Entropy Crisis, Ideal Glass Transition and Polymer Melting: Exact Solution on a Husimi Cactus

We introduce an extension of the lattice model of melting of semiflexible polymers originally proposed by Flory. Along with a bending penalty, present in the original model and involving three sites of the lattice, we introduce an interaction energy that corresponds to the presence of a pair of parallel bonds and a second interaction energy associated with the presence of a hairpin turn. Both these new terms represent four-site interactions. The model is solved exactly on a Husimi cactus, which approximates a square lattice. We study the phase diagram of the system as a function of the energies. For a proper choice of the interaction energies, the model exhibits a first-order melting transition between a liquid and a crystalline phase. The continuation of the liquid phase below this temperature gives rise to a supercooled liquid, which turns continuously into a new low-temperature phase, called metastable liquid. This liquid-liquid transition seems to have some features that are characteristic of the critical transition predicted by the mode-coupling theory.Comment: To be published in Physical Review E, 68 (2) (2003

Configurational Entropy and its Crisis in Metastable States: Ideal Glass Transition in a Dimer Model as a Paragidm of a Molecular Glass

We discuss the need for discretization to evaluate the configurational entropy in a general model. We also discuss the prescription using restricted partition function formalism to study the stationary limit of metastable states. We introduce a lattice model of dimers as a paradigm of molecular fluid and study metastability in it to investigate the root cause of glassy behavior. We demonstrate the existence of the entropy crisis in metastable states, from which it follows that the entropy crisis is the root cause underlying the ideal glass transition in systems with particles of all sizes. The orientational interactions in the model control the nature of the liquid-liquid transition observed in recent years in molecular glasses.Comment: 36 pages, 9 figure

SURFACE WATER DYNAMICS OF INLAND WATER BODIES OF INDIA USING GOOGLE EARTH ENGINE

Dynamics, distribution and quality of water has a direct impact on environment and its dependent human activities. Regular monitoring of these hydrological processes help in understanding water cycle and better management policy making. Recent increase in remote sensing satellites offer multiple observations with high spatial and temporal resolution, thus calling for extensive use of high end computational resources. Google Earth Engine(GEE) is an open Application Programing Interface (API), which offers free computational resources and satellite data on cloud computational platform minimising the users need for computational resources and data availability. Five year Landsat-8 imagery (2013–18) from GEE database has been used to study the surface water extent of large inland water bodies (surface area greater than 6000 ha) of India. We have used a pixel based classification system to delineate water and non-water pixels. A knowledge based Decision Tree (DT) model has been employed to cluster the classes according to Normalized Difference Vegetation Index (NDVI) and Modified Normalized Difference Water Index (MNDWI) distribution. We report an anomalous departure from the 5-year trend line suggesting that the maximum decrease of water extent was found in year 2015–2016. Analysis of the decay pattern of reservoirs can provide timely inputs for better policy making and management of water resources. To understand the decay pattern, a Modified Gaussian model fit on time series of surface extent helps to determine maximum water extent, peak extent day and storage cycle of the water body

contact.engineering -- Create, analyze and publish digital surface twins from topography measurements across many scales

The optimization of surface finish to improve performance occurs largely through trial and error, despite significant advancements in the relevant science. There are three central challenges that account for this disconnect: (1) the challenge of integration of many different types of measurement for the same surface to capture the multi-scale nature of roughness; (2) the technical complexity of implementing spectral analysis methods, and of applying mechanical or numerical models to describe surface performance; (3) a lack of consistency between researchers and industries in how surfaces are measured, quantified, and communicated. Here we present a freely-available internet-based application which attempts to overcome all three challenges. First, the application enables the user to upload many different topography measurements taken from a single surface, including using different techniques, and then integrates all of them together to create a digital surface twin. Second, the application calculates many of the commonly used topography metrics, such as root-mean-square parameters, power spectral density (PSD), and autocorrelation function (ACF), as well as implementing analytical and numerical calculations, such as boundary element modeling (BEM) for elastic and plastic deformation. Third, the application serves as a repository for users to securely store surfaces, and if they choose, to share these with collaborators or even publish them (with a digital object identifier) for all to access. The primary goal of this application is to enable researchers and manufacturers to quickly and easily apply cutting-edge tools for the characterization and properties-modeling of real-world surfaces. An additional goal is to advance the use of open-science principles in surface engineering by providing a FAIR database where researchers can choose to publish surface measurements for all to use.Comment: 19 pages, 6 figure

GROWTH OF INVASIVE AQUATIC MACROPHYTES OVER TAPI RIVER

Aquatic macrophytes are important elements of freshwater ecosystems, fulfilling a pivotal role in the ecological functions of these environments and biogeochemical cycles. Although aquatic macrophytes are beneficial, some species can hinder human activity. They can clog reservoirs and reduce water availability for human needs. Surveys of macrophytes are hindered by logistic problems, and remote sensing represents a powerful alternative, allowing comprehensive assessment and monitoring. The objectives of this study was to map temporal changes in the macrophytes using time series multispectral dataset over Tapi River, Surat. The field trip was conducted over the Tapi River on 22nd June 2018, where in-situ spectral response dataset were acquired using ASD Spectroradiometer. Water samples were also collected over three locations, one before entering the city (Kamrej), second at the Sarthana water treatment plant and third at the outer end (causeway). The nutrient concentration was less before entering the city (Ammonical Nitrogen 0.056 mg/L and phosphate 0.0145 mg/l), while higher concentration (Ammonical Nitrogen 0.448 mg/l and phosphate 0.05 mg/l) was observed within the city. Maps of aquatic macrophytes fractional cover were produced using Resourcesat-2/2A (LISS-III) dataset covering a period of 2012–2018. Maximum extent was observed in February-March of every year. Although during monsoon, lot of agriculture run-off and nutrients will come into the river, but main flow of water will dilute its concentration. During summer, the same nutrient concentration will boost these macrophytes due to less availability of stream water. Within the area of 16 km2 between Kamrej and causeway, 3.35 % was covered by macrophytes during March 2013. This area coverage increase to 36.41 % in March 2018. Based on these maps, we discuss how remote sensing could support monitoring strategies and provide insight into spatial variability, and by identifying hotspot areas where invasive species could become a threat to ecosystem functioning

