new series expansion data for surface and bulk resistivity and conductivity in two dimensional percolation low density series expansions are obtained for random resistor networks the expansions are obtained on the square lattice to order 18 and on the triangular lattice to order 14 bulk and surface expansions are given for both resistive and conductive susceptibilities the balance of the evidence obtained from analysing these series is in favour of the value for the critical exponent of the resistance scale and supports the existence of only a single such scale for bulk and surface susceptibilities this value is in agreement with earlier monte carlo work

quantum discord for qubit qudit systems we present two formulae to calculate quantum discord a kind of quantum correlation between a qubit and a second party of arbitrary dimension d the first formula is the original entropic definition and the second is a recently proposed geometric distance measure which leads to an analytical formulation the tracing over the qubit in the entropic calculation is reduced to a very simple prescription and when the d dimensional system is a so calledx state the density matrix having non zero elements only along the diagonal and anti diagonal the entropic calculation can also be carried out analytically such states of the full bipartite qubit qudit system may be named extended x states whose density matrix is built of four block matrices each visually appearing as an x the optimization involved in the entropic calculation is generally over two parameters reducing to one for many cases and avoided altogether for an overwhelmingly large set of density matrices as our numerical investigations demonstrate in the case of n 2 extended x states encompass the entire 15 dimensional parameter space that is they represent the full qubit qubit system

the resistive susceptibility of a three dimensional random diode insulator network the resistive susceptibility chi r p of harris and fisch is expanded graphically for the directed simple cubic bond problem as a power series in the diode density p up to p11 standard pade analysis shows that chi r p diverges with the exponent gamma r 2 70 or 0 04 and using a scaling relation the exponent t for the conductivity of the infinite cluster is estimated to be t 1 29 or 0 02

diffusion in three dimensional random systems at their percolation thresholds extensive monte carlo simulations of theant in the labyrinth problem on randoml l l simple cubic lattices are performed forl up to 960 on a cray ymp supercomputer the exponentk for the rms displacementr witht inr t k is found to bek 0 190 0 003 as a second approach large percolation clusters with chemical shells up to 300 are generated on a simple cubic lattice at criticality the diffusion equation is then solved by using the exact enumeration technique the corresponding critical exponentd w is found to be 1 d w 0 250 0 003

maximally genuine multipartite entangled mixed x states of n qubits for every possible spectrum of dimensional density operators we construct an n qubit x state of the same spectrum and maximal genuine multipartite gm concurrence hence characterizing a global unitary transformation that constrained to output x states maximizes the gm concurrence of an arbitrary input mixed state of n qubits we also apply semidefinite programming methods to obtain n qubit x states with maximal gm concurrence for a given purity and to provide an alternative proof of optimality of a recently proposed set of density matrices for the purpose the so called x mems furthermore we introduce a numerical strategy to tailor a quantum operation that converts between any two given density matrices using a relatively small number of kraus operators we apply our strategy to design short operator sum representations for the transformation between any given n qubit mixed state and a corresponding x mems of the same purity

conductivity exponents from the analysis of series expansions for random resistor networks there has been considerable controversy in recent years over the value of the conductivity exponent t this exponent can be deduced from series expansions via the scaling relations t zeta d 2 nu where zeta is deduced from differences between the exponents of the resistive gamma r percolative gamma p and conductive gamma c susceptibility the author finds that allowance for non analytic confluent corrections to scaling and the use of recent pc estimates leads to estimates for gamma r gamma p and gamma c that are somewhat different to those of fisch and harris 1978 however the differences between these exponents do not change significantly moreover the change in accepted estimates of nu in the last five years cancels some of this remaining discrepancy and she concludes using the relation zeta gamma r gamma p that t 1 31 d 2 t 2 04 d 3 t 2 39 d 4 t 2 72 d 5 with an error of about or 0 10 in each case the d 2 estimate is in significantly better agreement with those of other methods than that of fisch and harris

averages over percolation clusters on a cayley tree averages over percolation clusters gamma of the form sigma gamma p gamma x gamma n gamma k identical to chi k p are considered where n gamma is the number of sites in the cluster x gamma is some property of the cluster and p gamma is the probability per site of forming such a cluster at bond concentration p

perimeter polynomials for bond percolation processes perimeter polynomials are given for the bond percolation problem on the following lattices the triangular up to d9 simple quadratic d13 honeycomb d17 face centred cubic d7 body centred cubic d8 simple cubic d9 and diamond d13 the total number of bond clusters grouped by size is given to two further orders in each case

