Exact spectral functions of a non-Fermi liquid in one dimension

We study the exact one-electron propagator and spectral function of a solvable model of interacting electrons due to Schulz and Shastry. The solution previously found for the energies and wave functions is extended to give spectral functions that turn out to be computable, interesting, and nontrivial. They provide one of the few examples of cases where the spectral functions are known asymptotically as well as exactly.

Numerical modeling of heat and mass transfer in laser surface alloying: Non-equilibrium solidification effects

A transient macroscopic model is developed for studying heat and mass transfer in a single-pass laser surface alloying process, with particular emphasis on non-equilibrium solidification considerations. The solution for species concentration distribution requires suitable treatment of non-equilibrium mass transfer conditions. In this context, microscopic features pertaining to non-equilibrium effects on account of solutal undercooling are incorporated through the formulation of a modified partition-coefficient. The effective partition-coefficient is numerically modeled by Means of a number of macroscopically observable parameters related to the solidifying domain. The numerical model is so developed that the modifications on account of non-equilibrium solidification considerations can be conveniently implemented in existing numerical codes based on equilibrium solidification considerations.

In-situ measurements of concentration and temperature during transient solidification of aqueous solution of ammonium chloride using laser interferometry

The variation in temperature and concentration plays a crucial role in predicting the final microstructure during solidification of a binary alloy. Most of the experimental techniques used to measure concentration and temperature are intrusive in nature and affect the flow field. In this paper, the main focus is laid on in-situ, non-intrusive, transient measurement of concentration and temperature during the solidification of a binary mixture of aqueous ammonium chloride solution (a metal-analog system) in a top cooled cavity using laser based Mach-Zehnder Interferometric technique. It was found from the interferogram, that the angular deviation of fringe pattern and the total number of fringes exhibit significant sensitivity to refractive index and hence are functions of the local temperature and concentration of the NH4Cl solution inside the cavity. Using the fringe characteristics, calibration curves were established for the range of temperature and concentration levels expected during the solidification process. In the actual solidification experiment, two hypoeutectic solutions (5% and 15% NH4Cl) were chosen. The calibration curves were used to determine the temperature and concentration of the solution inside the cavity during solidification of 5% and 15% NH4Cl solution at different instants of time. The measurement was carried out at a fixed point in the cavity, and the concentration variation with time was recorded as the solid-liquid interface approached the measurement point. The measurement exhibited distinct zones of concentration distribution caused by solute rejection and Rayleigh Benard convection. Further studies involving flow visualization with laser scattering confirmed the Rayleigh Benard convection. Computational modeling was also performed, which corroborated the experimental findings. (C) 2011 Elsevier Ltd. All rights reserved.

Dimethyl sulfoxide induced structural transformations and non-monotonic concentration dependence of conformational fluctuation around active site of lysozyme

Experimental studies have observed significant changes in both structure and function of lysozyme (and other proteins) on addition of a small amount of dimethyl sulfoxide (DMSO) in aqueous solution. Our atomistic molecular dynamic simulations of lysozyme in water-DMSO reveal the following sequence of changes on increasing DMSO concentration. (i) At the initial stage (around 5% DMSO concentration) protein's conformational flexibility gets markedly suppressed. From study of radial distribution functions, we attribute this to the preferential solvation of exposed protein hydrophobic residues by the methyl groups of DMSO. (ii) In the next stage (10-15% DMSO concentration range), lysozome partially unfolds accompanied by an increase both in fluctuation and in exposed protein surface area. (iii) Between 15-20% concentration ranges, both conformational fluctuation and solvent accessible protein surface area suddenly decrease again indicating the formation of an intermediate collapse state. These results are in good agreement with near-UV circular dichroism (CD) and fluorescence studies. We explain this apparently surprising behavior in terms of a structural transformation which involves clustering among the methyl groups of DMSO. (iv) Beyond 20% concentration of DMSO, the protein starts its final sojourn towards the unfolding state with further increase in conformational fluctuation and loss in native contacts. Most importantly, analysis of contact map and fluctuation near the active site reveal that both partial unfolding and conformational fluctuations are centered mostly on the hydrophobic core of active site of lysozyme. Our results could offer a general explanation and universal picture of the anomalous behavior of protein structure-function observed in the presence of cosolvents (DMSO, ethanol, tertiary butyl alcohol, dioxane) at their low concentrations. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3694268]

Three-Component Self-Assembly of a Series of Triply Interlocked Pd12 Coordination Prisms and Their Non-Interlocked Pd6 Analogues

