Distributions Of Various Quantities Research Articles

High-resolution reconstruction and a-priori modeling of turbulent flames in the context of large eddy simulation using the convolutional neural network

In large eddy simulation (LES) of turbulent combustion, accurate modeling of the unresolved scalar flux and filtered reaction source terms is challenging. In the present work, a convolutional neutral network (CNN) was developed for the high-resolution reconstruction of the unfiltered progress variable, velocity and reaction rate based on the filtered quantities that are available from LES or by filtering the direct numerical simulation (DNS) data. The unclosed terms in the filtered progress variable transport equation were then modeled using the reconstructed quantities from the proposed CNN model and the approximate deconvolution method (ADM). Two DNS cases, i.e., case A and case B, with different Karlovitz numbers (Ka) were performed to assess the performance of the models a−priori. The unfiltered and filtered DNS results were first presented. It was found that the small-scale wrinkling structures of the flames and turbulence are largely filtered out, and the reaction zone is broadened by filtering. Then, the progress variable, velocity and reaction rate were reconstructed from the filtered DNS data. The results of reconstruction by ADM and the CNN model were compared with those from the DNS. It was found that the distributions of various quantities predicted by the CNN model agree well with those of the DNS. Finally, the unresolved scalar flux and reaction source terms in the filtered progress variable transport equation were modeled. The statistics of the modeled results were analyzed and it was shown that the CNN model performs better than ADM. Overall, the CNN model is promising for the data reconstruction and model development of turbulent combustion.

Parametric uncertainty quantification using proper generalized decomposition applied to neutron diffusion

SummaryIn this paper, a proper generalized decomposition (PGD) approach is employed for uncertainty quantification purposes. The neutron diffusion equation with external sources, a diffusion‐reaction problem, is used as the parametric model. The uncertainty parameters include the zone‐wise constant material diffusion and reaction coefficients as well as the source strengths, yielding a large uncertain space in highly heterogeneous geometries. The PGD solution, parameterized in all uncertain variables, can then be used to compute mean, variance, and more generally probability distributions of various quantities of interest. In addition to parameterized properties, parameterized geometrical variations of three‐dimensional models are also considered in this paper. To achieve and analyze a parametric PGD solution, algorithms are developed to decompose the model's parametric space and semianalytically integrate solutions for evaluating statistical moments. Varying dimensional problems are evaluated to showcase PGD's ability to solve high‐dimensional problems and analyze its convergence.

Behavior analysis of virtual-item gambling.

From the gambling logs of an online lottery game we extract the probability distribution of various quantities (e.g., bet value, total pool size, waiting time between successive gambles) as well as related correlation coefficients. We view the net change of income of each player as a random walk. The mean-squared displacement of these net income random walks exhibits a transition between a superdiffusive and a normal diffusive regime. We discuss different random-walk models with truncated power-law step lengths distributions that allow us to reproduce some of the properties extracted from the gambling logs. Analyzing the mean-squared displacement and the first-passage time distribution for these models allows us to identify the key features needed for observing this crossover from superdiffusion to normal diffusion.

Characteristics of interfacial signatures on a wind-driven gravity-capillary wave

[1] Direct numerical simulation of a wind-driven gravity-capillary wave and the underlying turbulent flow is conducted to identify the characteristic signatures of various surface parameters, including temperature, gas flux, velocities, and roughness, and to reveal the impacts of the nonbreaking surface waves on these surface flow and tracer parameters. Three characteristic surface signatures and the corresponding flow processes are identified: the carrier gravity wave, the parasitic capillary wavelets, and the elongated streaks. The elongated streaks are induced by both the coherent streamwise vortices formed within the turbulent shear layer and the Langmuir circulations arising from nonlinear interaction between the carrier gravity wave and the drift current. All three surface signatures can be observed in the distributions of various quantities, although some are more apparent than the others. Image-processing techniques, employing empirical mode decomposition and phase averaging, are developed to decompose the distinct signatures thus to quantify the contributions by the responsible flow processes. It is found that elongated streaks prevail the distribution of surface temperature and gas flux, indicating that Langmuir cells and the coherent eddies contribute to the major interfacial heat and gas transport. These eddies also induced strong cross-stream velocity divergence at the water surface, which exhibits resemblant elongated distribution as that of gas flux (correlation coefficient � 0.6). High correlation between the surface distributions of temperature and gas flux is observed (correlation coefficient � 0.8 to 0.9), suggesting that the spatial and temporal distribution of surface temperature is a good proxy tracer of interfacial gas transfer.

