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Nonstationary countable Markov chains with continuous time and absorption at zero are considered. We study the convergence rate to the limit mode. As examples, we consider simple nonstationary random walks.
We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become blocked. Given an initial number of vertices N growing to infinity, we study statistical properties of the proportion of explored (active or blocked) nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the jamming constant, through a diffusion approximation for the exploration process which can be described as a unidimensional process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e., random sequential adsorption. As opposed to exploration processes on homogeneous random graphs, these do not allow for such a dimensional reduction. Instead we derive a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and we obtain generic bounds for the fluid limit and jamming constant: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, using coupling techinques, we give trajectorial interpretations of the generic bounds.
Sufficient conditions for recurrence and positivity of diffusion process defined by stochastic differential equation, using Liapunov function
Generalization of binary processes, discussing time domain and frequency domain analysis
General theory describing discontinuous processes and application to hydrodynamic inhomogeneities such as combustion waves, combustion zone motion
Optimal control and stability for stochastic systems, viewing linear diffusion models based upon Gaussian-Markov process as finite dimensional linear system driven by white noise
Sufficient conditions for optimal stochastic control of diffusion processes governed by vector equations satisfying local Lipschitz conditions
Most existing deconvolution techniques are incapable of determining phase properties of wavelets from time series data; to assure a unique solution, minimum phase is usually assumed. It is demonstrated, for moving average processes of order one, that deconvolution filtering using the absolute value norm provides an estimate of the wavelet shape that has the correct phase character when the random driving process is nonnormal. Numerical tests show that this result probably applies to more general processes.
Random walk theory applied to electron motion in early stage of He breakdown in electric field, based on integral and differential cross section data
Curve crossings by normal processes and reliability implications with applications to performance quality and reliability in physical systems
Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.
Prior to 2005, the EDF initial version for the radiological inventory of graphite was based on the maximum values of the measures, namely a very pessimistic way. In 2008, a scientific method was developed by EDF to evaluate the inventory by reverse activation calculation, in order to limit the overestimation. The radiological inventory computation principles can be compared to those of all engineering studies. First, the calculation is simplified by taking margins, and if the results are not satisfactory enough, some simplifications are suppressed to reduce these margins even if computation becomes more complicated. On EDF piles, the gain obtained in 2008 represented a factor 50 relative to the initial version of Cl-36, even with a very penalizing multiplicative factor for uncertainty. Today, the accurate calculation of the uncertainty no longer justifies such a factor. A gain of about 150 now occurs compared to the initial version of Cl-36. It is more than 2 orders of magnitude, which is already enough to assess again the necessary type of disposal because Cl-36 is one of the key radionuclides. After global presentation of graphite waste management in France, the paper focuses on the inventory scientific process of EDF nuclear graphite, the purity of graphite and its consequences, its particular sampling, the lessons learned, the initial method description, the link with the demonstration of the completely random point process of chlorine in nuclear graphite and the last suggested precise uncertainty computation of inventory of Cl-36. The method confirmation for concentration assessment, the history of the EDF method development and its benefits are also emphasized. (authors)
An experimental study was conducted to investigate the generation process of random small-scale turbulence in an originally laminar mixing layer. The evolutions of the two types of deterministic structures, the spanwise and streamwise vortices, were first clarified in order to determine their roles in the transition process. A scaling rule for the streamwise distance from the trailing edge of the splitter plate to the vortex merging position was found for various velocity ratios. After this stremwise lengthscale was determined, it became clear that the spanwise wavelength of the streamwise vortices doubled after the merging of the spanwise structures which nominally doubled streamwise wavelengths. The most interesting finding was that the random small-scale eddies were produced by the interactions between the merging spanwise structures and the streamwise vortices.
The current controversy existing in reference to the regularity vs. clustering in cloud fields is examined by means of analysis and simulation studies based upon nearest-neighbor cumulative distribution statistics. It is shown that the Poisson representation of random point processes is superior to pseudorandom-number-generated models and that pseudorandom-number-generated models bias the observed nearest-neighbor statistics towards regularity. Interpretation of this nearest-neighbor statistics is discussed for many cases of superpositions of clustering, randomness, and regularity. A detailed analysis is carried out of cumulus cloud field spatial distributions based upon Landsat, AVHRR, and Skylab data, showing that, when both large and small clouds are included in the cloud field distributions, the cloud field always has a strong clustering signal.
Network-scale travel time prediction not only enables traffic management centers (TMC) to proactively implement traffic management strategies, but also allows travelers make informed decisions about route choices between various origins and destinations. In this paper, a random forest estimator was proposed to predict travel time in a network. The estimator was trained using two years of historical travel time data for a case study network in St. Louis, Missouri. Both temporal and spatial effects were considered in the modeling process. The random forest models predicted travel times accurately during both congested and uncongested traffic conditions. The computational times for the models were low, thus useful for real-time traffic management and traveler information applications.
