A finite population model of mlecular evolution: theory and computation

This article is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work has impacted antiviral treatment and vaccine design strategies. Yet, predictions of the quasispecies model are at best viewed as a guideline, primarily because it assumes an infinite population size, whereas realistic population sizes can be quite small. In this paper we consider a population genetics-based model aimed at understanding the evolution of such organisms with finite population sizes and present a rigorous study of the convergence and computational issues that arise therein. Our first result is structural and shows that, at any time during the evolution, as the population size tends to infinity, the distribution of genomes predicted by our model converges to that predicted by the quasispecies model. This justifies the continued use of the quasispecies model to derive guidelines for intervention. While the stationary state in the quasispecies model is readily obtained, due to the explosion of the state space in our model, exact computations are prohibitive. Our second set of results are computational in nature and address this issue. We derive conditions on the parameters of evolution under which our stochastic model mixes rapidly. Further, for a class of widely used fitness landscapes we give a fast deterministic algorithm which computes the stationary distribution of our model. These computational tools are expected to serve as a framework for the modeling of strategies for the deployment of mutagenic drugs.

A finite-rate-of-innovation signal sampling perspective of the source-filter model of speech production

We consider the speech production mechanism and the asso- ciated linear source-filter model. For voiced speech sounds in particular, the source/glottal excitation is modeled as a stream of impulses and the filter as a cascade of second-order resonators. We show that the process of sampling speech signals can be modeled as filtering a stream of Dirac impulses (a model for the excitation) with a kernel function (the vocal tract response),and then sampling uniformly. We show that the problem of esti- mating the excitation is equivalent to the problem of recovering a stream of Dirac impulses from samples of a filtered version. We present associated algorithms based on the annihilating filter and also make a comparison with the classical linear prediction technique, which is well known in speech analysis. Results on synthesized as well as natural speech data are presented.

Strong-coupling expansion for ultracold bosons in an optical lattice at finite temperatures in the presence of superfluidity

We develop a strong-coupling (t << U) expansion technique for calculating the density profile for bosonic atoms trapped in an optical lattice with an overall harmonic trap at finite temperature and finite on-site interaction in the presence of superfluid regions. Our results match well with quantum Monte Carlo simulations at finite temperature. We also show that the superfluid order parameter never vanishes in the trap due to the proximity effect. Our calculations for the scaled density in the vacuum-to-superfluid transition agree well with the experimental data for appropriate temperatures. We present calculations for the entropy per particle as a function of temperature which can be used to calibrate the temperature in experiments. We also discuss issues connected with the demonstration of universal quantum critical scaling in the experiments.

An extended finite element model coupled with level set method for stable pitting corrosion

Mass balance between metal and electrolytic solution, separated by a moving interface, in stable pit growth results in a set of governing equations which are solved for concentration field and interface position (pit boundary evolution), which requires only three inputs, namely the solid metal concentration, saturation concentration of the dissolved metal ions and diffusion coefficient. A combined eXtended Finite Element Model (XFEM) and level set method is developed in this paper. The extended finite element model handles the jump discontinuity in the metal concentrations at the interface, by using discontinuous-derivative enrichment formulation for concentration discontinuity at the interface. This eliminates the requirement of using front conforming mesh and re-meshing after each time step as in conventional finite element method. A numerical technique known as level set method tracks the position of the moving interface and updates it over time. Numerical analysis for pitting corrosion of stainless steel 304 is presented. The above proposed method is validated by comparing the numerical results with experimental results, exact solutions and some other approximate solutions.

An extended finite-element model coupled with level set method for analysis of growth of corrosion pits in metallic structures

Mass balance between metal and electrolytic solution, separated by a moving interface, in stable pit growth results in a set of governing equations which are solved for concentration field and interface position (pit boundary evolution). The interface experiences a jump discontinuity in metal concentration. The extended finite-element model (XFEM) handles this jump discontinuity by using discontinuous-derivative enrichment formulation, eliminating the requirement of using front conforming mesh and re-meshing after each time step as in the conventional finite-element method. However, prior interface location is required so as to solve the governing equations for concentration field for which a numerical technique, the level set method, is used for tracking the interface explicitly and updating it over time. The level set method is chosen as it is independent of shape and location of the interface. Thus, a combined XFEM and level set method is developed in this paper. Numerical analysis for pitting corrosion of stainless steel 304 is presented. The above proposed model is validated by comparing the numerical results with experimental results, exact solutions and some other approximate solutions. An empirical model for pitting potential is also derived based on the finite-element results. Studies show that pitting profile depends on factors such as ion concentration, solution pH and temperature to a large extent. Studying the individual and combined effects of these factors on pitting potential is worth knowing, as pitting potential directly influences corrosion rate.

