Role of multicritical points in addressing some key problems concerning condensed matter science

We illustrate the potential of using higher order critical points in the deeper understanding of several interesting problems of condensed matter science, e.g. critical adsorption, finite size effects, morphology of critical fluctuations, reversible aggregation of colloids, dynamics of the ordering process, etc.

Role of free valences and spin densities on the migrating atom in location of saddle points in radical-exchange reactions

The principle of the conservation of bond orders during radical-exchange reactions is examined using Mayer's definition of bond orders. This simple intuitive approximation is not valid in a quantitative sense. Ab initio results reveal that free valences (or spin densities) develop on the migrating atom during reactions. For several examples of hydrogen-transfer reactions, the sum of the reaction coordinate bond orders in the transition state was found to be 0.92 +/- 0.04 instead of the theoretical 1.00 because free valences (or spin densities) develop on the migrating atom during reactions. It is shown that free valence is almost equal to the square of the spin density on the migrating hydrogen atom and the maxima in the free valence (or spin density) profiles coincide (or nearly coincide) with the saddle points in the corresponding energy profiles.

Fixed points in a Hopfield model with random asymmetric interactions

We calculate analytically the average number of fixed points in the Hopfield model of associative memory when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. Addition of the antisymmetric part causes an exponential decrease in the total number of fixed points. If the relative strength of the antisymmetric component is small, then its presence does not cause any substantial degradation of the quality of retrieval when the memory loading level is low. We also present results of numerical simulations which provide qualitative (as well as quantitative for some aspects) confirmation of the predictions of the analytic study. Our numerical results suggest that the analytic calculation of the average number of fixed points yields the correct value for the typical number of fixed points.

The Case for Non-Cooperative Multihoming of Users to Access Points in IEEE 802.11 WLANs

In many cases, a mobile user has the option of connecting to one of several IEEE 802.11 access points (APs),each using an independent channel. User throughput in each AP is determined by the number of other users as well as the frame size and physical rate being used. We consider the scenario where users could multihome, i.e., split their traffic amongst all the available APs, based on the throughput they obtain and the price charged. Thus, they are involved in a non-cooperative game with each other. We convert the problem into a fluid model and show that under a pricing scheme, which we call the cost price mechanism, the total system throughput is maximized,i.e., the system suffers no loss of efficiency due to selfish dynamics. We also study the case where the Internet Service Provider (ISP) could charge prices greater than that of the cost price mechanism. We show that even in this case multihoming outperforms unihoming, both in terms of throughput as well as profit to the ISP.

The Nature of Bond Critical Points in Dinuclear Copper(I) Complexes

Closed-shell contacts between two copper(I) ions are expected to be repulsive. However, such contacts are quite frequent and are well documented. Crystallographic characterization of such contacts in unsupported and bridged multinuclear copper(I) complexes has repeatedly invited debates on the existence of cuprophilicity. Recent developments in the application of Baders theory of atoms-in-molecules (AIM) to systems in which weak hydrogen bonds are involved suggests that the copper(I)copper(I) contacts would benefit from a similar analysis. Thus the nature of electron-density distributions in copper(I) dimers that are unsupported, and those that are bridged, have been examined. A comparison of complexes that are dimers of symmetrical monomers and those that are dimers of two copper(I) monomers with different coordination spheres has also been made. AIM analysis shows that a bond critical point (BCP) between two Cu atoms is present in most cases. The nature of the BCP in terms of the electron density, ?, and its Laplacian is quite similar to the nature of critical points observed in hydrogen bonds in the same systems. The ? is inversely correlated to Cu?Cu distance. It is higher in asymmetrical systems than what is observed in corresponding symmetrical systems. By examining the ratio of the local electron potential-energy density (Vc) to the kinetic energy density (Gc), |Vc|/Gc at the critical point suggests that these interactions are not perfectly ionic but have some shared nature. Thus an analysis of critical points by using AIM theory points to the presence of an attractive metallophilic interaction similar to other well-documented weak interactions like hydrogen bonding.