Simulation and estimation of probabilities of phases of the Pacific Decadal Oscillation

The Pacific Decadal Oscillation (PDO) index defines the leading mode of monthly sea surface temperature (SST) anomalies in the North Pacific Ocean. Time series analysis in both the frequency and time domains is applied to 107 years of monthly PDO index values. Simulations of a model fitted to the data are used to estimate p-values associated with particular events observed in the raw data. The simulations are further used to estimate the distribution of various quantities, such as the length (in years) of a positive phase, or the absolute difference between the longest positive and negative phase (in years). The results show that the probability of occurrence of a negative phase surrounded by two positive phases within a 107-year period is approximately 9.9%. The raw data's mean positive phase length is close to the simulation mean and median, while the absolute difference in maximum positive/negative phase lengths corresponds to a p-value of 14.9%. The methodology developed in this paper can be useful to ecologists in assessing the potential ecological effects due to PDO variation, and for estimating the probabilities associated with future phases or other events. Copyright © 2009 John Wiley & Sons, Ltd.

Simulation study of the magnetized sheath of a dusty plasma

Numerical solutions of stationary multifluid equations are used to study the formation and properties of the magnetized sheath near the boundary of a dusty plasma. The impacts of the strength of the magnetic field, the dust and plasma number densities, and the electron temperature on the sheath structure and spatial distributions of various quantities are investigated. It is shown that for a given angle of incidence of the magnetic field, there is a threshold magnetic field intensity above which some kind of large regular inhomogeneities develop on the spatial profile of the dust particles. The sheath thickness, the electron and ion number densities, and the absolute dust charge are strongly affected by the variation in the dust number density. The sheath demonstrates a nonlinear dependence on the electron temperature; as the electron temperature rises, the sheath first is broadened and the absolute wall potential decreases but then at higher temperatures the sheath becomes narrower and the absolute wall potential increases.

Pulling an adsorbed polymer chain off a solid surface

The thermally assisted detachment of a self-avoiding polymer chain from an adhesive surface by an external force applied to one of the chain-ends is investigated. We perform our study in the "fixed height" statistical ensemble where one measures the fluctuating force, exerted by the chain on the last monomer when a chain-end is kept fixed at height h over the solid plane at different adsorption strength [Formula: see text]. The phase diagram in the h-[Formula: see text] plane is calculated both analytically and by Monte Carlo simulations. We demonstrate that in the vicinity of the polymer desorption transition a number of properties like fluctuations and probability distribution of various quantities behave differently, if h rather than f is used as an independent control parameter.

Quasi-similarity model of synthetic jets

Actuators generating synthetic jets (and related hybrid-synthetic jets) are currently of increasing importance and it is useful to have for their design a simple model evaluating spatial distributions of various quantities of interest in the generated jet. In this paper, such a model – a set o simple ordinary differential equations – is derived and shown to describe synthetic jets remarkably well. It uses the Tollmien hypothesis of the length scale of the vortices proportional to the local jet diameter. The experiments show that for the best fit the proportionality multiplier should vary with the streamwise distance X 1 * from the nozzle. This variation leads to the new concept of quasi-similarity. The model was tested by application to synthetic jet data obtained at large distances X 1 * where an interesting change occurs in the character of the dependence.

A direct approach to sojourn times in a busy period of an M/M/1 queue

In this paper we present a direct approach to obtaining joint distributions of various quantities of interest in a busy period in an M/M/1 queue. These quantities are: the sojourn times and waiting times of all the customers in the busy period, the busy period length and the number of customers served in a busy period. Since the evolution of the total workload process between two successive customer arrivals is deterministic, this work gives statistic of the complete evolution of the workload process within a busy period.