genuine quantum and classical correlations in multipartite systems generalizing the quantifiers used to classify correlations in bipartite systems we define genuine total quantum and classical correlations in multipartite systems the measure we give is based on the use of relative entropy to quantify the distance between two density matrices moreover we show that for pure states of three qubits both quantum and classical bipartite correlations obey a ladder ordering law fixed by two body mutual informations or equivalently by one qubit entropies

the role of phases in detecting three qubit entanglement we propose separability criteria for three qubit states in terms of diagonal and anti diagonal entries to detect entanglement with positive partial transposes we report that the phases that is the angular parts of anti diagonal entries play a crucial role in determining whether a given three qubit state is separable or entangled and they must obey even an identity for separability in some cases these criteria are strong enough to detect ppt positive partial transpose entanglement with nonzero volume in several cases when all the entries are zero except for diagonal and anti diagonal entries we characterize separability using phases these include the cases when anti diagonal entries of such states share a common magnitude and when ranks are less than or equal to six we also compute the lengths of rank six cases and find three qubit separable states with lengths 8 whose maximum ranks of partial transposes are 7

low concentration series in general dimension we discuss recent work on the development and analysis of low concentration series for many models the recent breakthrough in the extremely efficient no free end method of series generation facilitates the derivation of 15th order series for multiple moments in general dimension the 15th order series have been obtained for lattice animals percolation and the edwards anderson ising spin glass in the latter cases multiple moments have been found from complete graph tables through to 13th order general dimension 13th order series have been derived for the resistive susceptibility the moments of the logarithms of the distribution of currents in resistor networks and the average transmission coefficient in the quantum percolation problem 11th order series have been found for several other systems including the crossover from animals to percolation the full resistance distribution nonlinear resistive susceptibility and current distribution in dilute resistor networks diffusion on percolation clusters the dilute ising model dilute antiferromagnet in a field and random field ising model and self avoiding walks on percolation clusters series for the dilute spin 1 2 quantum heisenberg ferromagnet are in the process of development analysis of these series gives estimates for critical thresholds amplitude ratios and critical exponents for all dimensions where comparisons are possible our series results are in good agreement with bothe expansion results near the upper critical dimension and with exact results when available in low dimensions and are competitive with other numerical approaches in intermediate realistic dimensions

numerical simulation of self sustained oscillation of a voice producing element based on navier stokes equations and the finite element method surgical removal of the larynx results in radically reduced production of voice and speech to improve voice quality a voice producing element vpe is developed based on the lip principle called after the lips of a musician while playing a brass instrument to optimize the vpe a numerical model is developed in this model the finite element method is used to describe the mechanical behavior of the vpe the flow is described by two dimensional incompressible navier stokes equations the interaction between vpe and airflow is modeled by placing the grid of the vpe model in the grid of the aerodynamical model and requiring continuity of forces and velocities by applying and increasing pressure to the numerical model pulses comparable to glottal volume velocity waveforms are obtained by variation of geometric parameters their influence can be determined to validate this numerical model an in vitro test with a prototype of the vpe is performed experimental and numerical results show an acceptable agreement

series expansion evidence supporting the alexander orbach conjecture in two dimensions the authors extend the series expansion of fisch and harris 1978 for the resistive susceptibility chi r p by a further six terms on the square lattice this leads to a more precise estimate of the corresponding exponent gamma r 3 65 or 0 02 they also obtain the exact relation chi r p 2e tau mod f where tau is the sum of the relaxation times for charge diffusion on the cluster containing the origin and the expectation value is subject to the condition that the latter is finite a known scaling relation for the fracton dimension df in terms of gamma r and the static exponents is derived without the usual reference to the infinite cluster using the estimate of gamma r they find df 1 334 or 0 007 which is consistent with the ao conjecture df 4 3 they also note that gamma r is the same for directed and undirected percolation to within the accuracy of the calculations

on the relationship between the critical exponents of percolation conductivity and static exponents of percolation the author argues that the critical exponent t of random conductance networks near the percolation threshold is given by t d 1 nu for low dimensionalities and t 1 beta for high dimensionalities where nu is the correlation length exponent beta the backbone exponent and d is dimensionality the author argues that what separates the two regimes is a critical fractal dimensionality dl which equals 2 the author also argues that dl is also a critical fractal dimensionality for fractals such as lattice animals and diffusion limited aggregates the result for low dimensionalities has been also obtained by aharony and stauffer by a different argument

separability criterion for three qubit states with a four dimensional norm we give a separability criterion for three qubit states in terms of diagonal and anti diagonal entries this gives us a complete characterization of separability when all the entries are zero except for diagonal and anti diagonals the criterion is expressed in terms of a norm arising from anti diagonal entries we compute this norm in several cases so that we get criteria with which we can decide the separability by routine computations

