Instability of the self-similar flow into a cavity

In this paper we have investigated the instability of the self-similar flow behind the boundary of a collapsing cavity. The similarity solutions for the flow into a cavity in a fluid obeying a gas law p = Kργ, K = constant and 7 ≥ γ > 1 has been solved by Hunter, who finds that for the same value of γ there are two self-similar flows, one with accelerating cavity boundary and other with constant velocity cavity boundary. We find here that the first of these two flows is unstable. We arrive at this result only by studying the propagation of disturbances in the neighbourhood of the singular point.

Kinematic and Mechanical Profile of the Self-Actuation of Thermosalient Crystal Twins of 1,2,4,5-Tetrabromobenzene: A Molecular Crystalline Analogue of a Bimetallic Strip

A paradigm shift from hard to flexible, organic-based optoelectronics requires fast and reversible mechanical response from actuating materials that are used for conversion of heat or light into mechanical motion. As the limits in the response times of polymer-based actuating materials are reached, which are inherent to the less-than-optimal coupling between the light/heat and mechanical energy in them, 1 a conceptually new approach to mechanical actuation is required to leapfrog the performance of organic actuators. Herein, we explore single crystals of 1,2,4,5-tetrabromobenzene (TBB) as actuating elements and establish relations between their kinematic profile and mechanical properties. Centimeter-size acicular crystals of TBB are the only naturally twinned crystals out of about a dozen known materials that exhibit the thermosalient effect-an extremely rare and visually impressive crystal locomotion. When taken over a phase transition, crystals of this material store mechanical strain and are rapidly self-actuated to sudden jumps to release the internal strain, leaping up to several centimeters. To establish the structural basis for this colossal crystal motility, we investigated the mechanical profile of the crystals from macroscale, in response to externally induced deformation under microscope, to nanoscale, by using nanoindentation. Kinematic analysis based on high-speed recordings of over 200 twinned TBB crystals exposed to directional or nondirectional heating unraveled that the crystal locomotion is a kinematically complex phenomenon that includes at least six kinematic effects. The nanoscale tests confirm the highly elastic nature, with an elastic deformation recovery (60%) that is far superior to those of molecular crystals reported earlier. This property appears to be critical for accumulation of stress required for crystal jumping. Twinned crystals of TBB exposed to moderate directional heating behave as all-organic analogue of a bimetallic `strip, where the lattice misfit between the two crystal components drives reveriible deformation of the crystal.

Self-consistent microscopic treatment of the effects of self-motion of the probe on ionic and dipolar solvation dynamics

A simple but self-consistent microscopic theory for the time dependent solvation energy of both ions and dipoles is presented which includes, for the first time, the details of the self-motion of the probe on its own solvation dynamics. The theory leads to several interesting predictions. The most important of them is that, for dipolar solvation, both the rotational and the translational motions of the dipolar solute probe can significantly accelerate the rate of solvation. In addition, the rotational self-motion of the solute can also give rise to an additional mechanism of nonexponentiality in solvation time correlation functions in otherwise slow liquids. A comparison between the present theoretical predictions and the recent experimental studies of Maroncelli et al. on solvation dynamics of aniline in l-propanol seems to indicate that the said experiments have missed the initial solvent response up to about 45 ps. After mapping the experimental results on the redefined time scale, the theoretical results can explain the experimental results for solvation of aniline in 1-propanol very well. For ionic solvation, the translational motion is significant for light solutes only. For example, for Li+ in water, translational motion speeds up the solvation by about 20%. The present theory demonstrates that in dipolar solvation the partial quenching of the self-motion due to the presence of specific solute-solvent interactions (such as H-bonding) may lead to a much slower solvation than that when the self-motion is present. This point has been discussed. In addition, we present the theoretical results for solvation of aniline in propylene carbonate, Here, the solvation is predicted to be complete within 15-20 ps.

