnitude smaller than the resolution of the commanded voltages. We developed a simulator based on the LPF design to compute the close-to-reality actuation voltages and consequently, the resulting actuation forces. The simulator is applied in post-processing the LPF data.
We investigate the solution of low-rank matrix approximation problems using the truncated singular value decomposition (SVD). For this purpose, we develop and optimize graphics processing unit (GPU) implementations for the randomized SVD and a blocked variant of the Lanczos approach. Our work takes advantage of the fact that the two methods are composed of very similar linear algebra building blocks, which can be assembled using numerical kernels from existing high-performance linear algebra libraries. Furthermore, the experiments with several sparse matrices arising in representative real-world applications and synthetic dense test matrices reveal a performance advantage of the block Lanczos algorithm when targeting the same approximation accuracy.
Solutions of the Itô stochastic differential equation in a random environment are considered. The random environment is formed by the generalized telegraph process. It is proved that the initial problem is equivalent to a system of two stochastic differential equations with nonrandom coefficients. The first equation is the Itô equation, and the initial process is its solution. The second equation is an equation with Poisson process, and its solution is a generalized telegraph process. The theorems of existence and uniqueness of strong and weak solutions are proved.
The Continuous Stellar Tracking Attitude Reference (CSTAR) system is an in-house project for Space Station to provide high accuracy, drift free attitude and angular rate information for the GN&C system. The outputs of the solid state star trackers are processed to provide attitude information; rate data is then derived from the attitude. Rate derivation is based on discrete time polynomial approximation techniques. This gives simple algorithms which allow for interpolation by other users. Attitude rate is modeled as a constant with low amplitude, low frequency sinusoids superimposed. The rate processor is parameterized to account for the effects of random errors, sample rate, data processing rate and perturbation frequency. The baseline system may be characterized as follows: the three sigma attitude accuracy is 0.01 degrees, the three sigma rate accuracy is 0.0001 degrees per second, the sample rate is 100 Hertz, the sampled signal is bandlimited to 0.5 Hertz, and the data processing rate is 10 Hertz. The above system requires a differentiator of length 127. This will track rate perturbations of frequencies less than 0.01 Hertz with low systematic errors.
The factors that affect the preferred positions of cations in ionic solid solutions were investigated utilizing vibrational spectroscopy. Solid solutions of the sulfate and chromate ions codoped with La(+3) and Ca(+2) in a KBr host lattice were examined as a function of the polyvalent cation concentration. The cation-anion pairing process was found to be random for Ca(+2), whereas the formation of La(+3)-SO4(-2) ion pairs with a C2 sub v bonding geometry is highly preferential to any type of La(+3)-CrO4(-2) ion pair formation. The relative populations of ion pair site configurations are discussed in terms of an energy-entropy competition model which can be applied to the partition of trace elements during magmatic processes.
Self-organization and evolution of magnetoplasma structures in the upper layers of the solar convection zone are discussed as a process of diffuse aggregation of magnetic flux tubes. Equations describing the tube motion under the action of magnetic interaction forces, hydrodynamic forces, and random forces are written explicitly. The process of aggregation of magnetic flux tubes into magnetic flux clusters of different shapes and dimensions is simulated numerically. The obtained structures are compared with the observed morphological types of sunspot groups. The quantitative comparison with the observational data was performed by comparing the fractal dimensions of the photospheric magnetic structures observed in solar active regions with those of structures obtained in the numerical experiment. The model has the following free parameters: the numbers of magnetic flux tubes with opposite polarities on the considered area element (Nn and Ns), the average radius of the cross section of the magnetic flux tube (a), its effective length (l), the twist factor of the tube field (k), and the absolute value of the average velocity of chaotic tube displacements (d). Variations in these parameters in physically reasonable limits leads to the formation of structures (tube clusters of different morphological types) having different fractal dimensions. Using the NOAA 10488 active region, which appeared and developed into a complicated configuration near the central meridian, as an example, it is shown that good quantitative agreement between the fractal dimensions is achieved at the following parameters of the model: Nn = Ns = 250 ± 50; a = 150 ± 50 km; l ∼ 5000 km, and d = 80 ± 10 m/s. These results do not contradict the observational data and theoretical estimates obtained in the framework of the Parker “spaghetti” model and provide new information on the physical processes resulting in the origin and evolution of local magnetic plasma structures in the near-photospheric layers of the solar convection zone.