Athermal Nonlinear Elastic Constants of Amorphous Solids

We derive expressions for the lowest nonlinear elastic constants of amorphous solids in athermal conditions (up to third order), in terms of the interaction potential between the constituent particles. The effect of these constants cannot be disregarded when amorphous solids undergo instabilities like plastic flow or fracture in the athermal limit; in such situations the elastic response increases enormously, bringing the system much beyond the linear regime. We demonstrate that the existing theory of thermal nonlinear elastic constants converges to our expressions in the limit of zero temperature. We motivate the calculation by discussing two examples in which these nonlinear elastic constants play a crucial role in the context of elasto-plasticity of amorphous solids. The first example is the plasticity-induced memory that is typical to amorphous solids (giving rise to the Bauschinger effect). The second example is how to predict the next plastic event from knowledge of the nonlinear elastic constants. Using the results of this paper we derive a simple differential equation for the lowest eigenvalue of the Hessian matrix in the external strain near mechanical instabilities; this equation predicts how the eigenvalue vanishes at the mechanical instability and the value of the strain where the mechanical instability takes place.Comment: 17 pages, 2 figures

Fuzzy image segmentation of generic shaped clusters

The segmentation performance of any clustering algorithm is very sensitive to the features in an image, which ultimately restricts their generalisation capability. This limitation was the primary motivation in our investigation into using shape information to improve the generality of these algorithms. Fuzzy shape-based clustering techniques already consider ring and elliptical profiles in segmentation, though most real objects are neither ring nor elliptically shaped. This paper addresses this issue by introducing a new shape-based algorithm called fuzzy image segmentation of generic shaped clusters (FISG) that incorporates generic shape information into the framework of the fuzzy c-means (FCM) algorithm. Both qualitative and quantitative analyses confirm the superiority of FISG compared to other shape-based fuzzy clustering methods including, Gustafson-Kessel algorithm, ring-shaped, circular shell, c-ellipsoidal shells and elliptic ring-shaped clusters. The new algorithm has also been shown to be application independent so it can be applied in areas such as video object plane segmentation in MPEG-4 based coding

Spin Hall effect in a Kagome lattice driven by Rashba spin-orbit interaction

Using four-terminal Landauer-B\"{u}ttiker formalism and Green's function technique, in this present paper, we calculate numerically spin Hall conductance (SHC) and longitudinal conductance of a finite size kagome lattice with Rashba spin-orbit (SO) interaction both in presence and absence of external magnetic flux in clean limit. In the absence of magnetic flux, we observe that depending on the Fermi surface topology of the system SHC changes its sign at different values of Fermi energy, along with the band center. Unlike the infinite system (where SHC is a universal constant $\pm \frac{e}{8 \pi}$), here SHC depends on the external parameters like SO coupling strength, Fermi energy, etc. We show that in the presence of any arbitrary magnetic flux, periodicity of the system is lost and the features of SHC tends to get reduced because of elastic scattering. But again at some typical values of flux ($\phi=1/2, 1/4, 3/4..., etc.) the system retains its periodicity depending on its size and the features of spin Hall effect (SHE) reappears. Our predicted results may be useful in providing a deeper insight into the experimental realization of SHE in such geometries.Comment: 10 pages, 10 figure

Equilibrium glassy phase in a polydisperse hard sphere system

The phase diagram of a polydisperse hard sphere system is examined by numerical minimization of a discretized form of the Ramakrishnan-Yussouff free energy functional. Crystalline and glassy local minima of the free energy are located and the phase diagram in the density-polydispersity plane is mapped out by comparing the free energies of different local minima. The crystalline phase disappears and the glass becomes the equilibrium phase beyond a "terminal" value of the polydispersity. A crystal to glass transition is also observed as the density is increased at high polydispersity. The phase diagram obtained in our study is qualitatively similar to that of hard spheres in a quenched random potential.Comment: 4 pages, 4 figure

Precise toppling balance, quenched disorder, and universality for sandpiles

A single sandpile model with quenched random toppling matrices captures the crucial features of different models of self-organized criticality. With symmetric matrices avalanche statistics falls in the multiscaling BTW universality class. In the asymmetric case the simple scaling of the Manna model is observed. The presence or absence of a precise toppling balance between the amount of sand released by a toppling site and the total quantity the same site receives when all its neighbors topple once determines the appropriate universality class.Comment: 5 Revtex pages, 4 figure

Stochastic model of transcription factor-regulated gene expression

We consider a stochastic model of transcription factor (TF)-regulated gene expression. The model describes two genes: Gene A and Gene B which synthesize the TFs and the target gene proteins respectively. We show through analytic calculations that the TF fluctuations have a significant effect on the distribution of the target gene protein levels when the mean TF level falls in the highest sensitive region of the dose-response curve. We further study the effect of reducing the copy number of Gene A from two to one. The enhanced TF fluctuations yield results different from those in the deterministic case. The probability that the target gene protein level exceeds a threshold value is calculated with a knowledge of the probability density functions associated with the TF and target gene protein levels. Numerical simulation results for a more detailed stochastic model are shown to be in agreement with those obtained through analytic calculations. The relevance of these results in the context of the genetic disorder haploinsufficiency is pointed out. Some experimental observations on the haploinsufficiency of the tumour suppressor gene, Nkx3.1, are explained with the help of the stochastic model of TF-regulated gene expression.Comment: 17 pages, 11 figures. Accepted for publication in Physical Biolog