Relationship between entropy and diffusion: A statistical mechanical derivation of Rosenfeld expression for a rugged energy landscape

Diffusion-a measure of dynamics, and entropy-a measure of disorder in the system are found to be intimately correlated in many systems, and the correlation is often strongly non-linear. We explore the origin of this complex dependence by studying diffusion of a point Brownian particle on a model potential energy surface characterized by ruggedness. If we assume that the ruggedness has a Gaussian distribution, then for this model, one can obtain the excess entropy exactly for any dimension. By using the expression for the mean first passage time, we present a statistical mechanical derivation of the well-known and well-tested scaling relation proposed by Rosenfeld between diffusion and excess entropy. In anticipation that Rosenfeld diffusion-entropy scaling (RDES) relation may continue to be valid in higher dimensions (where the mean first passage time approach is not available), we carry out an effective medium approximation (EMA) based analysis of the effective transition rate and hence of the effective diffusion coefficient. We show that the EMA expression can be used to derive the RDES scaling relation for any dimension higher than unity. However, RDES is shown to break down in the presence of spatial correlation among the energy landscape values. (C) 2015 AIP Publishing LLC.

Three-dimensional warping in strip-based composite four-bar mechanisms

This work intends to demonstrate the effect of geometrically non-linear cross-sectional analysis of certain composite beam-based four-bar mechanisms in predicting the three-dimensional warping of the cross-section. The only restriction in the present analysis is that the strains within each elastic body remain small (i.e., this work does not deal with materials exhibiting non-linear constitutive laws at the 3-D level). Here, all component bars of the mechanism are made of fiber-reinforced laminates. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. Each component of the mechanism is modeled as a beam based on geometrically non-linear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and non-linear 1-D analyses along the three beam reference curves. The splitting of the three-dimensional beam problem into two- and one-dimensional parts, called dimensional reduction, results in a tremendous savings of computational effort relative to the cost of three-dimensional finite element analysis, the only alternative for realistic beams. The analysis of beam-like structures made of laminated composite materials requires a much more complicated methodology. Hence, the analysis procedure based on Variational Asymptotic Method (VAM), a tool to carry out the dimensional reduction, is used here. The representative cross-sections of all component bars are analyzed using two different approaches: (1) Numerical Model and (2) Analytical Model. Four-bar mechanisms are analyzed using the above two approaches for Omega = 20 rad/s and Omega = pi rad/s and observed the same behavior in both cases. The noticeable snap-shots of the deformation shapes of the mechanism about 1000 frames are also reported using commercial software (I-DEAS + NASTRAN + ADAMS). The maximum out-of-plane warping of the cross-section is observed at the mid-span of bar-1, bar-2 and bar-3 are 1.5 mm, 250 mm and 1.0 mm, respectively, for t = 0:5 s. (C) 2015 Elsevier Ltd. All rights reserved.

Modelling and analysis of an open-loop induction motor drive incorporating the effect of inverter dead-time

The objective of this paper is to study the influence of inverter dead-time on steady as well as dynamic operation of an open-loop induction motor drive fed from a voltage source inverter (VSI). Towards this goal, this paper presents a systematic derivation of a dynamic model for an inverter-fed induction motor, incorporating the effect of inverter dead-time, in the synchronously revolving dq reference frame. Simulation results based on this dynamic model bring out the impact of inverter dead-time on both the transient response and steady-state operation of the motor drive. For the purpose of steady-state analysis, the dynamic model of the motor drive is used to derive a steady-state model, which is found to be non-linear. The steady-state model shows that the impact of dead-time can be seen as an additional resistance in the stator circuit, whose value depends on the stator current. Towards precise evaluation of this dead-time equivalent resistance, an analytical expression is proposed for the same in terms of inverter dead-time, switching frequency, modulation index and load impedance. The notion of dead-time equivalent resistance is shown to simplify the solution of the non-linear steady-state model. The analytically evaluated steady-state solutions are validated through numerical simulations and experiments.

Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments.

