MaxEnt and dynamical information

The MaxEnt solutions are shown to display a variety of behaviors (beyond the traditional and customary exponential one) if adequate dynamical information is inserted into the concomitant entropic-variational principle. In particular, we show both theoretically and numerically that power laws and power laws with exponential cut-offs emerge as equilibrium densities in proportional and other dynamics

The structure of flame filaments in chaotic flows

The structure of flame filaments resulting from chaotic mixing within a combustion reaction is considered. The transverse profile of the filaments is investigated numerically and analytically based on a one-dimensional model that represents the effect of stirring as a convergent flow. The dependence of the steady solutions on the Damkohler number and Lewis number is treated in detail. It is found that, below a critical Damkohler number Da(crit), the flame is quenched by the flow. The quenching transition appears as a result of a saddle-node bifurcation where the stable steady filament solution collides with an unstable one. The shape of the steady solutions for the concentration and temperature profiles changes with the Lewis number and the value of Da(crit) increases monotonically with the Lewis number. Properties of the solutions are studied analytically in the limit of large Damkohler number and for small and large Lewis number.Comment: 17 pages, 13 figures, to be published in Physica

Fabrication of an autonomously self-healing flexible thin-film capacitor by slot-die coating

Flexible pressure sensors with self-healing abilities for wearable electronics are being developed, but generally either lack autonomous self-healing properties or require sophisticated material processing methods. To address this challenge, we developed flexible, low-cost and autonomously self-healing capacitive sensors using a crosslinked poly(dimethylsiloxane) through metal-ligand interactions processed into thin films via slot-die coating. These films have excellent self-healing properties, approximately 1.34 × 105 μm3 per hour at room temperature and 2.87 × 105 μm3 per hour at body temperature (37 °C). Similarly, no significant change in capacitance under bending strain was observed on these flexible thin-films when assembled on poly(ethyleneterephthalate) (PET) substrates; capacitors showed good sensitivity at low pressure regimes. More importantly, the devices fully recovered their sensitivity after being damaged and healed, which is directly attributed to the rapid and autonomous self-healing of the dielectric materials

On the Interpretation of Energy as the Rate of Quantum Computation

Over the last few decades, developments in the physical limits of computing and quantum computing have increasingly taught us that it can be helpful to think about physics itself in computational terms. For example, work over the last decade has shown that the energy of a quantum system limits the rate at which it can perform significant computational operations, and suggests that we might validly interpret energy as in fact being the speed at which a physical system is "computing," in some appropriate sense of the word. In this paper, we explore the precise nature of this connection. Elementary results in quantum theory show that the Hamiltonian energy of any quantum system corresponds exactly to the angular velocity of state-vector rotation (defined in a certain natural way) in Hilbert space, and also to the rate at which the state-vector's components (in any basis) sweep out area in the complex plane. The total angle traversed (or area swept out) corresponds to the action of the Hamiltonian operator along the trajectory, and we can also consider it to be a measure of the "amount of computational effort exerted" by the system, or effort for short. For any specific quantum or classical computational operation, we can (at least in principle) calculate its difficulty, defined as the minimum effort required to perform that operation on a worst-case input state, and this in turn determines the minimum time required for quantum systems to carry out that operation on worst-case input states of a given energy. As examples, we calculate the difficulty of some basic 1-bit and n-bit quantum and classical operations in an simple unconstrained scenario.Comment: Revised to address reviewer comments. Corrects an error relating to time-ordering, adds some additional references and discussion, shortened in a few places. Figures now incorporated into tex

Use of non-adiabatic geometric phase for quantum computing by nuclear magnetic resonance

Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled logic gates by controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of errors. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1>, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using these geometric phase gates we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system

Moduli Webs and Superpotentials for Five-Branes

We investigate the one-parameter Calabi-Yau models and identify families of D5-branes which are associated to lines embedded in these manifolds. The moduli spaces are given by sets of Riemann curves, which form a web whose intersection points are described by permutation branes. We arrive at a geometric interpretation for bulk-boundary correlators as holomorphic differentials on the moduli space and use this to compute effective open-closed superpotentials to all orders in the open string couplings. The fixed points of D5-brane moduli under bulk deformations are determined.Comment: 41 pages, 1 figur

Morse theory of the moment map for representations of quivers

The results of this paper concern the Morse theory of the norm-square of the moment map on the space of representations of a quiver. We show that the gradient flow of this function converges, and that the Morse stratification induced by the gradient flow co-incides with the Harder-Narasimhan stratification from algebraic geometry. Moreover, the limit of the gradient flow is isomorphic to the graded object of the Harder-Narasimhan-Jordan-H\"older filtration associated to the initial conditions for the flow. With a view towards applications to Nakajima quiver varieties we construct explicit local co-ordinates around the Morse strata and (under a technical hypothesis on the stability parameter) describe the negative normal space to the critical sets. Finally, we observe that the usual Kirwan surjectivity theorems in rational cohomology and integral K-theory carry over to this non-compact setting, and that these theorems generalize to certain equivariant contexts.Comment: 48 pages, small revisions from previous version based on referee's comments. To appear in Geometriae Dedicat

On non-local variational problems with lack of compactness related to non-linear optics

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.Comment: 30 page

Population growth and reproductive potential of five important fishes from the freshwater bodies of Bangladesh

Population growth (length-weight relationship), and reproductive potential (e.g. fecundity, and sex-ratio) of five important fish species (‘mola’: Amblypharyngodon mola, ‘puti’: Puntius sophore, ‘tengra’: Mystus vittatus, ‘shing’: Heteropneustes fossilis and ‘taki’: Channa punctatus) collected from two important fresh water bodies (namely Hilna beel and Beel Kumari beel) Rajshahi, Bangladesh, were studied. Population growth pattern by length-weight relationship (W=aLb ) for the species differed, and exhibited positive allometric growth (P. sophore in Hilna beel), isometric growth (A. mola and C. punctatus in Hilna beel) and negative allometric growth (M. vittatus & H. fossilis in Hilna beel and A. mola, P. sophore, M. vittatus, C. punctatus and H. fossilis in Beel Kumari beel). The results denoted that fecundity of mature females followed a non-linear relationship (F=aLb ) with total length and exhibited positive allometric growth (b>3) with some exception (A. mola in Hilna beel and M. vittatus in Beel Kumari beel). Fecundity of mature females also increased with total body weight and ovary weight following a linear relationship (F=a+bW). Differences in values of sexratios with seasons for all species in this study may have resulted from different environmental factors as well as breeding seasons. The findings of this study would be useful in imposing adequate regulations for the conservation of these fascinating fishes in the fresh water bodies of Bangladesh