Dynamics of rotating triple systems: statistical escape theory versus numerical simulations

Dynamical evolution of 120 000 equal-mass rotating triple systems is investigated. The system rotation is described by the parameter w = -L 2 0 E 0 /G 2 m 5 0 , where G is the gravitational constant, m 0 is the mass of a body, and L 0 and E 0 are the angular momentum and the total energy of the triple system, respectively. We consider the values of w = 0.005, 0.1, 1, 2, 4 and 6. For each w, 20 000 triple systems are studied. The initial coordinates and velocities of the components are randomly chosen. The initial data are chosen in two different ways: the first one assumes a hierarchical structure initially and the second one does not. The evolution of each triple system is calculated until either the escape of one of the bodies occurs or the time exceeds 1000 mean crossing times of the system. The orbital parameters of the final binary and the escaper are recorded for each run. We compare the results of numerical simulations and predictions of a statistical escape theory. The statistical theory is based on the assumption of ergodicity, that is, the only information on the initial conditions remaining at the time of the escape of the third body is contained in the conserved total energy, total angular momentum and the mass values. The distributions of various quantities are derived from the allowable phase-space volumes. The distribution of binary energy agrees with earlier results by Heggie, with the angular momentum dependence of Mikkola & Valtonen being added. The eccentricities are distributed in general accordance with Monaghan's work, while the triple systems break up like in radioactive decay, as was previously found by Valtonen & Aarseth. The escape directions are preferentially perpendicular to the total angular momentum vector; the more so, the greater the angular momentum. The escape-angle distributions are derived from the statistical theory and are found to be in agreement with the numerical data. The relative orientations and magnitudes of the binary and third-body angular momenta are also explained based on the statistical theory.

Nucleation and growth in one dimension. I. The generalized Kolmogorov-Johnson-Mehl-Avrami model

Motivated by a recent application of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model to the study of DNA replication, we consider the one-dimensional (1D) version of this model. We generalize previous work to the case where the nucleation rate is an arbitrary function I (t) and obtain analytical results for the time-dependent distributions of various quantities (such as the island distribution). We also present improved computer simulation algorithms to study the 1D KJMA model. The analytical results and simulations are in excellent agreement.

Supersymmetric standard model spectra from RCFT orientifolds

We present supersymmetric, tadpole-free d = 4 , N = 1 orientifold vacua with a three family chiral fermion spectrum that is identical to that of the standard model. Starting with all simple current orientifolds of all Gepner models we perform a systematic search for such spectra. We consider several variations of the standard four-stack intersecting brane realization of the standard model, with all quarks and leptons realized as bifundamentals and perturbatively exact baryon and lepton number symmetries, and with a U ( 1 ) Y vector boson that does not acquire a mass from Green–Schwarz terms. The number of supersymmetric Higgs pairs H 1 + H 2 is left free. In order to cancel all tadpoles, we allow a “hidden” gauge group, which must be chirally decoupled from the standard model. We also allow for non-chiral mirror-pairs of quarks and leptons, non-chiral exotics and (possibly chiral) hidden, standard model singlet matter, as well as a massless B–L vector boson. All of these less desirable features are absent in some cases, although not simultaneously. In particular, we found cases with massless Chan–Paton gauge bosons generating nothing more than SU ( 3 ) × SU ( 2 ) × U ( 1 ) . We obtain almost 180 000 rationally distinct solutions (not counting hidden sector degrees of freedom), and present distributions of various quantities. We analyse the tree level gauge couplings, and find a large range of values, remarkably centered around the unification point.

Characterization and modeling of weighted networks

We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network which are representatives of critical infrastructure and social system, respectively. The main empirical results are (i) the broad distributions of various quantities and (ii) the existence of weight-topology correlations. These measurements show that weights are relevant and that in general the modeling of complex networks must go beyond topology. We review a model which provides an explanation for the features observed in several real-world networks. This model of weighted network formation relies on the dynamical coupling between topology and weights, considering the rearrangement of new links are introduced in the system.

On the relationship between the eulerian and lagrangian statistics of a brownian particle

Statistics of particles (smoke aerosol in the atmosphere) reaching a prescribed spatial region are analyzed. The effects of both regular and random forces acting on the particles are taken into account. A method is proposed for calculating the probability distributions of various quantities (time required to reach a prescribed location, particle velocity in its vicinity, etc.), and its scope is determined as depending on the parameters of the problem.