Quenching across quantum critical points in periodic systems: Dependence of scaling laws on periodicity

We study the quenching dynamics of a many-body system in one dimension described by a Hamiltonian that has spatial periodicity. Specifically, we consider a spin-1/2 chain with equal xx and yy couplings and subject to a periodically varying magnetic field in the (z) over cap direction or, equivalently, a tight-binding model of spinless fermions with a periodic local chemical potential, having period 2q, where q is a positive integer. For a linear quench of the strength of the magnetic field (or chemical potential) at a rate 1/tau across a quantum critical point, we find that the density of defects thereby produced scales as 1/tau(q/(q+1)), deviating from the 1/root tau scaling that is ubiquitous in a range of systems. We analyze this behavior by mapping the low-energy physics of the system to a set of fermionic two-level systems labeled by the lattice momentum k undergoing a nonlinear quench as well as by performing numerical simulations. We also show that if the magnetic field is a superposition of different periods, the power law depends only on the smallest period for very large values of tau, although it may exhibit a crossover at intermediate values of tau. Finally, for the case where a zz coupling is also present in the spin chain, or equivalently, where interactions are present in the fermionic system, we argue that the power associated with the scaling law depends on a combination of q and the interaction strength.

Long-range Coulomb interactions and nanoscale electronic inhomogeneities in correlated oxides

Electronic, magnetic, or structural inhomogeneities ranging in size from nanoscopic to mesoscopic scales seem endemic and are possibly generic to colossal magnetoresistance manganites and other transition metal oxides. They are hence of great current interest and understanding them is of fundamental importance. We show here that an extension, to include long-range Coulomb interactions, of a quantum two-fluid l-b model proposed recently for manganites [Phys. Rev. Lett. 92, 157203 (2004)] leads to an excellent description of such inhomogeneities. In the l-b model two very different kinds of electronic states, one localized and polaronic (l) and the other extended or broad band (b) coexist. For model parameters appropriate to manganites and even within a simple dynamical mean-field theory (DMFT) framework, it describes many of the unusual phenomena seen in manganites, including colossal magnetoresistance (CMR), qualitatively and quantitatively. However, in the absence of long-ranged Coulomb interaction, a system described by such a model would actually phase separate, into macroscopic regions of l and b electrons, respectively. As we show in this paper, in the presence of Coulomb interactions, the macroscopic phase separation gets suppressed and instead nanometer scale regions of polarons interspersed with band electron puddles appear, constituting a kind of quantum Coulomb glass. We characterize the size scales and distribution of the inhomogeneity using computer simulations. For realistic values of the long-range Coulomb interaction parameter V-0, our results for the thresholds for occupancy of the b states are in agreement with, and hence support, the earlier approach mentioned above based on a configuration averaged DMFT treatment which neglects V-0; but the present work has features that cannot be addressed in the DMFT framework. Our work points to an interplay of strong correlations, long-range Coulomb interaction, and dopant ion disorder, all inevitably present in transition metal oxides as the origin of nanoscale inhomogeneities rather than disorder frustrated phase competition as is generally believed. As regards manganites, it argues against explanations for CMR based on disorder frustrated phase separation and for an intrinsic origin of CMR. Based on this, we argue that the observed micrometer (meso) scale inhomogeneities owe their existence to extrinsic causes, e.g., strain due to cracks and defects. We suggest possible experiments to validate our speculation.

Succinate esters: odd-even effects in melting points

Dialkyl succinates show a pattern of alternating behavior in their melting points, as the number of C atoms in the alkane side chain increases, unlike in the dialkyl oxalates Joseph et al. (2011). Acta Cryst. B67, 525-534]. Dialkyl succinates with odd numbers of C atoms in the alkyl side chain show higher melting points than the immediately adjacent analogues with even numbers. The crystal structures and their molecular packing have been analyzed for a series of dialkyl succinates with 1 - 4 C atoms in the alkyl side chain. The energy difference (Delta E) between the optimized and observed molecular conformations, density, Kitaigorodskii packing index (KPI) and C-H center dot center dot center dot O interactions are considered to rationalize this behavior. In contrast to the dialkyl oxalates where a larger number of moderately strong C-H center dot center dot center dot O interactions were characteristic of oxalates with elevated melting points, here the molecular packing and the density play a major role in raising the melting point. On moving from oxalate to succinate esters the introduction of the C2 spacer adds two activated H atoms to the asymmetric unit, resulting in the formation of stronger C-H center dot center dot center dot O hydrogen bonds in all succinates. As a result the crystallinity of long-chain alkyl substituted esters improves enormously in the presence of hydrogen bonds from activated donors.

Screened and unscreened phases in sedimenting suspensions

A coarse-grained stochastic hydrodynamical description of velocity and concentration fluctuations in steadily sedimenting suspensions is constructed and analyzed using self-consistent and renormalization-group methods. We find a nonequilibrium phase transition from an "unscreened" phase in which we recover the Caflisch-Luke [Phys. Fluids 28, 759 (1985)] divergence of the velocity variance to a "screened" phase where the fluctuations have a finite correlation length depending on the volume fraction phi as phi(-1/3), in agreement with Segre et al. [Phys. Rev. Lett. 79, 2574 (1997)] (if their observation of a phi-independent diffusivity is used), and the velocity variance is independent of system size.

