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arXiv2011

The Theory of Uncertainty for Derived Results: Properties of Equations Representing Physicochemical Evaluation Systems

Any physiochemical variable (Ym) is always determined from certain measured variables {Xi}. The uncertainties {ui} of measuring {Xi} are generally a priori ensured as acceptable. However, there is no general method for assessing uncertainty (em) in the desired Ym, i.e. irrespective of whatever might be its system-specific-relationship (SSR) with {Xi}, and/ or be the causes of {ui}. We here therefore study the behaviors of different typical SSRs. The study shows that any SSR is characterized by a set of parameters, which govern em. That is, em is shown to represent a net SSR-driven (purely systematic) change in ui(s); and it cannot vary for whether ui(s) be caused by either or both statistical and systematic reasons. We thus present the general relationship of em with ui(s), and discuss how it can be used to predict a priori the requirements for an evaluated Ym to be representative, and hence to set the guidelines for designing experiments and also really appropriate evaluation models. Say: Y_m= f_m ({X_i}_(i=1)^N), then, although: e_m= g_m ({u_i}_(i=1)^N), "N" is not a key factor in governing em. However, simply for varying "fm", the em is demonstrated to be either equaling a ui, or >ui, or even <ui. Further, the limiting error (d_m^(Lim.)) in determining an Ym is also shown to be decided by "fm" (SSR). Thus, all SSRs are classified into two groups: (I) the SSRs that can never lead "d_m^(Lim.)" to be zero; and (II) the SSRs that enable "d_m^(Lim.)" to be zero. In fact, the theoretical-tool (SSR) is by pros and cons no different from any discrete experimental-means of a study, and has resemblance with chemical reactions as well.

physics.data-an↗
arXiv2008

GEANT4 and CREME96 comparison using only proton fluxes

CREME96 and GEANT4 are two well known particle transport codes through matter in space science. We present a comparison between the proton fluxes outgoing from an aluminium target, obtained by using both tools. The primary proton flux is obtained by CREME96 only, covering an energy range from MeV to hundreds GeV with the same result in both cases. We studied different thickness targets and two different GEANT4 physics lists in order to show how the spectra of the outgoing proton fluxes are modified. Our findings show consistent agreement of simulation data by each tool, with regards both GEANT4 physics lists and every thickness target analysed.

physics.comp-ph↗
arXiv2007

Diffusion-limited unbinding of small peptides from PDZ domains

PDZ domains are typical examples of binding motifs mediating the formation of protein-protein assemblies in many different cells. A quantitative characterization of the mechanisms intertwining structure, chemistry and dynamics with the PDZ function represent a challenge in molecular biology. Here we investigated the influence of native state topology on the thermodynamics and the dissociation kinetics for a complex PDZ-peptide via Molecular Dynamics simulations based on a coarse-grained description of PDZ domains. Our native-centric approach neglects chemical details but incorporates the basic structural information to reproduce the protein functional dynamics as it couples to the binding. We found that at physiological temperatures the unbinding of a peptide from the PDZ domain becomes increasingly diffusive rather than thermally activated, as a consequence of the significant reduction of the free energy barrier with temperature. In turn, this results in a significant slowing down of the process of two orders of magnitude with respect to the conventional Arrhenius extrapolation from low temperature calculations. Finally, a detailed analysis of a typical unbinding event based on the rupture times of single peptide-PDZ contacts allows to shed further light on the dissociation mechanism and to elaborate a coherent picture of the relation between function and dynamics in PDZ domains.

physics.bio-ph↗
arXiv2009

The Finite Difference Time Domain Method for Computing Single-Particle Density Matrix

A general method for numerical computation of the thermal density matrix of a single-particle quantum system is presented. The Schrodinger equation in imaginary time tau is solved numerically by the finite difference time domain (FDTD) method using a set of initial wave functions at tau=0 . By choosing this initial set appropriately, the set of wave functions generated by the FDTD method can be used to construct the thermal density matrix. The theoretical basis of the method, a numerical algorithm for its implementation, and illustrative examples in one, two and three dimensions are given in this paper. The numerical results show that the procedure is efficient and accurately determines the density matrix and thermodynamic properties of single-particle systems. Extensions of the method to more general cases are briefly indicated.

physics.comp-ph↗
arXiv2008

A Small Parameter Method for Few-Body Problems

A procedure to solve few-body problems which is based on an expansion over a small parameter is developed. The parameter is the ratio of potential energy to kinetic energy in the subspace of states having not small hyperspherical quantum numbers, K>K_0. Dynamic equations are reduced perturbatively to those in the finite subspace with K \le K_0. The contribution from the subspace with K>K_0 is taken into account in a closed form, i.e. without an expansion over basis functions.

nucl-th↗
arXiv2008

When the spatial networks split?

