Many polynomial invariants of knots and links, including the Jones and HOMFLY-PT polynomials, are widely used in practice but #P-hard to compute. It was shown by Makowsky in 2001 that computing the Jones polynomial is fixed-parameter tractable in the treewidth of the link diagram, but the parameterised complexity of the more powerful HOMFLY-PT polynomial remained an open problem. Here we show t...

This paper examines the Asymmetric AdaBoost algorithm introduced by Viola and Jones for cascaded face detection. The Viola and Jones face detector uses cascaded classifiers to successively filter, or reject, non-faces. In this approach most non-faces are easily rejected by the earlier classifiers in the cascade, thus reducing the overall number of computations. This requires earlier cascade cla...

the problem of steady magnetohydrodynamic boundary layer flow of an electrically conducting nanofluid due to an exponentially permeable stretching sheet with heat source/sink in presence of thermal radiation is numerically investigated. the effect of transverse brownian motion and thermophoresis on heat transfer and nano particle volume fraction considered. the governing partial differential eq...

We studied the possibility to approximate a Lennard-Jones interaction by a pairwise contact potential. First we used a Lennard-Jones potential to design off-lattice, protein-like heteropolymer sequences, whose lowest energy (native) conformations were then identified by molecular dynamics. Then we turned to investigate whether one can find a pairwise contact potential, whose ground states are t...

Submitted for the MAR16 Meeting of The American Physical Society Study of adiabatic connection in ground-state density functional theory MANOJ HARBOLA, RABEET CHAUHAN, Indian Inst of Tech-Kanpur, RABEET S. CHAUHAN COLLABORATION — By employing modified [1] variational form of Le-Sech wavefunctions [2] for two-electron systems, accurate wavefunctions for He-like atoms corresponding to their groun...

The influence of temperature on interfacial fluid slip, as measured by molecular-dynamics simulations a Couette flow comprising Lennard-Jones and rigid crystalline walls, is examined function the fluid-solid interaction strength. Two different types thermal behavior are observed, namely, slippery sticky cases. first characterized steep unlimited increase slip length at low temperatures, while s...

Liquid–liquid interfaces and nucleation in partially miscible Lennard–Jones ~LJ! mixtures are considered using density functional theory. We present phase diagrams, interfacial liquid–vapor and liquid–liquid profiles, and gas–liquid as well as liquid–liquid surface tensions for two types of mixtures having different mixing rules for the LJ energy parameter. A simple local density approximation ...

The heterogeneous nucleation of liquid droplet on a solid surface was simulated with the molecular dynamics method. Argon vapor was represented by 5760 Lennard-Jones molecules and the solid surface was represented by one layer of 1020 harmonic molecules with the constant temperature heat bath model using the phantom molecules. The potential parameter between solid molecule and vapor molecule wa...

We report results of calculations of the second through sixth virial coefficients for four prototype Lennard-Jones (LJ) mixtures that have been the subject of previous studies in the literature. Values are reported for temperatures ranging from T=0.6 to T=10.0, where here the temperature is given units of the LJ energy parameter of one of the components. Thermodynamic stability of the mixtures ...

We consider a classical dilute particle system in a large box with pairinteraction given by a Lennard-Jones-type potential. The inverse temperature is picked proportionally to the logarithm of the particle density. We identify the free energy per particle in terms of a variational formula and show that this formula exhibits a cascade of phase transitions as the temperature parameter ranges from...