Recursive Estimation in Capture-Recapture Methods

An important problem in statistical ecology is how to determine the size of an animal population. The best known technique is the capture-recapture technique. A random sample of individuals is captured, tagged in some way and released back into the population. After allowing time for the marked and unmarked individuals to mix sufficiently, a second random sample is taken and the marked ones are observed. Using measure change techniques, we estimate recursively conditional distributions of various quantities.

SEMDEM — educational software for bipolar semiconductor devices

The SEMDEM program helps to examine the physical phenomena taking place inside semiconductor power devices during their operation, both in static and dynamic conditions. Distributions of various quantities, such as electric potential, electron and hole density, current density, etc., inside a p-i-n diode or a p-n-p-n thyristor can be observed simultaneously in separate windows on the screen, together with the corresponding point on a static characteristic or a transient waveform. The possibility of modification of various parameters allows for interesting observations of influence of these parameters on static or dynamic characteristics of the analysed semiconductor devices.

Sheath structure in a plane probe inmersed in an electronegative plasma

The sheath zone near a plane probe inmersed in an electronegative plasma is analyzed. A theoretical model for the sheath zone was used to derive a new expression for the Bohm criterion. The new expression holds at any negative probe potential. Solving the model equations allows one to obtain a wealth of information including the spatial distribution of various quantities (electric field, potential, and particle densities), the sheath thickness, and the floating potential.

Molecular dynamics simulations of liquid water: Voronoi polyhedra and network topology

We have carried out various runs at different temperatures simulating liquid water via the TIP4P model, a well tested and widely used 4-site intermolecular potential. Voronoi polyhedra have been constructed and the distributions of various quantities analyzed. The higher the temperature, the more the distributions are similar to those of a normal liquid: as a reference for a corresponding liquid without hydrogen bonds, we have examined hydrogen sulphide. The typical shape of the Voronoi polyhedra is not too far from the polyhedra of a perfect ice I h crystal, although the numbers of vertices and faces are almost doubled. Indeed the actual number of vertices increases rapidly toward the liquid value as the crystal is perturbed by thermal motions. It is remarkable that the total surface and volume are always found closely correlated. It denotes a quasi-constant shape, i.e. the various shapes are not dependent on the volume. Indeed a direct analysis shows that there is no correlation between volume and shape. A quantitative characterization of the Voronoi polyhedra shape is proposed, through an “asphericity” parameter, whose distribution is found to be greatly affected by temperature: a net shift of the centre of the curve toward the value for the ice is found as the temperature is lowered. Finally it is found that there is a positive correlation between the potential energy of a molecule and the local volume, thus indicating that the hypothesis that the four-bonded molecules have a local density lower than average is incorrect.

Some turbulent/non-turbulent properties of the outer intermittent region of a boundary layer

A detailed study of the intermittency in the outer region of a flat-plate turbulent boundary layer has been carried out using digital sampling and processing techniques. Conditional averages are used to generate mean and fluctuating components for the turbulent and non-turbulent zones of fluid. More particularly, point averages of these variables, taken with reference to the instantaneous position of the turbulent/non-turbulent interface, have been made to show the distribution of various quantities through the turbulent front. The results indicate that significant differences exist at leading and trailing edges of the turbulent bursts and a more complete picture of the motion of an average large eddy is deduced.

The Mechanism of Pseudo-Shock Waves

In the pseudo-shock of duct flow, the static pressure at the wall surface increases gradually along the duct. This phenomenon has been explained by the well known Crocco's shockless model. His model, however, has some problems as follows : (1) It cannot present the distribution of various quantities related to the distance along the duct and the length of the pseudo-shock, since all the quantities are calculated as the functions of the ratio of the flow rate of the dissipative low velocity region to the total flow rate. (2) There is a discrepancy of velocities between the high and low speed regions at the final section of pseudo-shock. In order to correct these defects, a diffusion model for pseudo-shock has been presented in this paper by reforming his shockless model. The theoretical values of the length of pseudo-shock and the pressure distribution along the duct obtained by this model are able to explain the experimental data by the authors and other researchers quantitatively. Closer agreements are obtained in the case of higher Mach number at the initial section.