Influence of the Methane-Zeolite A Interaction Potential on the Concentration Dependence of Self-diffusivity

Studies on the diffusion of methane in a zeolite structure type LTA (as per IZA nomenclature) have indicated that different types of methane zeolite potentials exist in the literature in which methane is treated within the united-atom model. One set of potentials, referred to as model A, has a methane oxygen diameter of 3.14 angstrom, while another set of potential parameters, model B, employs a larger value of 3.46 angstrom. Fritzsche and co-workers (1993) have shown that these two potentials lead to two distinctly different energetic barriers for the passage of methane through the eight-ring window in the cation-free form of zeolite A. Here, we compute the variation of the self-diffusivity (D) with loading (c) for these two types of potentials and show that this slight variation in the diameter changes the concentration dependence qualitatively: thus, D decreases monotonically with c for model A, while D increases and goes through a maximum before finally decreasing for model B. This effect and the surprising congruence of the diffusion coefficients for both models at high loadings is examined in detail at the molecular level. Simulations for different temperatures reveal the Arrhenius behaviour of the self-diffusion coefficient. The apparent activation energy is found to vary with the loading. We conclude that beside the cage-to-cage jumps, which are essential for the migration of the guest molecules, at high concentrations migration within the cage and guest guest interactions with other molecules become increasingly dominant influences on the diffusion coefficient and make the guest zeolite interaction less important for both model A and model B.

A charge self-consistent LDA plus DMFT study of the spectral properties of hexagonal NiS

The electronic structure and spectral properties of hexagonal NiS have been studied in the high temperature paramagnetic phase and low temperature anti-ferromagnetic phase. The calculations have been performed using charge self-consistent density-functional theory in local density approximation combined with dynamical mean-field theory (LDA+DMFT). The photoemission spectra (PES) and optical properties have been computed and compared with the experimental data. Our results show that the dynamical correlation effects are important to understand the spectral and optical properties of NiS. These effects have been analyzed in detail by means of the computed real and imaginary part of the self-energy.

Role of supersymmetric heavy Higgs boson production in the self-coupling measurement of 125 GeV Higgs boson at the LHC

Measurement of the self-coupling of the 125 GeV Higgs boson is one of the most crucial tasks for a high luminosity run of the LHC, and it can only be measured in the di-Higgs final state. In the minimal supersymmetric standard model, heavy CP even Higgs (H) can decay into a lighter 125 GeV Higgs boson (h) and, therefore, can influence the rate of di-Higgs production. We investigate the role of single H production in the context of measuring the self-coupling of h. We have found that the H -> hh decay can change the value of Higgs (h) self-coupling substantially, in a low tan beta regime where the mass of the heavy Higgs boson lies between 250 and 600 GeV and, depending on the parameter space, it may be seen as an enhancement of the self-coupling of the 125 GeV Higgs boson.

Choice of the End Functional Groups in Tri(p-phenylenevinylene) Derivatives Controls Its Physical Gelation Abilities

New supramolecular organogels based on all-trans-tri(p-phenylenevinylene) (TPV) systems possessing different terminal groups, e.g., oxime, hydrazone, phenylhydrazone, and semicarbazone have been synthesized. The self-assembly properties of the compounds that gelate in specific organic solvents and the aggregation motifs of these molecules in the organogels were investigated using UV−vis, fluorescence, FT-IR, and 1H NMR spectroscopy, electron microscopy, differential scanning calorimetry (DSC), and rheology. The temperature variable UV−vis and fluorescence spectroscopy in different solvents clearly show the aggregation pattern of the self-assemblies promoted by hydrogen bonding, aromatic π-stacking, and van der Waals interactions among the individual TPV units. Gelation could be controlled by variation in the number of hydrogen-bonding donors and acceptors in the terminal functional groups of this class of gelators. Also wherever gelation is observed, the individual fibers in gels change to other types of networks in their aggregates depending on the number of hydrogen-bonding sites in the terminal functions. Comparison of the thermal stability of the gels obtained from DSC data of different gelators demonstrates higher phase transition temperature and enthalpy for the hydrazone-based gelator. Rheological studies indicate that the presence of more hydrogen-bonding donors in the periphery of the gelator molecules makes the gel more viscoelastic solidlike. However, in the presence of more numbers of hydrogen-bonding donor/acceptors at the periphery of TPVs such as with semicarbazone a precipitation as opposed to gelation was observed. Clearly, the choice of the end functional groups and the number of hydrogen-bonding groups in the TPV backbone holds the key and modulates the effective length of the chromophore, resulting in interesting optical properties.