Template-assisted formation of multicomponent Pd6 coordination prisms and formation of their self-templated triply interlocked Pd12 analogues in the absence of an external template have been established in a single step through Pd?N/Pd?O coordination. Treatment of cis-[Pd(en)(NO3)2] with K3tma and linear pillar 4,4'-bpy (en=ethylenediamine, H3tma=benzene-1,3,5-tricarboxylic acid, 4,4'-bpy=4,4'-bipyridine) gave intercalated coordination cage [{Pd(en)}6(bpy)3(tma)2]2[NO3]12 (1) exclusively, whereas the same reaction in the presence of H3tma as an aromatic guest gave a H3tma-encapsulating non-interlocked discrete Pd6 molecular prism [{Pd(en)}6(bpy)3(tma)2(H3tma)2][NO3]6 (2). Though the same reaction using cis-[Pd(NO3)2(pn)] (pn=propane-1,2-diamine) instead of cis-[Pd(en)(NO3)2] gave triply interlocked coordination cage [{Pd(pn)}6(bpy)3(tma)2]2[NO3]12 (3) along with non-interlocked Pd6 analogue [{Pd(pn)}6(bpy)3(tma)2](NO3)6 (3'), and the presence of H3tma as a guest gave H3tma-encapsulating molecular prism [{Pd(pn)}6(bpy)3(tma)2(H3tma)2][NO3]6 (4) exclusively. In solution, the amount of 3' decreases as the temperature is decreased, and in the solid state 3 is the sole product. Notably, an analogous reaction using the relatively short pillar pz (pz=pyrazine) instead of 4,4'-bpy gave triply interlocked coordination cage [{Pd(pn)}6(pz)3(tma)2]2[NO3]12 (5) as the single product. Interestingly, the same reaction using slightly more bulky cis-[Pd(NO3)2(tmen)] (tmen=N,N,N',N'-tetramethylethylene diamine) instead of cis-[Pd(NO3)2(pn)] gave non-interlocked [{Pd(tmen)}6(pz)3(tma)2][NO3]6 (6) exclusively. Complexes 1, 3, and 5 represent the first examples of template-free triply interlocked molecular prisms obtained through multicomponent self-assembly. Formation of the complexes was supported by IR and multinuclear NMR (1H and 13C) spectroscopy. Formation of guest-encapsulating complexes (2 and 4) was confirmed by 2D DOSY and ROESY NMR spectroscopic analyses, whereas for complexes 1, 3, 5, and 6 single-crystal X-ray diffraction techniques unambiguously confirmed their formation. The gross geometries of H3tma-encapsulating complexes 2 and 4 were obtained by universal force field (UFF) simulations.

Hydration dynamics of protein molecules in aqueous solution: Unity among diversity

Dielectric dispersion and NMRD experiments have revealed that a significant fraction of water molecules in the hydration shell of various proteins do not exhibit any slowing down of dynamics. This is usually attributed to the presence of the hydrophobic residues (HBR) on the surface, although HBRs alone cannot account for the large amplitude of the fast component. Solvation dynamics experiments and also computer simulation studies, on the other hand, repeatedly observed the presence of a non-negligible slow component. Here we show, by considering three well-known proteins (lysozyme, myoglobin and adelynate kinase), that the fast component arises partly from the response of those water molecules that are hydrogen bonded with the backbone oxygen (BBO) atoms. These are structurally and energetically less stable than those with the side chain oxygen (SCO) atoms. In addition, the electrostatic interaction energy distribution (EIED) of individual water molecules (hydrogen bonded to SCO) with side chain oxygen atoms shows a surprising two peak character with the lower energy peak almost coincident with the energy distribution of water hydrogen bonded to backbone oxygen atoms (BBO). This two peak contribution appears to be quite general as we find it for lysozyme, myoglobin and adenylate kinase (ADK). The sharp peak of EIED at small energy (at less than 2 k(B)T) for the BBO atoms, together with the first peak of EIED of SCO and the HBRs on the protein surface, explain why a large fraction (similar to 80%) of water in the protein hydration layer remains almost as mobile as bulk water Significant slowness arises only from the hydrogen bonds that populate the second peak of EIED at larger energy (at about 4 k(B)T). Thus, if we consider hydrogen bond interaction alone, only 15-20% of water molecules in the protein hydration layer can exhibit slow dynamics, resulting in an average relaxation time of about 5-10 ps. The latter estimate assumes a time constant of 20-100 ps for the slow component. Interestingly, relaxation of water molecules hydrogen bonded to back bone oxygen exhibit an initial component faster than the bulk, suggesting that hydrogen bonding of these water molecules remains frustrated. This explanation of the heterogeneous and non-exponential dynamics of water in the hydration layer is quantitatively consistent with all the available experimental results, and provides unification among diverse features.