We consider a three dimensional spatial network, where $N$ nodes are randomly distributed within a cube $L\times L\times L$. Each two nodes are connected if their mutual distance does not excess a given cutoff $a$. We analyse numerically the probability distribution of the critical density $ρ_c=N(a_c/L)^3$, where one or more nodes become separated; $ρ_c$ is found to increase with $N$ as $N^{0.105}$, where $N$ is between 20 and 300. The results can be useful for a design of protocols to control sets of wearable sensors.

physics.comp-ph↗
arXiv2008

What Is There Between Any Two Nodes in a Complex Network?

This article focuses on the identification of the number of paths with different lengths between pairs of nodes in complex networks and how, by providing comprehensive information about the network topology, such an information can be effectively used for characterization of theoretical and real-world complex networks, as well as for identification of communities.

physics.soc-ph↗
arXiv2008

Optimal design of composite granular protectors

We employ an evolutionary algorithm to investigate the optimal design of composite protectors using one-dimensional granular chains composed of beads of various sizes, masses, and stiffnesses. We define a fitness function using the maximum force transmitted from the protector to a "wall" that represents the body to be protected and accordingly optimize the {topology} (arrangement), {size}, and {material} of the chain. We obtain optimally randomized granular protectors characterized by high-energy equipartition and the transformation of incident waves into interacting solitary pulses. We consistently observe that the pulses traveling to the wall combine to form an extended (long-wavelength), small-amplitude pulse.

cond-mat.mtrl-sci↗
arXiv2012

The Modeling of Time-Structured Multiturn Injection into Fermilab Main Injector (Microbunch Injection with Parasitic Longitudinal Painting)

This paper presents the modeling of time-structured multiturn injection for an upgraded Main Injector with the 8-GeV Superconducting RF proton driver, or an ILC-style linac, or a Project-X linac. The Radio-Frequency mismatch between a linac and the upgraded Main Injector will induce parasitic longitudinal painting in RF-phase direction. Several different scenarios with a choice of different RF parameters for single RF system and double RF system in the presence of longitudinal space charge have been investigated. From the studies of microbunch injection with the aid of ESME (2003) numerical simulations, it is found that the dual RF system with a choice of appropriate RF parameters allows us to overcome the space-charge limitation set by beam intensity during the multiturn-injection process. A double RF system with a harmonic ratio (R_H = H_2/H_1) of 2.0 and a voltage ratio (R_V = V_2/V_1) of 0.5 are most favored to reduce both longitudinal and transverse effects of space charge in the Main Injector.

physics.acc-ph↗
arXiv2008

Time Parallel Scalable Multiphysics/Multiscale Framework

We propose a new computational framework that combines the recently developed time-parallel (TP) and the compound wavelet matrix (CWM) methods. The framework, termed tpCWM, offers significant computational acceleration by making multiscale/multiphysics simulations computationally scalable in time and space domains. We demonstrate the accuracy and the scalability of the method on a prototype problem with oscillatory trajectory. The method corrects the coarse solution by iterative use of the CWM, which compounds the fine and the coarse solutions for the processes. Computational savings, over the fine solution as well as the TP method, in terms of the real time required to perform the simulations, can reach several orders of magnitude. We believe that this method is general enough to be applicable to a wide-class of computational physics problems. Tendency towards large number of cores and processors in parallel computers is compatible with the computational scalability of the algorithm.