Phase diagram of the half-filled ionic Hubbard model

We study the phase diagram of the ionic Hubbard model (IHM) at half filling on a Bethe lattice of infinite connectivity using dynamical mean-field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential Delta and the on-site Hubbard U. We find that for a finite Delta and at zero temperature, long-range antiferromagnetic (AFM) order sets in beyond a threshold U = U-AF via a first-order phase transition. For U smaller than U-AF the system is a correlated band insulator. Both methods show a clear evidence for a quantum transition to a half-metal (HM) phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U. We show that the results obtained within both methods have good qualitative and quantitative consistency in the intermediate-to-strong-coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first-order phase transition at a transition temperature T-AF(U,Delta) or, equivalently, on decreasing U below U-AF(T,Delta)], within both methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low-energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T, DMFT + CTQMC shows a second phase transition (not seen within DMFT + IPT) on increasing U beyond U-AF. At U-N > U-AF, when the Neel temperature T-N for the effective Heisenberg model becomes lower than T, the AFM order is lost via a second-order transition. For U >> Delta, T-N similar to t(2)/U(1 - x(2)), where x = 2 Delta/U and thus T-N increases with increase in Delta/U. In the three-dimensional parameter space of (U/t, T/t, and Delta/t), as T increases, the surface of first-order transition at U-AF(T,Delta) and that of the second-order transition at U-N(T,Delta) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first- and second-order phase transitions.

Biocompatibility property of 100% strontium-substituted SiO2-Al2O3-P2O5-CaO-CaF2 glass ceramics over 26 weeks implantation in rabbit model: Histology and micro-Computed Tomography analysis

One of the desired properties for any new biomaterial composition is its long-term stability in a suitable animal model and such property cannot be appropriately assessed by performing short-term implantation studies. While hydroxyapatite (HA) or bioglass coated metallic biomaterials are being investigated for in vivo biocompatibility properties, such study is not extensively being pursued for bulk glass ceramics. In view of their inherent brittle nature, the implant stability as well as impact of long-term release of metallic ions on bone regeneration have been a major concern. In this perspective, the present article reports the results of the in vivo implantation experiments carried out using 100% strontium (Sr)-substituted glass ceramics with the nominal composition of 4.5 SiO2-3Al(2)O(3)-1.5P(2)O(5)-3SrO-2SrF(2) for 26 weeks in cylindrical bone defects in rabbit model. The combination of histological and micro-computed tomography analysis provided a qualitative and quantitative understanding of the bone regeneration around the glass ceramic implants in comparison to the highly bioactive HA bioglass implants (control). The sequential polychrome labeling of bone during in vivo osseointegration using three fluorochromes followed by fluorescence microscopy observation confirmed homogeneous bone formation around the test implants. The results of the present study unequivocally confirm the long-term implant stability as well as osteoconductive property of 100% Sr-substituted glass ceramics, which is comparable to that of a known bioactive implant, that is, HA-based bioglass. (c) 2014 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 103B: 1168-1179, 2015.

A finite variant of the Toom Model

We present results for a finite variant of the one-dimensional Toom model with closed boundaries. We show that the steady state distribution is not of product form, but is nonetheless simple. In particular, we give explicit formulas for the densities and some nearest neighbour correlation functions. We also give exact results for eigenvalues and multiplicities of the transition matrix using the theory of R-trivial monoids in joint work with A. Schilling, B. Steinberg and N. M. Thiery.

Semi-analytical finite element analysis of a strip footing on an elastic reinforced soil

A plane strain elastic interaction analysis of a strip footing resting on a reinforced soil bed has been made by using a combined analytical and finite element method (FEM). In this approach the stiffness matrix for the footing has been obtained using the FEM, For the reinforced soil bed (halfplane) the stiffness matrix has been obtained using an analytical solution. For the latter, the reinforced zone has been idealised as (i) an equivalent orthotropic infinite strip (composite approach) and (ii) a multilayered system (discrete approach). In the analysis, the interface between the strip footing and reinforced halfplane has been assumed as (i) frictionless and (ii) fully bonded. The contact pressure distribution and the settlement reduction have been given for different depths of footing and scheme of reinforcement in soil. The load-deformation behaviour of the reinforced soil obtained using the above modelling has been compared with some available analytical and model test results. The equivalent orthotropic approach proposed in this paper is easy to program and is shown to predict the reinforcing effects reasonably well.

Gel-coated ion-exchange resin: A new kinetic model

Regenerable 'gel-coated' cationic resins with fast sorption kinetics and high sorption capacity have application potential for removal of trace metal ions even in large-scale operations. Poly(acrylic acid) has been gel-coated on high-surface area silica (pre-coated with ethylene-vinyl acetate copolymer providing a thin barrier layer) and insolubilized by crosslinking with a low-molecular-weight diepoxide (epoxy equivalent 180 g) in the presence of benzyl dimethylamine catalyst at 70 degrees C, In experiments performed for Ca2+ sorption from dilute aqueous solutions of Ca(NO,),, the gel-coated acrylic resin is found to have nearly 40% higher sorption capacity than the bead-form commercial methacrylic resin Amberlite IRC-50 and also several limes higher rate of sorption. The sorption on the gel-coated sorbent under vigorous agitation has the characteristics of particle diffusion control with homogeneous (gel) diffusion in resin phase. A new mathematical model is proposed for such sorption on gel-coated ion-exchange resin in finite bath and solved by applying operator-theoretic methods. The analytical solution so obtained shows goad agreement with experimental sorption kinetics at relatively low levels (< 70%) of resin conversion.

