Spatial Structures and Giant Number Fluctuations in Models of Active Matter

The large scale fluctuations of the ordered state in active matter systems are usually characterised by studying the "giant number fluctuations" of particles in any finite volume, as compared to the expectations from the central limit theorem. However, in ordering systems, the fluctuations in density ordering are often captured through their structure functions deviating from Porod law. In this paper we study the relationship between giant number fluctuations and structure functions, for different models of active matter as well as other non-equilibrium systems. A unified picture emerges, with different models falling in four distinct classes depending on the nature of their structure functions. For one class, we show that experimentalists may find Porod law violation, by measuring subleading corrections to the number fluctuations.Comment: 5 pages, 3 figure

Effects of partial crystallinity and quenched-in defects on corrosion of a rapidly solidified Ti-Cu alloy

Rapid solidification by planar flow casting has been found to have introduced deficiencies, viz. partial crystallinity, air pockets and compositional difference in the ribbons of rapidly solidified Ti42.9Cu57.1 alloy. In order to investigate the effects of these deficiencies on the corrosion of rapidly solidified Ti42.9Cu57.1 alloy ribbons, electrochemical behaviour of alloy ribbons has been investigated in the acidic chloride environments at room temperature by taking into consideration each side of the alloy ribbon separately. The alloy displayed passivity followed by pitting corrosion. In the as- solidified condition, air pockets appear to be the most detrimental defect from the viewpoint of corrosion resistance of the alloy ribbons

Thermodynamics of phase transition in higher dimensional AdS black holes

We investigate the thermodynamics of phase transition for $(n+1)$ dimensional Reissner Nordstrom (RN)-AdS black holes using a grand canonical ensemble. This phase transition is characterized by a discontinuity in specific heat. The phase transition occurs from a lower mass black hole with negative specific heat to a higher mass black hole with positive specific heat. By exploring Ehrenfest's scheme we show that this is a second order phase transition. Explicit expressions for the critical temperature and critical mass are derived. In appropriate limits the results for $(n+1)$ dimensional Schwarzschild AdS black holes are obtained.Comment: LaTex, 11 pages, 5 figures, To appear in JHE

Approximation of corner polyhedra with families of intersection cuts

We study the problem of approximating the corner polyhedron using intersection cuts derived from families of lattice-free sets in $\mathbb{R}^n$. In particular, we look at the problem of characterizing families that approximate the corner polyhedron up to a constant factor, which depends only on $n$ and not the data or dimension of the corner polyhedron. The literature already contains several results in this direction. In this paper, we use the maximum number of facets of lattice-free sets in a family as a measure of its complexity and precisely characterize the level of complexity of a family required for constant factor approximations. As one of the main results, we show that, for each natural number $n$, a corner polyhedron with $n$ basic integer variables and an arbitrary number of continuous non-basic variables is approximated up to a constant factor by intersection cuts from lattice-free sets with at most $i$ facets if $i> 2^{n-1}$ and that no such approximation is possible if $i \leq 2^{n-1}$. When the approximation factor is allowed to depend on the denominator of the fractional vertex of the linear relaxation of the corner polyhedron, we show that the threshold is $i > n$ versus $i \leq n$. The tools introduced for proving such results are of independent interest for studying intersection cuts

A note on matrix model with IR cutoff and AdS/CFT

We propose an effective model of strongly coupled gauge theory at finite temperature on $R^3$ in the presence of an infrared cutoff. It is constructed by considering the theory on $S^3$ with an infrared cutoff and then taking the size of the $S^3$ to infinity while keeping the cutoff fixed. This model reproduces various qualitative features expected from its gravity dual.Comment: 27 pages, 9 figures, an appendix added, other minor changes, journal versio

Pathogen-induced expression of harpinPss increases resistance in tobacco against fusarium oxysporum f. sp. nicotianae

HarpinPss (encoded by the hrpZ gene), a proteinaceous elicitor produced by Pseudomonas syringae pv. syringae, induces cell death in plants through hypersensitive response (HR). With an aim to generate transgenic tobacco resistant to fungal diseases, hrpZ was expressed in a secretable form, tagged with the signal peptide (SP) of PR1a, under the constitutive 35S promoter (P35S) or pathogen-inducible promoters (PIPs) like phenylalanine ammonia lyase (PAL), osmotin (OSM), and hypersensitive-related (HSR) promoters. The constitutive expression of the secretable form of hrpZ did not permit regeneration of transformed cells due to harpinPss-induced cell death. Transformants were recovered at a low frequency (2-6%) from leaf discs infected with Agrobacterium harbouring the SP-hrpZ driven by PIPs due to wound-induced leaky expression of harpinPss. The transgenic lines were confirmed by PCR using transgene-specific primers for SP-hrpZ. The expression of hrpZ under PIPs in transgenic lines was confirmed by Western blotting after challenging the leaves with Fusarium oxysporum f. sp. nicotianae. RT-PCR analysis also confirmed the expression of SP-hrpZ driven by PIPs in transgenic tobacco upon infection with F. oxysporum f. sp. nicotianae. The expression of harpinPss in these transgenic lines was accompanied by expression of defense-response genes such as PR1, PR2, PR3, HSR and HIN1. Transgenic tobacco plants showed enhanced resistance to F. oxysporum f. sp. nicotianae. Our findings suggest the potential use of an elicitor gene (hrpZ), driven by PIPs (PAL, OSM, and HSR) for the development of resistant plants

On the maximum size of an anti-chain of linearly separable sets and convex pseudo-discs

We show that the maximum cardinality of an anti-chain composed of intersections of a given set of n points in the plane with half-planes is close to quadratic in n. We approach this problem by establishing the equivalence with the problem of the maximum monotone path in an arrangement of n lines. For a related problem on antichains in families of convex pseudo-discs we can establish the precise asymptotic bound: it is quadratic in n. The sets in such a family are characterized as intersections of a given set of n points with convex sets, such that the difference between the convex hulls of any two sets is nonempty and connected.Comment: 10 pages, 3 figures. revised version correctly attributes the idea of Section 3 to Tverberg; and replaced k-sets by "linearly separable sets" in the paper and the title. Accepted for publication in Israel Journal of Mathematic