Abstract Chemomechanical weakening of layered phyllosilicate muscovite mica was studied as a function of chemical environment via in situ liquid-nanoindentation under four conditions (dry, deionized water, and two NaCl solutions of different pH). While traditional indentation analyses of layered materials with extreme mechanical anisotropy have been limited due to displacement bursts (pop-ins), here the bursts were used as proxies for delamination, fracture, and spalling events. Since displacement bursts during an indent represent a stochastic process, 120 indents were conducted for each condition to generate statistically significant amounts of data. In total, over 9000 bursts were assessed using a load–displacement threshold criterion, classifying this as a high-throughput nanoscale fracture technique. For each burst, initiation load, initiation displacement, plastic zone volume at initiation, and energy dissipation were analyzed. A power-law relationship between the burst load and burst energy was noted which separated the bursts into two continuous distributions: (1) bursts due only to the mechanics of the indent and (2) bursts due to both the mechanics of the indent and the environment. By using a cumulative probability distribution, it was found that the NaCl solutions decreased the minimum plastic zone volume necessary to initiate a displacement burst by an order of magnitude relative to the dry condition. Finally, the underlying mechanisms explaining the trends in initiation volume as a function of environment were discussed, with a focus on the chemomechanical degradation processes via chemical attack and cation exchange.
A general theory is presented for the origin of a self-replicating chemical system, termed an autogen, which is capable of both crude replication and translation (protein synthesis). The theory requires the availability of free energy and monomers to the system, a significant background low-yield synthesis of kinetically stable oligopeptides and oligonucleotides, the localization of the oligomers, crude oligonucleotide selectivity of amino acids during oligopeptide synthesis, crude oligonucleotide replication, and two short peptide families which catalyze replication and translation, to produce a localized group of at least one copy each of two protogenes and two protoenzymes. The model posits a process of random oligomerization, followed by the random nucleation of functional components and the rapid autocatalytic growth of the functioning autogen to macroscopic amounts, to account for the origin of the first self-replicating system. Such a process contains steps of such high probability and short time periods that it is suggested that the emergence of an autogen in a laboratory experiment of reasonable time scale may be possible.
Existing, competing theories for coronal and interplanetary type III solar radio bursts appeal to one or more of modulational instability, electrostatic (ES) decay processes, or stochastic growth physics to preserve the electron beam, limit the levels of Langmuir-like waves driven by the beam, and produce wave spectra capable of coupling nonlinearly to generate the observed radio emission. Theoretical constraints exist on the wavenumbers and relative sizes of the wave bandwidth and nonlinear growth rate for which Langmuir waves are subject to modulational instability and the parametric and random phase versions of ES decay. A constraint also exists on whether stochastic growth theory (SGT) is appropriate. These constraints are evaluated here using the beam, plasma, and wave properties (1) observed in specific interplanetary type III sources, (2) predicted nominally for the corona, and (3) predicted at heliocentric distances greater than a few solar radii by power-law models based on interplanetary observations. It is found that the Langmuir waves driven directly by the beam have wavenumbers that are almost always too large for modulational instability but are appropriate to ES decay. Even for waves scattered to lower wavenumbers (by ES decay, for instance), the wave bandwidths are predicted to be too large and the nonlinear growth rates too small for modulational instability to occur for the specific interplanetary events studied or the great majority of Langmuir wave packets in type III sources at arbitrary heliocentric distances. Possible exceptions are for very rare, unusually intense, narrowband wave packets, predominantly close to the Sun, and for the front portion of very fast beams traveling through unusually dilute, cold solar wind plasmas. Similar arguments demonstrate that the ES decay should proceed almost always as a random phase process rather than a parametric process, with similar exceptions. These results imply that it is extremely rare for modulational instability or parametric decay to proceed in type III sources at any heliocentric distance: theories for type III bursts based on modulational instability or parametric decay are therefore not viable in general. In contrast, the constraint on SGT can be satisfied and random phase ES decay can proceed at all heliocentric distances under almost all circumstances. (The contrary circumstances involve unusually slow, broad beams moving through unusually hot regions of the Corona.) The analyses presented here strongly justify extending the existing SGT-based model for interplanetary type III bursts (which includes SGT physics, random phase ES decay, and specific electromagnetic emission mechanisms) into a general theory for type III bursts from the corona to beyond 1 AU. This extended theory enjoys strong theoretical support, explains the characteristics of specific interplanetary type III bursts very well, and can account for the detailed dynamic spectra of type III bursts from the lower corona and solar wind.