Probability Distribution Of Length Research Articles

Flights in a pseudo-chaotic system

We consider the problem of transport in a one-parameter family of piecewise rotations of the torus, for rotation number approaching 1∕4. This is a zero-entropy system which in this limit exhibits a divided phase space, with island chains immersed in a "pseudo-chaotic" region. We identify a novel mechanism for long-range transport, namely the adiabatic destruction of accelerator-mode islands. This process originates from the approximate translational invariance of the phase space and leads to long flights of linear motion, for a significant measure of initial conditions. We show that the asymptotic probability distribution of the flight lengths is determined by the geometric properties of a partition of the accelerator-mode island associated with the flight. We establish the existence of flights travelling distances of order O(1) in phase space. We provide evidence for the existence of a scattering process that connects flights travelling in opposite directions.

Measuring the Folding Landscape of a Harmonically Constrained Biopolymer

Pioneering studies have shown that the probability distribution of opening length for a DNA hairpin, recorded under constant force using an optical trap, can be used to reconstruct the energy landscape of the transition. However, measurements made under constant force are subject to some limitations. Under constant force a system with a sufficiently high energy barrier spends most of its time in the closed or open conformation, with relatively few statistics collected in the transition state region. We describe a measurement scheme in which the system is driven progressively through the transition by an optical trap and an algorithm is used to extract the energy landscape of the transition from the fluctuations recorded during this process. We illustrate this technique in simulations and demonstrate its effectiveness in experiments on a DNA hairpin. We find that the combination of this technique with the use of short DNA handles facilitates a high-resolution measurement of the hairpin's folding landscape with a very short measurement time.

Thermal Degradation of Adsorbed Bottle-Brush Macromolecules: A Molecular Dynamics Simulation

The scission kinetics of bottle-brush molecules in solution and on an adhesive substrate is modeled by means of Molecular Dynamics simulation with Langevin thermostat. Our macromolecules comprise a long flexible polymer backbone with $L$ segments, consisting of breakable bonds, along with two side chains of length $N$, tethered to each segment of the backbone. In agreement with recent experiments and theoretical predictions, we find that bond cleavage is significantly enhanced on a strongly attractive substrate even though the chemical nature of the bonds remains thereby unchanged. We find that the mean bond life time $<\tau>$ decreases upon adsorption by more than an order of magnitude even for brush molecules with comparatively short side chains $N=1 \div 4$. The distribution of scission probability along the bonds of the backbone is found to be rather sensitive regarding the interplay between length and grafting density of side chains. The life time $<\tau>$ declines with growing contour length $L$ as $<\tau>\propto L^{-0.17}$, and with side chain length as $<\tau>\propto N^{-0.53}$. The probability distribution of fragment lengths at different times agrees well with experimental observations. The variation of the mean length $L(t)$ of the fragments with elapsed time confirms the notion of the thermal degradation process as a first order reaction.

The distributions of chain lengths in a crosslinked polyisoprene network

A fundament of classical rubber elasticity theory is the Gaussian chain approximation formula, P(n,r) for the probability distribution of end-to-end distances of a polymer chain composed of n beads. It is considered to provide a realistic distribution of end-to-end distances, r, provided that the length of the polymer chain is much greater than its average end-to-end distance. By considering the number of beads (n) to be the independent variable, we can use P(n,r) to construct the probability distributions of network chain lengths, for fixed r. Since the network crosslinks reduce the probability for the occurrence of longer chains, the formula must be modified by a correction factor that takes this effect into account. We find that, both the shape of the n-probability distribution, its height, and the position of the peak vary significantly with r. We provide a numerical procedure for constructing networks that respect these distributions. The algorithm was implemented in a three-dimensional, random polymer-and-node network model to construct polyisoprene networks at two common crosslink densities. Although the procedure does not constrain the density, we find that the networks constructed have densities very close to the measured bulk density.