2.5-dimensional solution of the advective accretion disk:a self-similar approach

We provide a 2.5-dimensional solution to a complete set of viscous hydrodynamical equations describing accretion- induced outflows and plausible jets around black holes/compact objects. We prescribe a self-consistent advective disk-outflow coupling model, which explicitly includes the information of vertical flux. Inter-connecting dynamics of an inflow-outflow system essentially upholds the conservation laws. We provide a set of analytical family of solutions through a self-similar approach. The flow parameters of the disk-outflow system depend strongly on the viscosity parameter α and the cooling factor.

Magnetic Field Due to the Self-Gravity-Induced Electric Polarization of a Rotating Massive Body

he notion of the gravity-induced electric field has been applied to an entire self-gravitating massive body. The resulting electric polarization of the otherwise neutral body, when taken in conjunction with the latter's rotation, is shown to generate an axial-magnetic field of the right type and order of magnitude for certain astrophysical objects. In the present treatment the electric polarization is calculated in the ion-continuum Thomas-Fermi approximation while the electrodynamics of the continuous medium is treated in the nonrelativistic approximation.

Self-tuning minimum-variance control of nonlinear systems of the Hammerstein model

Self-tuning is applied to the control of nonlinear systems represented by the Hammerstein model wherein the nonlinearity is any odd-order polynomial. But control costing is not feasible in general. Initial relay control is employed to contain the deviations.

Unraveling the packing pattern leading to gelation using SS NMR and X-ray diffraction: direct observation of the evolution of self-assembled fibers

A detailed understanding of the mode of packing patterns that leads to the gelation of low molecular mass gelators derived from bile acid esters was carried out using solid state NMR along with complementary techniques such as powder X-ray diffraction (PXRD), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and polarizing optical microscopy (POM). Solid state C-13{H-1} cross polarization (CP) magic angle spinning (MAS) NMR of the low molecularmass gel in its native state was recorded for the first time. A close resemblance in the packing patterns of the gel, xerogel and bulk solid states was revealed upon comparing their C-13{H-1} CPMAS NMR spectral pattern. A doublet resonance pattern of C-13 signals in C-13{H-1}CPMAS NMR spectra were observed for the gelator molecules, whereas the non-gelators showed simple singlet resonance or resulted inthe formation of inclusion complexes/solvates. PXRD patterns revealed a close isomorphous nature of the gelators indicating the similarity in the mode of the packing pattern in their solid state. Direct imaging of the evolution of nanofibers (sol-gel transition) was carried out using POM, which proved the presence of self-assembled fibrillar networks (SAFINs) in the gel. Finally powder X-ray structure determination revealed the presence of two non-equivalent molecules in an asymmetric unit which is responsible for the doublet resonance pattern in the solid state NMR spectra.

Symmetry Properties of the Large-Deviation Function of the Velocity of a Self-Propelled Polar Particle

A geometrically polar granular rod confined in 2D geometry, subjected to a sinusoidal vertical oscillation, undergoes noisy self-propulsion in a direction determined by its polarity. When surrounded by a medium of crystalline spherical beads, it displays substantial negative fluctuations in its velocity. We find that the large-deviation function (LDF) for the normalized velocity is strongly non-Gaussian with a kink at zero velocity, and that the antisymmetric part of the LDF is linear, resembling the fluctuation relation known for entropy production, even when the velocity distribution is clearly non-Gaussian. We extract an analogue of the phase-space contraction rate and find that it compares well with an independent estimate based on the persistence of forward and reverse velocities.