Linearization and Reconstruction of Non-linear Diffuse Optical Tomographic Image

Diffuse optical tomography (DOT) is one of the ways to probe highly scattering media such as tissue using low-energy near infra-red light (NIR) to reconstruct a map of the optical property distribution. The interaction of the photons in biological tissue is a non-linear process and the phton transport through the tissue is modelled using diffusion theory. The inversion problem is often solved through iterative methods based on nonlinear optimization for the minimization of a data-model misfit function. The solution of the non-linear problem can be improved by modeling and optimizing the cost functional. The cost functional is f(x) = x(T)Ax - b(T)x + c and after minimization, the cost functional reduces to Ax = b. The spatial distribution of optical parameter can be obtained by solving the above equation iteratively for x. As the problem is non-linear, ill-posed and ill-conditioned, there will be an error or correction term for x at each iteration. A linearization strategy is proposed for the solution of the nonlinear ill-posed inverse problem by linear combination of system matrix and error in solution. By propagating the error (e) information (obtained from previous iteration) to the minimization function f(x), we can rewrite the minimization function as f(x; e) = (x + e)(T) A(x + e) - b(T)(x + e) + c. The revised cost functional is f(x; e) = f(x) + e(T)Ae. The self guided spatial weighted prior (e(T)Ae) error (e, error in estimating x) information along the principal nodes facilitates a well resolved dominant solution over the region of interest. The local minimization reduces the spreading of inclusion and removes the side lobes, thereby improving the contrast, localization and resolution of reconstructed image which has not been possible with conventional linear and regularization algorithm.

Low-thermal-budget solution processing of thin films of zinc ferrite and other complex oxides

Further miniaturization of magnetic and electronic devices demands thin films of advanced nanomaterials with unique properties. Spinel ferrites have been studied extensively owing to their interesting magnetic and electrical properties coupled with stability against oxidation. Being an important ferrospinel, zinc ferrite has wide applications in the biological (MRI) and electronics (RF-CMOS) arenas. The performance of an oxide like ZnFe2O4 depends on stoichiometry (defect structure), and technological applications require thin films of high density, low porosity and controlled microstructure, which depend on the preparation process. While there are many methods for the synthesis of polycrystalline ZnFe2O4 powder, few methods exist for the deposition of its thin films, where prolonged processing at elevated temperature is not required. We report a novel, microwave-assisted, low temperature (<100°C) deposition process that is conducted in the liquid medium, developed for obtaining high quality, polycrystalline ZnFe2O4 thin films on technologically important substrates like Si(100). An environment-friendly solvent (ethanol) and non-hazardous oxide precursors (β-diketonates of Zn and Fe in 1:2 molar ratio), forming a solution together, is subjected to irradiation in a domestic microwave oven (2.45 GHz) for a few minutes, leading to reactions which result in the deposition of ZnFe2O4 films on Si (100) substrates suspended in the solution. Selected surfactants added to the reactant solution in optimum concentration can be used to control film microstructure. The nominal temperature of the irradiated solution, i.e., film deposition temperature, seldom exceeds 100°C, thus sharply lowering the thermal budget. Surface roughness and uniformity of large area depositions (50x50 mm2) are controlled by tweaking the concentration of the mother solution. Thickness of the films thus grown on Si (100) within 5 min of microwave irradiation can be as high as several microns. The present process, not requiring a vacuum system, carries a very low thermal budget and, together with a proper choice of solvents, is compatible with CMOS integration. This novel solution-based process for depositing highly resistive, adherent, smooth ferrimagnetic films on Si (100) is promising to RF engineers for the fabrication of passive circuit components. It is readily extended to a wide variety of functional oxide films.

Surfactant free, non-aqueous method, for the deposition of ZnO nanoparticle thin films on Si(100) substrate with tunable ultraviolet (UV) emission

We report, strong ultraviolet (UV) emission from ZnO nanoparticle thin film obtained by a green synthesis, where the film is formed by the microwave irradiation of the alcohol solution of the precursor. The deposition is carried out in non-aqueous medium without the use of any surfactant, and the film formation is quick (5 min). The film is uniform comprising of mono-disperse nanoparticles having a narrow size distribution (15-22 nm), and that cover over an entire area (625 mm(2)) of the substrate. The growth rate is comparatively high (30-70 nm/min). It is possible to tune the morphology of the films and the UV emission by varying the process parameters. The growth mechanism is discussed precisely and schematic of the growth process is provided.

Exact internal controllability for a hyperbolic problem in a domain with highly oscillating boundary

In this paper, by using the Hilbert Uniqueness Method (HUM), we study the exact controllability problem described by the wave equation in a three-dimensional horizontal domain bounded at the bottom by a smooth wall and at the top by a rough wall. The latter is assumed to consist in a plane wall covered with periodically distributed asperities whose size depends on a small parameter epsilon > 0, and with a fixed height. Our aim is to obtain the exact controllability for the homogenized equation. In the process, we study the asymptotic analysis of wave equation in two setups, namely solution by standard weak formulation and solution by transposition method.