Performance evaluation for connection oriented service in the next generation Internet

In this paper, the principle of connection oriented service in the next generation Internet is analyzed. Considering the finite capacity, a Geom/ G/1/K queueing model with Setup, Close Delay and Close Down is built based on the operating mechanism of the connection oriented service. By using the approach of embedded Markov chain and supplementary variable, this queueing model is analyzed. The probability distribution of the queue length and the Probability Generating Function (P.G.F.) of waiting time are derived under the steady state. Correspondingly, the performance measures in terms of average response time, blocking probability and system throughput of this connection oriented Internet service are given to describe the dependency relationships between these measures and the time length $T$ of the Close Delay timer mathematically. Both of the analytical results and the simulation results are provided to investigate and validate the influence of the system parameters on the system performance. The research work in this paper can provide theoretic bases for network design, network maintenance, network management and capacity design of the next generation network systems.

Performance modelling of autonomous vehicle storage and retrieval systems with generally distributed service times

This paper proposes extensions of system conceptualisation models for autonomous vehicle storage and retrieval systems (AVS/RSs) to deal with non-exponential lift service times when the number of lifts and vehicles are both design variables. These extensions are based on an adaptation of a computational algorithm for estimating the probability distribution of queue lengths in capacitated, non-Poisson queuing systems. Simulation-based validation studies suggest that the proposed model extensions yield estimation errors comparable to those observed in earlier studies restricted to cases where the number of vehicle and lifts is treated as a single design variable.

A comparative study of crossover in differential evolution

In order to understand the role of crossover in differential evolution, theoretical analysis and comparative study of crossover in differential evolution are presented in this paper. Two new crossover methods, namely consecutive binomial crossover and non-consecutive exponential crossover, are designed. The probability distribution and expectation of crossover length for binomial and exponential crossover used in this paper are derived. Various differential evolution algorithms with different crossover methods including mutation-only differential evolution are comprehensively compared at system level instead of parameter level. Based on the theoretical analysis and simulation results, the effect of crossover on the reliability and efficiency of differential evolution algorithms is discussed. Some insights are revealed.

Actin Cross-Linkers and the Shape of Stereocilia

Stereocilia are actin-based cellular protrusions essential for hearing. We propose that they are shaped by the detachment dynamics of actin cross-linkers, in particular espin. We account for experimentally observed stereocilium shapes, treadmilling velocity to length relationship, espin 1 localization profile, and microvillus length to espin level relationship. If the cross-linkers are allowed to reattach, our model yields a dynamical phase transition toward unbounded growth. Considering the simplified case of a noninteracting, one-filament system, we calculate the length probability distribution in the growing phase and its stationary form in a continuum approximation of the finite-length phase. Numerical simulations of interacting filaments suggest an anomalous power-law divergence of the protrusion length at the growth transition, which could be a universal feature of cross-linked depolymerizing systems.

A note on reconstructing animal social networks from independent small-group observations

Animal social networks are often built by aggregating a series of independent observations of two or more members of a group interacting or in association. Every time an observation is made, edges are drawn between each pair of individuals involved. I examined the effect of edge sample size on the reconstruction of social networks. I created different artificial networks and sampled edges from each. I estimated and compared the number of nodes, number of components, path length, clustering coefficient, network density, mean degree, betweenness centrality and degree probability distribution of the reconstructed networks to the true value of the network. I describe how the accuracy of these measures changes as the fraction of sampled edges increases. I show that edge sample size affects network measures in different ways and that when an incomplete sample is analysed, network properties can be considerably misrepresented. I also show that, because animal networks are typically small, simple curve fitting to the degree distribution P(k) should be done with caution, because different curve models can show significant fit for the same data. Overall, the results indicate that strong claims about animal social networks should not be made unless considerable effort has been made to collect an exhaustive number of association/interaction data points. If observations of associations/interactions are accumulated over a long period, the effect of increasing edge sample size could be mistaken for temporal change in social network and could also muddy the comparison of network structure between populations and between species.