Pronounced hydrogel formation by the self-assembled aggregates of N-alkyl disaccharide amphiphiles

Six disaccharide amphiphiles were synthesized and their hydrogel-forming behavior was extensively studied. These amphiphiles were based on maltose and lactose. Since the gels formed from some of these systems showed the ability to "trap" water molecules upon gelation, these gels were described as "hydrogels". When these gels were heated to similar to 70 degrees C, the samples turned into clear, isotropic fluids, and upon gradual cooling, the hydrogels could be reproduced. Thus these systems were also "thermoreversible". The low molecular mass (MW 565) of the gelators compared to that of a typical polymeric gelator forming substance implies pronounced aggregation of the disaccharide amphiphiles into larger microstructures during gelation. To discern the aggregate textures and morphologies, the specimen hydrogel samples were examined by high-resolution scanning electron microscopy (SEM). A possible reason for the exceptionally high water gelating capacities (>6000 molecules of water per gelator molecule) exhibited by these N-alkyl disaccharide amphiphiles is the presence of large interlamellar spaces into which the water molecules get entrapped due to surface tension. In contrast to their single-chain counterparts, the double-chain lactosyl and maltosylamine amphiphiles upon solubilization in EtOH-H2O afforded hydrogels with reduced mechanical strengths. Interestingly, the corresponding microstructures were found to be quite different from the corresponding hydrogels of their single-chain counterparts. Rheological studies provided further insights into the behavior of these hydrogels. Varying the chain length of the alcohol cosolvent could modulate the gelation capacities, melting temperatures, and the mechanical properties of these hydrogels. To explain the possible reasons of gelation, the results of molecular modeling and energy minimization studies were also included.

Spectral moment sum rules for the retarded Green's function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium

We derive exact expressions for the zeroth and the first three spectral moment sum rules for the retarded Green's function and for the zeroth and the first spectral moment sum rules for the retarded self-energy of the inhomogeneous Bose-Hubbard model in nonequilibrium, when the local on-site repulsion and the chemical potential are time-dependent, and in the presence of an external time-dependent electromagnetic field. We also evaluate these expressions for the homogeneous case in equilibrium, where all time dependence and external fields vanish. Unlike similar sum rules for the Fermi-Hubbard model, in the Bose-Hubbard model case, the sum rules often depend on expectation values that cannot be determined simply from parameters in the Hamiltonian like the interaction strength and chemical potential but require knowledge of equal-time many-body expectation values from some other source. We show how one can approximately evaluate these expectation values for the Mott-insulating phase in a systematic strong-coupling expansion in powers of the hopping divided by the interaction. We compare the exact moment relations to the calculated moments of spectral functions determined from a variety of different numerical approximations and use them to benchmark their accuracy. DOI: 10.1103/PhysRevA.87.013628

Induction of Supramolecular Chirality in the Self-Assemblies of Lipophilic Pyrimidine Derivatives by Choice of the Amino Acid-Based Chiral Spacer

A new family of supramolecular organogelators, based on chiral amino acid derivatives of 2,4,6-trichloro-pyrimidine-5-carbaldehyde, has been synthesized. L-alanine was incorporated as a spacer between the pyrimidine core and long hydrocarbon tails to compare the effect of chirality and hydrogen bonding to that of the achiral analogue. The role of aromatic moiety on the chiral spacer was also investigated by introducing L-phenyl alanine moieties. The presence of intermolecular hydrogen-bonding leading to the chiral self-assembly was probed by concentration-dependent FTIR and UV/Vis spectroscopies, in addition to circular dichroism (CD) studies. Temperature and concentration-dependent CD spectroscopy ascribed to the formation of -sheet-type H-bonded networks. The morphology and the arrangements of the molecules in the freeze-dried gels were examined by scanning electron microscopy (SEM), transmission electron microscopy (TEM), atomic force microscopy (AFM), and X-ray diffraction (XRD) techniques. Calculation of the length of each molecular system by energy minimization in its extended conformation and comparison with the small-angle XRD pattern reveals that this class of gelator molecules adopts a lamellar organization. Polarized optical microscopy (POM) and differential scanning calorimetry (DSC) indicate that the solid state phase behavior of these molecules is totally dependent on the choice of their amino acid spacers. Structure-induced aggregation properties based on the H-bonding motifs and the packing of the molecule in three dimensions leading to gelation was elucidated by rheological studies. However, viscoelasticity was shown to depend only marginally on the H-bonding interactions; rather it depends on the packing of the gelators to a greater extent.