Self-assembly processes resulting in linear structures are often observed in molecular biology, and include the formation of functional filaments such as actin and tubulin, as well as generally dysfunctional ones such as amyloid aggregates. Although the basic kinetic equations describing these phenomena are well-established, it has proved to be challenging, due to their non-linear nature, to derive solutions to these equations except for special cases. The availability of general analytical solutions provides a route for determining the rates of molecular level processes from the analysis of macroscopic experimental measurements of the growth kinetics, in addition to the phenomenological parameters, such as lag times and maximal growth rates that are already obtainable from standard fitting procedures. We describe here an analytical approach based on fixed-point analysis, which provides self-consistent solutions for the growth of filamentous structures that can, in addition to elongation, undergo internal fracturing and monomer-dependent nucleation as mechanisms for generating new free ends acting as growth sites. Our results generalise the analytical expression for sigmoidal growth kinetics from the Oosawa theory for nucleated polymerisation to the case of fragmenting filaments. We determine the corresponding growth laws in closed form and derive from first principles a number of relationships which have been empirically established for the kinetics of the self-assembly of amyloid fibrils.

Studies on two-phase co-current air/non-Newtonian shear-thinning fluid flows in inclined smooth pipes

In this work. co-current flow characteristics of air/non-Newtonian liquid systems in inclined smooth pipes are studied experimentally and theoretically using transparent tubes of 20, 40 and 60 turn in diameter. Each tube includes two 10 m lone pipe branches connected by a U-bend that is capable of being inclined to any angle, from a completely horizontal to a fully vertical position. The flow rate of each phase is varied over a wide range. The studied flow phenomena are bubbly, plug flow, slug flow, churn flow and annular flow. These are observed and recorded by a high flow. stratified flow. -speed camera over a wide range of operating conditions. The effects of the liquid phase properties, the inclination angle and the pipe diameter on two-phase flow characteristics are systematically studied. The Heywood-Charles model for horizontal flow was modified to accommodate stratified flow in inclined pipes, taking into account the average void fraction and pressure drop of the mixture flow of a gas/non-Newtonian liquid. The pressure drop gradient model of Taitel and Barnea for a gas/Newtonian liquid slug flow was extended to include liquids possessing shear-thinning flow behaviour in inclined pipes. The comparison of the predicted values with the experimental data shows that the models presented here provide a reasonable estimate of the average void fraction and the corresponding pressure drop for the mixture flow of a gas/ non-Newtonian liquid. (C) 2007 Elsevier Ltd. All rights reserved.

MIRACLE Project Plan

Social scientists have used agent-based models (ABMs) to explore the interaction and feedbacks among social agents and their environments. The bottom-up structure of ABMs enables simulation and investigation of complex systems and their emergent behaviour with a high level of detail; however the stochastic nature and potential combinations of parameters of such models create large non-linear multidimensional “big data,” which are difficult to analyze using traditional statistical methods. Our proposed project seeks to address this challenge by developing algorithms and web-based analysis and visualization tools that provide automated means of discovering complex relationships among variables. The tools will enable modellers to easily manage, analyze, visualize, and compare their output data, and will provide stakeholders, policy makers and the general public with intuitive web interfaces to explore, interact with and provide feedback on otherwise difficult-to-understand models.

On the Selection of Non-Invasive Methods Based on Speech Analysis Oriented to Automatic Alzheimer Disease Diagnosis

The work presented here is part of a larger study to identify novel technologies and biomarkers for early Alzheimer disease (AD) detection and it focuses on evaluating the suitability of a new approach for early AD diagnosis by non-invasive methods. The purpose is to examine in a pilot study the potential of applying intelligent algorithms to speech features obtained from suspected patients in order to contribute to the improvement of diagnosis of AD and its degree of severity. In this sense, Artificial Neural Networks (ANN) have been used for the automatic classification of the two classes (AD and control subjects). Two human issues have been analyzed for feature selection: Spontaneous Speech and Emotional Response. Not only linear features but also non-linear ones, such as Fractal Dimension, have been explored. The approach is non invasive, low cost and without any side effects. Obtained experimental results were very satisfactory and promising for early diagnosis and classification of AD patients.