Continuous-time random walk: Crossover from anomalous regime to normal regime

We consider decoupled continuous time random walk with finite characteristic waiting time and jump length variance. We take approximate jump length probability distribution and waiting time probability distribution given by a product of power-law and exponential function. Using this waiting time probability distribution we study diffusion behaviors for all the time. Due to the finite characteristic waiting time and jump length variance the model presents normal diffusive behavior in the long-time limit. However, the model can describe anomalous behavior at the short and intermediate times. In particular, the model can describe subdiffusive, normal, and superdiffusive behaviors at the short times. Moreover, exact solution for probability distribution of the system is also investigated.

Fluctuations in induced charge introduced by Te inclusions within CdZnTe radiation detectors

Recently, homogenization theory based on a multiple-scale perturbation of the electron transport equation has been used to derive a mathematical framework for modeling the excess charge lost to Te inclusions within radiation detectors based on semi-insulating cadmium zinc telluride (CdZnTe). In that theory, the heterogeneous material is mathematically replaced by a homogenized CdZnTe crystal whose effective electron attenuation length incorporates the additional uniform electron trapping caused by the inclusions. In this paper, the homogenization theory is extended to incorporate fluctuations in the induced charge (i.e., charge collection nonuniformities) introduced by the random position and size distributions of a noncorrelated population of small (i.e, &amp;lt;20 μm) Te inclusions. Analysis of the effective parameters derived within the homogenized framework is used to develop a probability distribution of effective electron attenuation lengths, and therefore effective mobility-lifetime products, as a function of both the position and size distribution of Te inclusions. Example distributions are detailed for the case of an exponential size distribution at various number densities. Further, it is demonstrated that the inclusion-induced material nonuniformities derived in this paper can be numerically sampled efficiently, making them applicable to Monte Carlo device simulation of realistic CdZnTe detectors. Simulated charge induction maps and pulse-height spectra are presented and compared to recently published measurements.

Studies on the probability distribution of homogeneous raw silk length (1)

Studies on the probability distribution of homogeneous raw silk length (1)

Tomography-Based Analysis of Radiative Transfer in Reacting Packed Beds Undergoing a Solid-Gas Thermochemical Transformation

A reacting packed-bed undergoing a high-temperature thermochemical solid-gas transformation is considered. The steam- and dry-gasification of carbonaceous materials to syngas is selected as the model reaction. The exact 3D digital geometrical representation of the packed-bed is obtained by computer tomography and used in direct pore-level simulations to characterize its morphological and radiative transport properties as a function of the reaction extent. Two-point correlation functions and mathematical morphology operations are applied to calculate porosities, specific surfaces, particle-size distributions, and representative elementary volumes. The collision-based Monte Carlo method is applied to determine the probability distribution of attenuation path length and direction of incidence at the solid-fluid boundary, which are linked to the extinction coefficient, scattering phase function, and scattering albedo. These effective properties can be then incorporated in continuum models of the reacting packed-bed.

Fractal dimensions of the Q-state Potts model for complete and external hulls

Fortuin–Kastelyn clusters in the criticalQ-state Potts model are conformally invariant fractals. We obtain simulation resultsfor the fractal dimension of the complete and external (accessible) hulls forQ = 1,2,3, and4, on clusters that wrap around a cylindrical system. We find excellent agreement betweenthese results and theoretical predictions. We also obtain the probability distributions of thehull lengths and maximal heights of the clusters in this geometry and provide a conjecturefor their form.

Master Equation Approach to Gypsum Needle Crystallization

We write and solve a master equation which governs the stochastic growth of interacting gypsum needles. Needle blocking by steric hindrance is reproduced in an effective way. The comparison of the results with submicrometric simulations enables us to choose a small number of fitting parameters to optimize the master equation approach. The stochastic description qualitatively predicts the main features of the dynamics, including the transition toward incomplete dissolution of plaster for increasing values of the number of nuclei per plaster grain. The master equation quantitatively reproduces some morphological properties of the final material, such as mean value and standard deviation of the probability distribution of needle length.