Closed-form solutions for non-uniform Euler-Bernoulli free-free beams

In this paper, the free vibration of a non-uniform free-free Euler-Bernoulli beam is studied using an inverse problem approach. It is found that the fourth-order governing differential equation for such beams possess a fundamental closed-form solution for certain polynomial variations of the mass and stiffness. An infinite number of non-uniform free-free beams exist, with different mass and stiffness variations, but sharing the same fundamental frequency. A detailed study is conducted for linear, quadratic and cubic variations of mass, and on how to pre-select the internal nodes such that the closed-form solutions exist for the three cases. A special case is also considered where, at the internal nodes, external elastic constraints are present. The derived results are provided as benchmark solutions for the validation of non-uniform free-free beam numerical codes. (C) 2013 Elsevier Ltd. All rights reserved.

End point estimates for Radon transform of radial functions on non-Euclidean spaces

We prove end point estimate for Radon transform of radial functions on affine Grasamannian and real hyperbolic space. We also discuss analogs of these results on the sphere.

Numerical modeling of the non-isothermal liquid droplet impact on a hot solid substrate

The heat transfer from a solid phase to an impinging non-isothermal liquid droplet is studied numerically. A new approach based on an arbitrary Lagrangian-Eulerian (ALE) finite element method for solving the incompressible Navier Stokes equations in the liquid and the energy equation within the solid and the liquid is presented. The novelty of the method consists in using the ALE-formulation also in the solid phase to guarantee matching grids along the liquid solid interface. Moreover, a new technique is developed to compute the heat flux without differentiating the numerical solution. The free surface and the liquid solid interface of the droplet are represented by a moving mesh which can handle jumps in the material parameter and a temperature dependent surface tension. Further, the application of the Laplace-Beltrami operator technique for the curvature approximation allows a natural inclusion of the contact angle. Numerical simulation for varying Reynold, Weber, Peclet and Biot numbers are performed to demonstrate the capabilities of the new approach. (C) 2014 Elsevier Ltd. All rights reserved.

Polymorphic phase transition among the titania crystal structures using a solution-based approach: from precursor chemistry to nucleation process

Nanocrystalline titania are a robust candidate for various functional applications owing to its non-toxicity, cheap availability, ease of preparation and exceptional photochemical as well as thermal stability. The uniqueness in each lattice structure of titania leads to multifaceted physico-chemical and opto-electronic properties, which yield different functionalities and thus influence their performances in various green energy applications. The high temperature treatment for crystallizing titania triggers inevitable particle growth and the destruction of delicate nanostructural features. Thus, the preparation of crystalline titania with tunable phase/particle size/morphology at low to moderate temperatures using a solution-based approach has paved the way for further exciting areas of research. In this focused review, titania synthesis from hydrothermal/solvothermal method, conventional sol-gel method and sol-gel-assisted method via ultrasonication, photoillumination and ILs, thermolysis and microemulsion routes are discussed. These wet chemical methods have broader visibility, since multiple reaction parameters, such as precursor chemistry, surfactants, chelating agents, solvents, mineralizer, pH of the solution, aging time, reaction temperature/time, inorganic electrolytes, can be easily manipulated to tune the final physical structure. This review sheds light on the stabilization/phase transformation pathways of titania polymorphs like anatase, rutile, brookite and TiO2(B) under a variety of reaction conditions. The driving force for crystallization arising from complex species in solution coupled with pH of the solution and ion species facilitating the orientation of octahedral resulting in a crystalline phase are reviewed in detail. In addition to titanium halide/alkoxide, the nucleation of titania from other precursors like peroxo and layered titanates are also discussed. The nonaqueous route and ball milling-induced titania transformation is briefly outlined; moreover, the lacunae in understanding the concepts and future prospects in this exciting field are suggested.

Modal tailoring and closed-form solutions for rotating non-uniform Euler-Bernoulli beams

In this paper, the free vibration of a rotating Euler-Bernoulli beam is studied using an inverse problem approach. We assume a polynomial mode shape function for a particular mode, which satisfies all the four boundary conditions of a rotating beam, along with the internal nodes. Using this assumed mode shape function, we determine the linear mass and fifth order stiffness variations of the beam which are typical of helicopter blades. Thus, it is found that an infinite number of such beams exist whose fourth order governing differential equation possess a closed form solution for certain polynomial variations of the mass and stiffness, for both cantilever and pinned-free boundary conditions corresponding to hingeless and articulated rotors, respectively. A detailed study is conducted for the first, second and third modes of a rotating cantilever beam and the first and second elastic modes of a rotating pinned-free beam, and on how to pre-select the internal nodes such that the closed-form solutions exist for these cases. The derived results can be used as benchmark solutions for the validation of rotating beam numerical methods and may also guide nodal tailoring. (C) 2014 Elsevier Ltd. All rights reserved.