Model Predictive Static Programming: A Computationally Efficient Technique For Suboptimal Control Design

Combining the philosophies of nonlinear model predictive control and approximate dynamic programming, a new suboptimal control design technique is presented in this paper, named as model predictive static programming (MPSP), which is applicable for finite-horizon nonlinear problems with terminal constraints. This technique is computationally efficient, and hence, can possibly be implemented online. The effectiveness of the proposed method is demonstrated by designing an ascent phase guidance scheme for a ballistic missile propelled by solid motors. A comparison study with a conventional gradient method shows that the MPSP solution is quite close to the optimal solution.

Infinite Dimensional Slow Modulations In A Delayed Model For Orthogonal Cutting Vibrations

We apply the method of multiple scales (MMS) to a well known model of regenerative cutting vibrations in the large delay regime. By ``large'' we mean the delay is much larger than the time scale of typical cutting tool oscillations. The MMS upto second order for such systems has been developed recently, and is applied here to study tool dynamics in the large delay regime. The second order analysis is found to be much more accurate than first order analysis. Numerical integration of the MMS slow flow is much faster than for the original equation, yet shows excellent accuracy. The main advantage of the present analysis is that infinite dimensional dynamics is retained in the slow flow, while the more usual center manifold reduction gives a planar phase space. Lower-dimensional dynamical features, such as Hopf bifurcations and families of periodic solutions, are also captured by the MMS. Finally, the strong sensitivity of the dynamics to small changes in parameter values is seen clearly.

Analysis of a finite composite plate with smooth rigid pin

A continuum method of analysis is presented in this paper for the problem of a smooth rigid pin in a finite composite plate subjected to uniaxial loading. The pin could be of interference, push or clearance fit. The plate is idealized to an orthotropic sheet. As the load on the plate is progressively increased, the contact along the pin-hole interface is partial above certain load levels in all three types of fit. In misfit pins (interference or clearance), such situations result in mixed boundary value problems with moving boundaries and in all of them the arc of contact and the stress and displacement fields vary nonlinearly with the applied load. In infinite domains similar problems were analysed earlier by ‘inverse formulation’ and, now, the same approach is selected for finite plates. Finite outer domains introduce analytical complexities in the satisfaction of boundary conditions. These problems are circumvented by adopting a method in which the successive integrals of boundary error functions are equated to zero. Numerical results are presented which bring out the effects of the rectangular geometry and the orthotropic property of the plate. The present solutions are the first step towards the development of special finite elements for fastener joints.

Indian Ocean sea surface salinity variations in a coupled model

The variability of the sea surface salinity (SSS) in the Indian Ocean is studied using a 100-year control simulation of the Community Climate System Model (CCSM 2.0). The monsoon-driven seasonal SSS pattern in the Indian Ocean, marked by low salinity in the east and high salinity in the west, is captured by the model. The model overestimates runoff int the Bay of Bengal due to higher rainfall over the Himalayan-Tibetan regions which drain into the Bay of Bengal through Ganga-Brahmaputra rivers. The outflow of low-salinity water from the Bay of Bengal is to strong in the model. Consequently, the model Indian Ocean SSS is about 1 less than that seen in the climatology. The seasonal Indian Ocean salt balance obtained from the model is consistent with the analysis from climatological data sets. During summer, the large freshwater input into the Bay of Bengal and its redistribution decide the spatial pattern of salinity tendency. During winter, horizontal advection is the dominant contributor to the tendency term. The interannual variability of the SSS in the Indian Ocean is about five times larger than that in coupled model simulations of the North Atlantic Ocean. Regions of large interannual standard deviations are located near river mouths in the Bay of Bengal and in the eastern equatorial Indian Ocean. Both freshwater input into the ocean and advection of this anomalous flux are responsible for the generation of these anomalies. The model simulates 20 significant Indian Ocean Dipole (IOD) events and during IOD years large salinity anomalies appear in the equatorial Indian Ocean. The anomalies exist as two zonal bands: negative salinity anomalies to the north of the equator and positive to the south. The SSS anomalies for the years in which IOD is not present and for ENSO years are much weaker than during IOD years. Significant interannual SSS anomalies appear in the Indian Ocean only during IOD years.

A couple stress model of blood flow in the microcirculation

A simple mathematical model depicting blood flow in the capillary is developed with an emphasis on the permeability property of the blood vessel based on Starling's hypothesis. In this study the effect of inertia has been neglected in comparison with the viscosity on the basis of the smallness of the Reynolds number of the flow in the capillary. The capillary blood vessel is approximated by a circular cylindrical tube with a permeable wall. The blood is represented by a couple stress fluid. With such an ideal model the velocity and pressure fields are determined. It is shown that an increase in the couple stress parameter increases the resistance to the flow and thereby decreases the volume rate flow. A comparison of the results with those of the Newtonian case has also been made.