on correction to scaling for two and three dimensional scalar and vector percolation a reanalysis of the resistancer of two and three dimensional superconducting networks at the percolation thresholdp c together with the previous results for the elastic modulik of such networks shows that there is aunified description of finite size scaling for scalar and vector transport properties of percolation systems for a network of linear sizel atp c and forboth scalar and vector percolation inboth two and three dimensions k andr scale withl asl x a 1 a 2 lnl 1 a 3 l 1 wherex is the ratio of the associated critical exponent ofk orr and the correlation length exponentv of percolation although our estimates ofx for the resistance of percolation networks are consistent with the previous results they do indicate that inboth two and three dimensions and forboth scalar and vector percolation the leading nonanalytic correction to scaling exponent iszero from a reanalysis of data on diffusion on percolation clusters atp c we propose that such correction to scaling terms are a general property ofdynamics of percolation clusters we also suggest that for two dimensional percolation the conductivity exponentt and the superconductivity exponents are given by s t v 4 187 144 1 2986 and the elasticity exponentf is given byf t 2v 571 144 3 9652 where is the exponent of the strength of the infinite percolation cluster

phonation threshold pressure a missing link in glottal aerodynamics phonation threshold pressure has previously been defined as the minimum lung pressure required to initiate phonation by modeling the dependence of this pressure on fundamental frequency it is shown that relatively simple aerodynamic relations for time varying flow in the glottis are obtained lung pressure and peak glottal flow are nearly linearly related but not proportional for this reason typical power law relations that have previously been proposed do not hold glottal impedance for time varying flow must be defined differentially rather than as a simple ratio between pressure and flow it is shown that the peak flow the peak flow derivative the open quotient and the speed quotient of inverse filtered glottal flow waveforms all depend explicitly on phonation threshold pressure data from singers are compared with those from nonsingers the primary difference is that singers obtain two to three times greater peak flow for a given lung pressure suggesting that they adjust their glottal or voca

the resistive susceptibility of random diode insulator networks the authors consider regular crystal lattices in which the bonds are either diodes probability p or insulators the mean number of backbone bonds lbb p when averaged over lattice points is found to be related to the mean size of clusters s p by lbb p zps p where z is the number of bonds directed away from any lattice site thus lbb diverges at pc with the mean size exponent gamma the resistive susceptibility chi r p of harris and fisch 1977 1978 is expanded graphically as a power series in p and it is found that term by term chi r p psi r p s p 2 where psi r p is obtained from chi r p by ignoring contributions from nodal graphs the above results are valid for bond and site dilution in any dimension for bond dilution on the square lattice the authors have determined psi r p to p17 and pade analysis of the resulting series for chi r p shows that it diverges with exponent gamma r 3 654 or 0 017 using a scaling relation the exponent t for the conductivity of the infinite cluster is estimated to be t 0 75 or 0 02

taming multiparticle entanglement we present an approach to characterize genuine multiparticle entanglement by using appropriate approximations in the space of quantum states this leads to a criterion for entanglement which can easily be calculated by using semidefinite programing and improves all existing approaches significantly experimentally it can also be evaluated when only some observables are measured furthermore it results in a computable entanglement monotone for genuine multiparticle entanglement based on this we develop an analytical approach for the entanglement detection in cluster states leading to an exponential improvement compared with existing schemes

series expansion study of the distribution of currents in the elements of a random diode insulator network the critical exponent zeta k of the kth moment of the current distribution for random diode insulator networks on the square and simple cubic lattices is calculated for a range of k using low density series expansion techniques it is also shown that zeta 1 nu sub where nu sub is the critical exponent of the parallel connectedness length for directed percolation the values of zeta k for the simple cubic lattice are well fitted by a simple exponential formula with zeta k 1 zeta k 1 1 1 2 the skal shklovskii scaling relation for the conductivity is generalised to the kth moment and it follows that the exponent k describing the divergence of flicker noise is given by kappa approximately d 1 nu perpendicular to nu sub zeta 4 2 zeta 2 the authors estimate this for both lattices

construction of multi qubit optimal genuine entanglement witnesses we interpret multi partite genuine entanglement witnesses as simultaneous positivity of various maps arising from them we apply this result to multi qubit x shaped hermitian matrices and characterize the conditions for them to be genuine entanglement witnesses in terms of entries furthermore we find all optimal entries among them they turn out to have spanning properties and so they detect a non zero volume set of multi qubit genuine entanglement we also characterize decomposability for x shaped entanglement witnesses