Liouville mode in gauge/gravity duality

We establish solutions corresponding to AdS\(_4\) static charged black holes with inhomogeneous two-dimensional horizon surfaces of constant curvature. Depending on the choice of the 2D constant curvature space, the metric potential of the internal geometry of the horizon satisfies the elliptic wave/elliptic Liouville equations. We calculate the charge diffusion and transport coefficients in the hydrodynamic limit of gauge/gravity duality and observe the exponential suppression in the diffusion coefficient and in the shear viscosity-per-entropy density ratio in the presence of an inhomogeneity on black hole horizons with planar, spherical, and hyperbolic geometry. We discuss the subtleties of the approach developed for a planar black hole with inhomogeneity distribution on the horizon surface in more detail and find, among others, a trial distribution function, which generates values of the shear viscosity-per-entropy density ratio falling within the experimentally relevant range. The solutions obtained are also extended to higher-dimensional AdS space. We observe two different DC conductivities in 4D and higher-dimensional effective strongly coupled dual media and formulate conditions under which the appropriate ratio of different conductivities is qualitatively the same as that observed in an anisotropic strongly coupled fluid. We briefly discuss ways of how the Liouville field could appear in condensed matter physics and outline prospects of further employing the gauge/gravity duality in CMP problems.     

Coulomb screening in graphene with topological defects

We analyze the screening of an external Coulomb charge in gapless graphene cone, which is taken as a prototype of a topological defect. In the subcritical regime, the induced charge is calculated using both the Green’s function and the Friedel sum rule. The dependence of the polarization charge on the Coulomb strength obtained from the Green’s function clearly shows the effect of the conical defect and indicates that the critical charge itself depends on the sample topology. Similar analysis using the Friedel sum rule indicates that the two results agree for low values of the Coulomb charge but differ for the higher strengths, especially in the presence of the conical defect. For a given subcritical charge, the transport cross-section has a higher value in the presence of the conical defect. In the supercritical regime we show that the coefficient of the power law tail of polarization charge density can be expressed as a summation of functions which vary log periodically with the distance from the Coulomb impurity. The period of variation depends on the conical defect. In the presence of the conical defect, the Fano resonances begin to appear in the transport cross-section for a lower value of the Coulomb charge. For both sub and supercritical regime we derive the dependence of LDOS on the conical defect. The effects of generalized boundary condition on the physical observables are also discussed.     

Theoretical representation of solvation in biochemical systems: From discrete solute-solvent interactions to bulk solvation

The interaction between solutes and simple solvents in dilute solutions is analyzed in a systematic way. Different theoretical methods to describe specific solute-solvent interactions and general solvation effects are presented. Finally, the importance of solvent-induced changes in solute properties is discussed through the use of mixed quantum mechanics/classical mechanics strategies. © 1996 John Wiley & Sons, Inc.     

一个关于肿瘤治疗的自由边界问题的数学分析

§1Introduction Avarietyofpartialdifferentialequationmodelsfortumorgrowthortherapyhave beendevelopedinthelastthreedecades[see2,3,16-18,21-26].Mostofthosemodelsare informoffreeboundaryproblems,andareverydiversified.Rigorousmathematical analysisofsuchfreeboundaryproblemshasdrawngreatinterest,andmanyinteresting resultshavebeenestablished[4-15].Inthispaperwedealwithamathematicalmodeldescribingtumorchemotherapy.In thismodelthetumorisviewedasdenselypacked,radially-symmetricsphereofradiusR(t)contain…     

Advances in Palladium-Catalyzed Carboxylation Reactions

In this short review, we highlight the advancements in the field of palladium-catalyzed carbon dioxide utilization for the synthesis of high value added organic molecules. The review is structured on the basis of the kind of substrate undergoing the Pd-catalyzed carboxylation process. Accordingly, after the introductory section, the main sections of the review will illustrate Pd-catalyzed carboxylation of olefinic substrates, acetylenic substrates, and other substrates (aryl halides and triflates).     

Energy Storage by Poly(<Emphasis Type="Italic">o</Emphasis>-anisidine) Matrix During Oxidative Hydrolysis

The chromaticity of poly(o-anisidine) (POAN) doped with different acids (HA), HA-doped POAN, has been studied by the spectrophotometric technique and the results were substantiated by molecular mechanics (MM+) calculations. The observed absorbance decrease (λ around 720 nm, dark green coloration) with increasing concentration of the inorganic oxidizing agent (KMnO₄) can be attributed to the oxidative hydrolysis mechanism. The oxidative hydrolysis constant (K _h) is highly dependent on the strength of the acid used. The HClO₄-doped POAN matrix has the ability to store about 128.878 kJ⋅g⁻¹ chromogenic energy (CE) at the wavelength 720 nm in a condensed lightweight form. MM+ calculations suggest that the potential energy (PE) in kJ⋅mol⁻¹ of the optimum molecular geometric (OMG) structure of the HClO₄-doped POAN matrix is at least two (2.052) times more stable than the OMG of the base form (POAN-EB) of the POAN matrix. Kinetic parameters of the oxidative hydrolysis reaction of the HA-doped POAN matrix were deduced from absorbance variations with time. The results of computer-oriented kinetic analysis indicate that the rate-controlling step for HA-doped POAN oxidative hydrolysis is governed by the Ginstling-Bronshein equation that represents three-dimensional diffusion (D4). Activation parameters for the oxidative hydrolysis of the HClO₄-doped POAN matrix were computed and discussed.     

Guanidine-based task-specific ionic liquids as catalysts for aza-Michael addition under solvent-free conditions

An efficient and facile protocol for aza-Michael addition of aliphatic and aromatic amines to electron-deficit alkenes using [TMG][Lac] as catalyst under solvent-free conditions was established.