Using the system dynamics paradigm in teaching and learning technological university subjets

2nd International Conference on Education and New Learning Technologies

Existence, uniqueness, and stability of solutions of a class of nonlinear partial differential equations

In this study we investigate the existence, uniqueness and asymptotic stability of solutions of a class of nonlinear integral equations which are representations for some time dependent non- linear partial differential equations. Sufficient conditions are established which allow one to infer the stability of the nonlinear equations from the stability of the linearized equations. Improved estimates of the domain of stability are obtained using a Liapunov Functional approach. These results are applied to some nonlinear partial differential equations governing the behavior of nonlinear continuous dynamical systems.

Lasing without or with inversion in an open four-level system with a phase-fluctuation driving field

The effect of exit rate and the ratio of atomic injection rate on gain behaviour has been investigated, and the effects of phase fluctuation on absorption, dispersion and population difference in an open four-level system have been analysed by using numerical simulation from the steady linear, analytical solution. The variation of the linewidth, Rabi frequency of the driving field, the exit rate or the ratio of atomic injection rate can change the lasing properties in the open system. The presence of finite linewidth due to driving-field phase fluctuation prevents the open four-level atomic system from obtaining a high refractive index along with zero absorption.

Mechanistic aspects of the Ziegler-Natta polymerization

The isotope effect on propagation rate was determined for four homogeneous ethylene polymerization systems. The catalytic system Cp_2Ti(Et)Cl + EtA1Cl_2 has a k^H_p/k^D_p = 1.035 ± 0.03. This result strongly supports an insertion mechanism which does not involve a hydrogen migration during the rate determining step of propagation (Cossee mechanism). Three metal-alkyl free systems were also studied. The catalyst I_2 (PMe_3)_3Ta(neopentylidene)(H) has a k^H_p/k^D_p = 1.709. It is interpreted as a primary isotope effect involving a non-linear a-hydrogen migration during the rate determining step of propagation (Green mechanism). The lanthanide complexes Cp*_2LuMe•Et_2O and Cp*_2YbMe•Et_2O have a k^H_p/k^D_p = 1.46 and 1.25, respectively. They are interpreted as primary isotope effects due to a partial hydrogen migration during the rate determining step of propagation.

The presence of a precoordination or other intermediate species during the polymerization of ethylene by the mentioned metal-alkyl free catalysts was sought by low temperature NMR spectroscopy. However, no evidence for such species was found. If they exist, their concentrations are very small or their lifetimes are shorter than the NMR time scale.

Two titanocene (alkenyl)chlorides (hexenyl 1 and heptenyl 2 were prepared from titanocene dichloride and a THF solution of the corresponding alkenylmagnesium chloride. They do not cyclize in solution when alone, but cyclization to their respective titanocene(methyl(cycloalkyl) chlorides occurs readily in the presence of a Lewis acid. It is demonstrated that such cyclization occurs with the alkenyl ligand within the coordination sphere of the titanium atom. Cyclization of 1 with EtAlCl_2 at 0°C occurs in less than 95 msec (ethylene insertion time), as shown by the presence of 97% cyclopentyl-capped oligomers when polymerizing ethylene with this system. Some alkyl exchange occurs (3%). Cyclization of 2 is slower under the same reaction conditions and is not complete in 95 msec as shown by the presence of both cyclohexyl-capped oligomers (35%) and odd number α-olefin oligomers (50%). Alkyl exchange is more extensive as evidenced by the even number n-alkanes (15%).

Cyclization of 2-d_1 (titanocene(hept-6-en-1-yl-1-d_1)chloride) with EtA1Cl_2 demonstrated that for this system there is no α-hydrogen participation during said process. The cyclization is believed to occur by a Cossee-type mechanism. There was no evidence for precoordination of the alkenyl double bond during the cyclization process.

