Phase boundaries as agents of structural change in macromolecules

We model long rod-like molecules, such as DNA and coiled-coil proteins, as one-dimensional continua with a multi-well stored energy function. These molecules suffer a structural change in response to large forces, characterized by highly typical force-extension behavior. We assume that the structural change proceeds via a moving folded/unfolded interface, or phase boundary, that represents a jump in strain and is governed by the Abeyaratne–Knowles theory of phase transitions. We solve the governing equations using a finite difference method with moving nodes to represent phase boundaries. Our model can reproduce the experimental observations on the overstretching transition in DNA and coiled-coils and makes predictions for the speed at which the interface moves. We employ different types of kinetic relations to describe the mobility of the interface and show that this leads to different classes of experimentally observed force-extension curves. We make connections with several existing theories, experiments and simulation studies, thus demonstrating the effectiveness of the phase transitions-based approach in a biological setting.     

Study of translational,librational and intra-molecular motion of adsorbed liquid water monolayers at various TiO2 interfaces

Equilibrium classical molecular dynamics (MD) simulations have been performed to investigate the vibrational motion of water in contact with rutile-(110), rutile-(100), rutile-(001), anatase-(101) and anatase-(001) surfaces at room temperature (300?K). The vibrational density of states (VDOS) of the first adsorbed monolayer of liquid water has been analysed for each surface. These have been compared with reported experimental INS values involving rutile and anatase polymorph surfaces, along with ab initio MD results. It is observed that good qualitative agreement is obtained for the rutile-(110) and the anatase-(101) surfaces with the corresponding experimental VDOS. A significant contribution from librational dynamics is found for planar rutile surfaces, but no such demarcation is seen in the experimental VDOS.     

Hydrogen bond dynamical properties of adsorbed liquid water monolayers with various TiO2 interfaces

Equilibrium classical molecular dynamics (MD) simulations have been performed to investigate the hydrogen-bonding kinetics of water in contact with rutile-(110), rutile-(101), rutile-(100), and anatase-(101) surfaces at room temperature (300?K). It was observed that anatase-(101) exhibits the longest-lived hydrogen bonds in terms of overall persistence, followed closely by rutile-(110). The relaxation times, defined as the integral of the autocorrelation of the hydrogen bond persistence function, were also longer for these two cases, while decay of the autocorrelation function was slower. The increased number and overall persistence of hydrogen bonds in the adsorbed water monolayers at these surfaces, particularly for anatase-(101), may serve to promote possible water photolysis activity thereon.     

Large Hecke eigenvalues and an Omega result for non-Saito–Kurokawa lifts

The Ramanujan Journal - We prove a result on the distribution of Hecke eigenvalues, $$\mu _F(p^r)$$ (for $$r=1,2$$ or 3) of a non-Saito–Kurokawa lift F of degree 2. As a consequence, we...     

Revisiting Best Linear Unbiased Estimation of Location-Scale Parameters Based on Optimally Selected Order Statistics Using Compound Design

Methodology and Computing in Applied Probability - We introduce here the compound optimal design strategy to determine the Best Linear Unbiased Estimates (BLUEs) of location and scale parameters...     

A general framework for frequentist model averaging

Science China Mathematics - Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as...     

Observation of magnetic cluster phase above Curie temperature in Fe2CrAl Heusler alloy

We present a detailed magnetic critical behavior study of Fe₂CrAl Heusler alloy, for the first time, with rigorous analysis of high precision magnetization data obtained over the critical temperature region. Our studies confirm that B2 type site-disordered in Fe₂CrAl alloy exhibits long-range ferromagnetic order below a well defined Curie temperature (T=208 K). Though the nature of this transition is found to be of second order, the estimated critical exponents β=0.42, γ=1.356 and δ=4.25, are in between the theoretically predicted values for three-dimensional Heisenberg and mean-field interaction models. However, it is noteworthy that the scaling relations are obeyed indicating renormalization of interactions around the Curie temperature (T_C), where magnetization data collapse into two separate branches, above and below T_C. This conclusively shows that calculated critical exponents as well as critical temperature are unambiguous and intrinsic to the system. However, magnetization vs temperature data shows another magnetic transition (at T=313 K) above the Curie temperature. It is shown that the short range magnetic correlation exist even beyond T_C with cluster moment ∼10² μ_B. This is attributed to a site disorder which results in formation of Cr clusters with short range ferromagnetic order.     

Enhanced non-metallic behavior on the verge of magnetic instability in Fe2V1−xNbxAl Heusler alloys

Structural, magnetic and transport behavior of Nb substituted Fe₂VAl alloys have been investigated in the present work. From the detailed analysis of these data it is observed that Nb content promotes a lattice expansion in L2₁ super-structure of Fe₂VAl. Magnetization data suggest that un-doped Fe₂VAl exhibits cluster glass behavior with a bimodal distribution of superparamagnetic clusters at lower temperatures, developed possibly due to the cluster size distribution. However, in Nb-substituted alloys, cluster size reduces and cluster density increases, which further reduces coupling between the clusters, resulting in a state of increased magnetic disorder up to a plausible 20% substitution. Concurrently resistivity increases at lower temperatures and shows a deviation from semiconductor like transport, which can be explained in terms of increasing spin dependent scattering and decreasing inter cluster interaction due to iso-electronic-but-larger-sized Nb substitution at V site. Present experimental results corroborate well with the theoretical predictions made in the literature.     

WebMTA: a web-interface for ab initio geometry optimization of large molecules using molecular tailoring approach

A web-interface for geometry optimization of large molecules using a linear scaling method, i.e., cardinality guided molecular tailoring approach (CG-MTA), is presented. CG-MTA is a cut-and-stitch, fragmentation-based method developed in our laboratory, for linear scaling of conventional ab initio techniques. This interface provides limited access to CG-MTA-enabled GAMESS. It can be used to obtain fragmentation schemes for a given spatially extended molecule depending on the maximum allowed fragment size and minimum cut radius values provided by the user. Currently, we support submission of single point or geometry optimization jobs at Hartree-Fock and density functional theory levels of theory for systems containing between 80 to 200 first row atoms and comprising up to 1000 basis functions. The graphical user interface is built using HTML and Python at the back end. The back end farms out the jobs on an in-house Linux-based cluster running on Pentium-4 Class or higher machines using an @Home-based parallelization scheme (http://chem.unipune.ernet.in/ approximately tcg/mtaweb/).     

A general framework for frequentist model averaging In Celebration of Professor Lincheng Zhao's 75th Birthday

Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that were known a priori. Model averaging approaches, on the other hand, try to combine estimators for a set of candidate models. Specifically, instead of deciding which model is the 'right' one, a model averaging approach suggests to fit a set of candidate models and average over the estimators using data adaptive weights.In this paper we establish a general frequentist model averaging framework that does not set any restrictions on the set of candidate models. It broaden, the scope of the existing methodologies under the frequentist model averaging development. Assuming the data is from an unknown model, we derive the model averaging estimator and study its limiting distributions and related predictions while taking possible modeling biases into account.We propose a set of optimal weights to combine the individual estimators so that the expected mean squared error of the average estimator is minimized. Simulation studies are conducted to compare the performance of the estimator with that of the existing methods. The results show the benefits of the proposed approach over traditional model selection approaches as well as existing model averaging methods.