physics.comp-ph↗
arXiv2008

Sensitivity of complex networks measurements

Complex networks obtained from the real-world networks are often characterized by incompleteness and noise, consequences of limited sampling as well as artifacts in the acquisition process. Because the characterization, analysis and modeling of complex systems underlain by complex networks are critically affected by the quality of the respective initial structures, it becomes imperative to devise methodologies for identifying and quantifying the effect of such sampling problems on the characterization of complex networks. Given that several measurements need to be applied in order to achieve a comprehensive characterization of complex networks, it is important to investigate the effect of incompleteness and noise on such quantifications. In this article we report such a study, involving 8 different measurements applied on 6 different complex networks models. We evaluate the sensitiveness of the measurements to perturbations in the topology of the network considering the relative entropy. Three particularly important types of progressive perturbations to the network are considered: edge suppression, addition and rewiring. The conclusions have important practical consequences including the fact that scale-free structures are more robust to perturbations. The measurements allowing the best balance of stability (smaller sensitivity to perturbations) and discriminability (separation between different network topologies) were also identified.

physics.soc-ph↗
arXiv2008

A Gear-like Predictor-Corrector method for Brownian Dynamics Simulation

We introduce a Predictor-Corrector type method suitable for performing many-particle Brownian Dynamics simulations. Since the method goes over to the Gear's method for Molecular Dynamics simulation in the limit of vanishing friction, we refer to it as a Gear-like algorithm. The algorithm has been tested on a one-dimensional, stochastically damped harmonic oscillator model, showing that it can cover a wide range of friction coefficients with a high-order accuracy, excellent stability, and a very small energy drift on the long time scales.

physics.plasm-ph↗
arXiv2010

Accurate Estimation of Solvation Free Energy Using Polynomial Fitting Techniques

This report details an approach to improve the accuracy and precision of free energy difference estimates using thermodynamic integration data (slope of the free energy with respect to the switching variable lambda) and its application to calculating solvation free energy. The central idea is to utilize polynomial fitting schemes to approximate the thermodynamic integration data to improve the accuracy and precision of the free energy difference estimates. In this report we introduce polynomial and spline interpolation techniques. Two systems with analytically solvable relative free energies are used to test the accuracy and precision of the interpolation approach (Shyu and Ytreberg, J Comput Chem 30: 2297-2304, 2009). We also use both interpolation and extrapolation methods to determine a small molecule salvation free energy. Our simulations show that, using such polynomial techniques and non-equidistant lambda values, the solvation free energy can be estimated with high accuracy without using soft-core scaling and separate simulations for Lennard-Jones and partial charges. The results from our study suggest these polynomial techniques, especially with use of non-equidistant lambda values, improve the accuracy and precision for dF estimates without demanding additional simulations. To allow researchers to immediately utilize these methods, free software and documentation is provided via http://www.phys.uidaho.edu/ytreberg/software

physics.comp-ph↗
arXiv2008

Fractality feature in oil price fluctuations

The scaling properties of oil price fluctuations are described as a non-stationary stochastic process realized by a time series of finite length. An original model is used to extract the scaling exponent of the fluctuation functions within a non-stationary process formulation. It is shown that, when returns are measured over intervals less than 10 days, the Probability Density Functions (PDFs) exhibit self-similarity and monoscaling, in contrast to the multifractal behavior of the PDFs at macro-scales (typically larger than one month). We find that the time evolution of the distributions are well fitted by a Levy distribution law at micro-scales. The relevance of a Levy distribution is made plausible by a simple model of nonlinear transfer

q-fin.ST↗
arXiv2010

Stability of Maximum likelihood based clustering methods: exploring the backbone of classifications (Who is keeping you in that community?)

Components of complex systems are often classified according to the way they interact with each other. In graph theory such groups are known as clusters or communities. Many different techniques have been recently proposed to detect them, some of which involve inference methods using either Bayesian or Maximum Likelihood approaches. In this article, we study a statistical model designed for detecting clusters based on connection similarity. The basic assumption of the model is that the graph was generated by a certain grouping of the nodes and an Expectation Maximization algorithm is employed to infer that grouping. We show that the method admits further development to yield a stability analysis of the groupings that quantifies the extent to which each node influences its neighbors group membership. Our approach naturally allows for the identification of the key elements responsible for the grouping and their resilience to changes in the network. Given the generality of the assumptions underlying the statistical model, such nodes are likely to play special roles in the original system. We illustrate this point by analyzing several empirical networks for which further information about the properties of the nodes is available. The search and identification of stabilizing nodes constitutes thus a novel technique to characterize the relevance of nodes in complex networks.

physics.soc-ph↗