Expanding the Toolkit for Synthetic Biology: Frameworks for Native-like Non-natural Gene Circuits

Synthetic biology combines biological parts from different sources in order to engineer non-native, functional systems. While there is a lot of potential for synthetic biology to revolutionize processes, such as the production of pharmaceuticals, engineering synthetic systems has been challenging. It is oftentimes necessary to explore a large design space to balance the levels of interacting components in the circuit. There are also times where it is desirable to incorporate enzymes that have non-biological functions into a synthetic circuit. Tuning the levels of different components, however, is often restricted to a fixed operating point, and this makes synthetic systems sensitive to changes in the environment. Natural systems are able to respond dynamically to a changing environment by obtaining information relevant to the function of the circuit. This work addresses these problems by establishing frameworks and mechanisms that allow synthetic circuits to communicate with the environment, maintain fixed ratios between components, and potentially add new parts that are outside the realm of current biological function. These frameworks provide a way for synthetic circuits to behave more like natural circuits by enabling a dynamic response, and provide a systematic and rational way to search design space to an experimentally tractable size where likely solutions exist. We hope that the contributions described below will aid in allowing synthetic biology to realize its potential.

Optimizations for the uniformity of the non-volatile volume grating in doubly doped LiNbO3 crystals

The formation of the non-uniformity of the non-volatile volume grating in doubly doped LiNbO3 crystals is studied in detail. We find that the non-uniformity of the grating is mainly caused by strong ultraviolet light absorption, and the average saturation space-charge field is small and the diffraction efficiency is low as a result of the non-uniformity of the grating. In order to optimize the uniformity of the grating, we propose the recording scheme by using two sensitizing beams simultaneously from the two opposite sides of the crystals. Theoretical simulations and experimental verifications are performed. Results show that the well uniformed grating with high diffraction efficiency can be obtained by using this optimization scheme. (c) 2004 Elsevier B.V. All rights reserved.

Transmission matrices and lumped parameter models for continuous systems

The use of transmission matrices and lumped parameter models for describing continuous systems is the subject of this study. Non-uniform continuous systems which play important roles in practical vibration problems, e.g., torsional oscillations in bars, transverse bending vibrations of beams, etc., are of primary importance.

A new approach for deriving closed form transmission matrices is applied to several classes of non-uniform continuous segments of one dimensional and beam systems. A power series expansion method is presented for determining approximate transmission matrices of any order for segments of non-uniform systems whose solutions cannot be found in closed form. This direct series method is shown to give results comparable to those of the improved lumped parameter models for one dimensional systems.

Four types of lumped parameter models are evaluated on the basis of the uniform continuous one dimensional system by comparing the behavior of the frequency root errors. The lumped parameter models which are based upon a close fit to the low frequency approximation of the exact transmission matrix, at the segment level, are shown to be superior. On this basis an improved lumped parameter model is recommended for approximating non-uniform segments. This new model is compared to a uniform segment approximation and error curves are presented for systems whose areas very quadratically and linearly. The effect of varying segment lengths is investigated for one dimensional systems and results indicate very little improvement in comparison to the use of equal length segments. For purposes of completeness, a brief summary of various lumped parameter models and other techniques which have previously been used to approximate the uniform Bernoulli-Euler beam is a given.

The predicting power of models for eutrophication

Restoration of water-bodies from eutrophication has proved to be extremely difficult. Mathematical models have been used extensively to provide guidance for management decisions. The aim of this paper is to elucidate important problems of using models for predicting environmental changes. First, the necessity for a proper uncertainty assessment of the model, upon calibration, has not been widely recognized. Predictions must not be a single time trajectory; they should be a band, expressing system uncertainty and natural variability. Availability of this information may alter the decision to be taken. Second, even with well-calibrated models, there is no guarantee they will give correct projections in situations where the model is used to predict the effects of measures designed to bring the system into an entirely different ”operating point”, as is typically the case in eutrophication abatement. The concept of educated speculation is introduced to partially overcome this difficulty. Lake Veluwe is used as a case to illustrate the point. Third, as questions become more detailed, such as ”what about expected algal composition”, there is a greater probability of running into fundamental problems that are associated with predicting the behaviour of complex non-linear systems. Some of these systems show extreme initial condition sensitivity and even, perhaps, chaotic behaviour, and are therefore fundamentally unpredictable.