Cleavage pattern of DNA caused by endonuclease: Theoretical modeling and experimental verification

In apoptotic cells, genomic DNA molecules are fragmented into multiple fragments with lengths that are integer multiples of approximately 180–200 base pairs (bp), i.e., the size of a single nucleosome. Here we propose a simple mathematical model for interpreting this cleavage pattern of DNA. Under the condition of a purely stochastic cleavage process, we derive a time evolution of the probability distribution of the fragment length by a Poisson distribution. We examine the applicability of our model by analyzing experimental results with apoptotic cells. Our model enables us to satisfactorily interpret the experimental trends. Interestingly, this theoretical fitting of the experimental data provides kinetic information for the cleavage reaction.

Force chains in a uniaxially compressed static granular matter in 2D

Granular matter is a large assemblage of dense-packing particles. The interparticle forces are transmitted through heterogeneous chain architecture. The force chains would display different responses as external loading varies, and it would be directly related to the macroscopic mechanical properties of the granular system. Therefore, understanding the properties of force chains is fundamental to the study in granular systems. In this work, we firstly analyzed three characteristic time scales involved in processes occurring in granular systems, and proposed three dimensionless numbers to measure their relative importance. Secondly, a series of numerical simulations were conducted on a uniaxial compression system consisting of 12400 polydispersed particles. Our results showed that the shape of force distributions are unaffected by system preparation history and packing fractions in the range from 0855 to 0886, but mainly affected by the static surface friction. By defining three conditions for evaluating strong force chain, the probability distribution of force chain length was found in the form of power law with an exponent of 172, which is independent of packing fractions and static surface frictions in this static system.

Predictions from a stochastic polymer model for the MinDE protein dynamics inEscherichia coli

The spatiotemporal oscillations of the Min proteins in the bacterium Escherichia coli play an important role in cell division. A number of different models have been proposed to explain the dynamics from the underlying biochemistry. Here, we extend a previously described discrete polymer model from a deterministic to a stochastic formulation. We express the stochastic evolution of the oscillatory system as a map from the probability distribution of maximum polymer length in one period of the oscillation to the probability distribution of maximum polymer length half a period later and solve for the fixed point of the map with a combined analytical and numerical technique. This solution gives a theoretical prediction of the distributions of both lengths of the polar MinD zones and periods of oscillations--both of which are experimentally measurable. The model provides an interesting example of a stochastic hybrid system that is, in some limits, analytically tractable.

Experimental analysis of tidal network growth and development

In this paper we present the results of a first series of laboratory experiments carried out in a large experimental apparatus, aimed at reproducing a typical lagoonal environment subject to tidal forcings. The experiments were designed in order to improve our understanding of the main processes governing tidal network initiation and its progressive morphodynamic evolution. During the experiments we observed the growth and development of tidal networks and analyzed their most relevant geomorphic features, taking into account the role played by the characteristics of the tidal forcing in driving the development of channeled patterns. The synthetic networks displayed geomorphic features which compare favorably with those of actual networks, showing that our experimental framework proves useful for analyzing the processes governing the formation and evolution of tidal channel networks. In particular, the synthetic networks develop via headward growth driven by the exceedance of a critical bottom shear stress, and display width-to-depth ratios and seaward exponential widening in accordance with observational evidence. Furthermore experimental networks reproduce statistical network characteristics of geomorphic relevance, such as the exponential probability distribution of unchanneled path lengths.

Atomic jumps during surface diffusion

The characteristics of atomic displacements during surface diffusion of Cu on Cu(111) are studied by means of molecular dynamics simulations. It is found that even at very low substrate temperatures, the majority of the jumps are correlated, i.e., the displacement directions are not randomly chosen but rather keep some sort of memory from the previous moves and are influenced by them. Long jumps, spanning several surface unit cells, are observed at all temperatures. From an analysis of their length probability distribution information can be obtained about the mechanisms of friction and energy transfer between the diffusing adatom and the substrate. Both long jumps and recrossings (displacements in which the adatom moves back and forth between two adjacent adsorption sites) appear with a higher activation energy than normal diffusion. Finally, the influence of the instantaneous atomic configuration of the substrate on the adatom's trajectory is also highlighted.