Free-Boundary Dynamics in Elasto-plastic Amorphous Solids: The Circular Hole Problem

We develop an athermal shear-transformation-zone (STZ) theory of plastic deformation in spatially inhomogeneous, amorphous solids. Our ultimate goal is to describe the dynamics of the boundaries of voids or cracks in such systems when they are subjected to remote, time-dependent tractions. The theory is illustrated here for the case of a circular hole in an infinite two-dimensional plate, a highly symmetric situation that allows us to solve much of the problem analytically. In spite of its special symmetry, this example contains many general features of systems in which stress is concentrated near free boundaries and deforms them irreversibly. We depart from conventional treatments of such problems in two ways. First, the STZ analysis allows us to keep track of spatially heterogeneous, internal state variables such as the effective disorder temperature, which determines plastic response to subsequent loading. Second, we subject the system to stress pulses of finite duration, and therefore are able to observe elasto-plastic response during both loading and unloading. We compute the final deformations and residual stresses produced by these stress pulses. Looking toward more general applications of these results, we examine the possibility of constructing a boundary-layer theory that might be useful in less symmetric situations.Comment: 30 pages (preprint format), 9 figure

N=2 Supersymmetric Scalar-Tensor Couplings

We determine the general coupling of a system of scalars and antisymmetric tensors, with at most two derivatives and undeformed gauge transformations, for both rigid and local N=2 supersymmetry in four-dimensional spacetime. Our results cover interactions of hyper, tensor and double-tensor multiplets and apply among others to Calabi-Yau threefold compactifications of Type II supergravities. As an example, we give the complete Lagrangian and supersymmetry transformation rules of the double-tensor multiplet dual to the universal hypermultiplet.Comment: 23 pages, LaTeX2e with amsmath.sty; v2: corrected typos and added referenc

Automorphic Instanton Partition Functions on Calabi-Yau Threefolds

We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our main focus lies on the problem of resumming the infinite series of D-brane and NS5-brane instantons, using the mathematical machinery of automorphic forms. We review the proposal that whenever the low-energy theory in D=3 exhibits an arithmetic "U-duality" symmetry G(Z) the total instanton partition function arises from a certain unitary automorphic representation of G, whose Fourier coefficients reproduce the BPS-degeneracies. For D=4, N=2 theories on R^3 x S^1 we argue that the relevant automorphic representation falls in the quaternionic discrete series of G, and that the partition function can be realized as a holomorphic section on the twistor space Z over M. We also offer some comments on the close relation with N=2 wall crossing formulae.Comment: 25 pages, contribution to the proceedings of the workshop "Algebra, Geometry and Mathematical Physics", Tjarno, Sweden, 25-30 October, 201

Non-supersymmetric extremal multicenter black holes with superpotentials

Using the superpotential approach we generalize Denef's method of deriving and solving first-order equations describing multicenter extremal black holes in four-dimensional N = 2 supergravity to allow non-supersymmetric solutions. We illustrate the general results with an explicit example of the stu model.Comment: 17 pages, v2: some clarifications adde

High order amplitude equation for steps on creep curve

We consider a model proposed by one of the authors for a type of plastic instability found in creep experiments which reproduces a number of experimentally observed features. The model consists of three coupled non-linear differential equations describing the evolution of three types of dislocations. The transition to the instability has been shown to be via Hopf bifurcation leading to limit cycle solutions with respect to physically relevant drive parameters. Here we use reductive perturbative method to extract an amplitude equation of up to seventh order to obtain an approximate analytic expression for the order parameter. The analysis also enables us to obtain the bifurcation (phase) diagram of the instability. We find that while supercritical bifurcation dominates the major part of the instability region, subcritical bifurcation gradually takes over at one end of the region. These results are compared with the known experimental results. Approximate analytic expressions for the limit cycles for different types of bifurcations are shown to agree with their corresponding numerical solutions of the equations describing the model. The analysis also shows that high order nonlinearities are important in the problem. This approach further allows us to map the theoretical parameters to the experimentally observed macroscopic quantities.Comment: LaTex file and eps figures; Communicated to Phys. Rev.

Type IIB Theory on Half-flat Manifolds

In this note we derive the low-energy effective action of type IIB theory compactified on half-flat manifolds and we show that this precisely coincides with the low-energy effective action of type IIA theory compactified on a Calabi-Yau manifold in the presence of NS three-form fluxes. We provide in this way a further check of the recently formulated conjecture that half-flat manifolds appear as mirror partners of Calabi-Yau manifolds when NS fluxes are turned on.Comment: 15 pages, no figure

The Kahler Cone as Cosmic Censor

M-theory effects prevent five-dimensional domain-wall and black-hole solutions from developing curvature singularities. While so far this analysis was performed for particular models, we now present a model-independent proof that these solutions do not have naked singularities as long as the Kahler moduli take values inside the extended Kahler cone. As a by-product we obtain information on the regularity of the Kahler-cone metric at boundaries of the Kahler cone and derive relations between the geometry of moduli space and space-time.Comment: 21 pages, 1 figure. Improved discussion of the relation between Kahler moduli and five-dimensional scalars. No changes in the conclusion

D3-instantons, Mock Theta Series and Twistors

The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2,Z). We prove that this is the case in the one-instanton approximation, by constructing a holomorphic action of SL(2,Z) on the linearized twistor space. Using the modular invariance of the D4-D2-D0 black hole partition function, we show that the standard Darboux coordinates in twistor space have modular anomalies controlled by period integrals of a Siegel-Narain theta series, which can be canceled by a contact transformation generated by a holomorphic mock theta series.Comment: 42 pages; discussion of isometries is amended; misprints correcte

Lack of gene-language correlation due to reciprocal female but directional male admixture in Austronesians and non-Austronesians of East Timor

Nusa Tenggara, including East Timor, located at the crossroad between Island Southeast Asia, Near Oceania, and Australia, are characterized by a complex cultural structure harbouring speakers from two different major linguistic groups of different geographic origins (Austronesian (AN) and non-Austronesian (NAN)). This provides suitable possibilities to study gene-language relationship; however, previous studies from other parts of Nusa Tenggara reported conflicting evidence about gene-language correlation in this region. Aiming to investigate gene-language relationships including sex-mediated aspects in East Timor, we analysed the paternally inherited non-recombining part of the Y chromosome (NRY) and the maternally inherited mitochondrial (mt) DNA in a representative collection of AN-and NAN-speaking groups. Y-SNP (single-nucleotide polymorphism) data were newly generated for 273 samples and combined with previously established Y-STR (short tandem repeat) data of the same samples, and with previously established mtDNA data of 290 different samples with, however, very similar representation of geographic and linguistic coverage of the country. We found NRY and mtDNA haplogroups of previously described putative East/Southeast Asian (E/SEA) and Near Oceanian (NO) origins in both AN and NAN speakers of East Timor, albeit in different proportions, suggesting reciprocal genetic admixture between both linguistic groups for females, but directional admixture for males. Our data underline the dual genetic origin of East Timorese in E/SEA and NO, and highlight that substantial genetic admixtur