Thermodynamics and structure of self-assembled networks

We study a generic model of self-assembling chains which can branch and form networks with branching points (junctions) of arbitrary functionality. The physical realizations include physical gels, wormlike micells, dipolar fluids and microemulsions. The model maps the partition function of a solution of branched, self-assembling, mutually avoiding clusters onto that of a Heisenberg magnet in the mathematical limit of zero spin components. The model is solved in the mean field approximation. It is found that despite the absence of any specific interaction between the chains, the entropy of the junctions induces an effective attraction between the monomers, which in the case of three-fold junctions leads to a first order reentrant phase separation between a dilute phase consisting mainly of single chains, and a dense network, or two network phases. Independent of the phase separation, we predict the percolation (connectivity) transition at which an infinite network is formed that partially overlaps with the first-order transition. The percolation transition is a continuous, non thermodynamic transition that describes a change in the topology of the system. Our treatment which predicts both the thermodynamic phase equilibria as well as the spatial correlations in the system allows us to treat both the phase separation and the percolation threshold within the same framework. The density-density correlation correlation has a usual Ornstein-Zernicke form at low monomer densities. At higher densities, a peak emerges in the structure factor, signifying an onset of medium-range order in the system. Implications of the results for different physical systems are discussed.Comment: Submitted to Phys. Rev.

Exact correlation functions of Bethe lattice spin models in external fields

We develop a transfer matrix method to compute exactly the spin-spin correlation functions of Bethe lattice spin models in the external magnetic field h and for any temperature T. We first compute the correlation function for the most general spin - S Ising model, which contains all possible single-ion and nearest-neighbor pair interactions. This general spin - S Ising model includes the spin-1/2 simple Ising model and the Blume-Emery-Griffiths (BEG) model as special cases. From the spin-spin correlation functions, we obtain functions of correlation length for the simple Ising model and BEG model, which show interesting scaling and divergent behavior as T approaches the critical temperature. Our method to compute exact spin-spin correlation functions may be applied to other Ising-type models on Bethe and Bethe-like lattices.Comment: 19 page

Affinity purification of bacterial outer membrane vesicles (OMVs) utilizing a His-tag mutant

To facilitate the rapid purification of bacterial outer membrane vesicles (OMVs), we developed two plasmid constructs that utilize a truncated, transmembrane protein to present an exterior histidine repeat sequence. We chose OmpA, a highly abundant porin protein, as the protein scaffold and utilized the lac promoter to allow for inducible control of the epitope-presenting construct. OMVs containing mutant OmpA-His6 were purified directly from Escherichia coli culture media on an immobilized metal affinity chromatography (IMAC) Ni-NTA resin. This enabling technology can be combined with other molecular tools directed at OMV packaging to facilitate the separation of modified/cargo-loaded OMV from their wt counterparts. In addition to numerous applications in the pharmaceutical and environmental remediation industries, this technology can be utilized to enhance basic research capabilities in the area of elucidating endogenous OMV function

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Oligodendroglial neoplasms with ganglioglioma-like maturation: a diagnostic pitfall

Although oligodendroglial neoplasms are traditionally considered purely glial, increasing evidence suggests that they are capable of neuronal or neurocytic differentiation. Nevertheless, ganglioglioma-like foci (GGLF) have not been previously described. Herein, we report seven examples where the primary differential diagnosis was a ganglioglioma with an oligodendroglial component. These five male and two female patients ranged in age from 29 to 63 (median 44) years at initial presentation and neuroimaging features were those of diffuse gliomas in general. At presentation, the glial component was oligodendroglioma in six and oligoastrocytoma in one; one was low-grade and six were anaplastic. A sharp demarcation from adjacent GGLF was common, although some intermingling was always present. The GGLF included enlarged dysmorphic and occasionally binucleate ganglion cells, Nissl substance, expression of neuronal antigens, GFAP-positive astrocytic elements, and low Ki-67 labeling indices. In contrast to classic ganglioglioma, however, cases lacked eosinophilic granular bodies and CD34-positive tumor cells. Scattered bizarre astrocytes were also common and one case had focal neurocytic differentiation. By FISH analysis, five cases showed 1p/19q codeletion. In the four cases with deletions and ample dysmorphic ganglion cells for analysis, the deletions were found in both components. At last follow-up, two patients suffered recurrences, one developed radiation necrosis mimicking recurrence, and one died of disease 7.5 years after initial surgery. We conclude that GGLF represents yet another form of neuronal differentiation in oligodendroglial neoplasms. Recognition of this pattern will prevent a misdiagnosis of ganglioglioma with its potential for under-treatment