Structural correlations in GexSe1-x glasses - a neutron diffraction study

Neutron diffraction measurement is carried out on GexSe1-x glasses, where 0.1 less than or equal to x less than or equal to 0.4, in a Q interval of 0.55-13.8 Angstrom(-1). The first sharp diffraction peak (FSDP) in the structure factor, S(Q), shows a systematic increase in the intensity and shifts to a lower Q with increasing Ge concentration. The coherence length of FSDP increases with x and becomes maximum for 0.33 less than or equal to x less than or equal to 0.4. The Monte-Carlo method, due to Soper, is used to generate S(Q) and also the pair correlation function, g(r). The generated S(Q) is in agreement with the experimental data for all x. Analysis of the first four peaks in the total correlation function, T(r), shows that the short range order in GeSe2 glass is due to Ge(Se-1/2)(4) tetrahedra, in agreement with earlier reports. Se-rich glasses contain Se-chains which are cross-linked with Ge(Se-1/2)(4) tetrahedra. Ge-2(Se-1/2)(6) molecular units are the basic structural units in Ge-rich, x = 0.4, glass. For x = 0.2, 0.33 and 0.4 there is evidence for some of the tetrahedra being in an edge-shared configuration. The number of edge-shared tetrahedra in these glasses increase with increasing Ge content.

Diffraction Of Elastic Waves By Two Parallel Rigid Strips Embedded In An Infinite Orthotropic Medium

The elastodynamic response of a pair of parallel rigid strips embedded in an infinite orthotropic medium due to elastic waves incident normally on the strips has been investigated. The mixed boundary value problem has been solved by the Integral Equation method. The normal stress and the vertical displacement have been derived in closed form. Numerical values of stress intensity factors at inner and outer edges of the strips and vertical displacement at points in the plane of the strips for several orthotropic materials have been calculated and plotted graphically to show the effect of material orthotropy.

Influence of non-stoichiometric defects on nonlinear absorption and refraction in Nd:Zn co-doped lithium niobate

Nonlinear absorption and refraction phenomena in stoichiometric lithium niobate (SLN) pure and co-doped with Zn and Nd, and congruent lithium niobate (CLN) were investigated using Z-scan technique. Femtosecond laser pulses from Ti:Sapphire laser (800 nm, 110 fs pulse width and 1 kHz repetition rate) were utilized for the experiment. The process responsible for nonlinear behavior of the samples was identified to be three photon absorption (3PA). This is in agreement with the band gap energies of the samples obtained from the linear absorption cut off and the slope of the plot of Ln(1 − TOA) vs. Ln(I0) using Sutherland’s theory (s = 2.1, for 3PA). The nonlinear refractive index (n2) of Zn doped samples was found to be lower than that of pure samples. Our experiments show that there exists a correlation between the nonlinear properties and the stoichiometry of the samples. The values of n2 fall into the same range as those obtained for the materials of similar band gap.

Electric-field-dependent average resistance and the resistance fluctuation in one-dimensional disordered systems

Following an invariant-imbedding approach, we obtain analytical expressions for the ensemble-averaged resistance (ρ) and its Sinai’s fluctuations for a one-dimensional disordered conductor in the presence of a finite electric field F. The mean resistance shows a crossover from the exponential to the power-law length dependence with increasing field strength in agreement with known numerical results. More importantly, unlike the zero-field case the resistance distribution saturates to a Poissonian-limiting form proportional to A‖F‖exp(-A‖F‖ρ) for large sample lengths, where A is constant.

A hydrodynamical study of the flow in renal tubules

The hydrodynamical problem of flow in proximal renal tubule is investigated by considering axisymmetric flow of a viscous, incompressible fluid through a long narrow tube of varying cross-section with reabsorption at the wall. Two cases for reabsorption have been studied (i) when the bulk flow,Q, decays exponentially with the axial distancex, and (ii) whenQ is an arbitrary function ofx such thatQ-Q 0 can be expressed as a Fourier integral (whereQ 0 is the flux atx=0). The analytic expressions for flow variables have been obtained by applying perturbation method in terms of wall parameter ε. The effects of ε on pressure drop across the tube, radial velocity and wall shear have been studied in the case of exponentially decaying bulk flow and it has been found that the results are in agreement with the existing ones for the renal tubules.