design of capacity approaching irregular low density parity check codes we design low density parity check ldpc codes that perform at rates extremely close to the shannon capacity the codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides our theoretical analysis of the codes is based on the work of richardson and urbanke see ibid vol 47 no 2 p 599 618 2000 assuming that the underlying communication channel is symmetric we prove that the probability densities at the message nodes of the graph possess a certain symmetry using this symmetry property we then show that under the assumption of no cycles the message densities always converge as the number of iterations tends to infinity furthermore we prove a stability condition which implies an upper bound on the fraction of errors that a belief propagation decoder can correct when applied to a code induced from a bipartite graph with a given degree distribution our codes are found by optimizing the degree structure of the underlying graphs we develop several strategies to perform this optimization we also present some simulation results for the codes found which show that the performance of the codes is very close to the asymptotic theoretical bounds

the equations of motion of curved pipes conveying fluid abstract the non linear differential equations of motion of a fluid conveying pipe the no flow configuration of which is in the shape of a one dimensional line arbitrarily curved and twisted in space are derived by making use of the newtonian approach the extensible dynamics of the beam is based on the timoshenko beam theory some significant differences with the equations available in the open literature are discussed the stressed by flow configuration is found to be the only equilibrium state adequate for the study of the linear stability of such pipe fluid systems

rate compatible puncturing of low density parity check codes in this correspondence we consider puncturing of low density parity check ldpc codes for additive white gaussian noise awgn channels we show that good puncturing patterns exist and that the puncturing can be performed in a rate compatible fashion furthermore rate compatible puncturing results in a small loss of performance with respect to threshold namely the punctured code is good in terms of threshold across a range of rates when compared with the optimal codes for each rate this allows one to implement a single mother encoder and decoder that is good across a wide range of rates

the equations of motion of initially stressed timoshenko tubular beams conveying fluid abstract in this paper the equations of motion of an initially stressed timoshenko tubular beam subjected to a tensile follower load and conveying fluid are derived by using the appropriate statement of hamilton s principle this latter is obtained first for open systems the instantaneous total mass of which does not necessarily remain constant in the course of deformation open denoting that there is momentum transport in and out of the system the equations of motion are derived separately for a cantilevered system and for one with both extremities of the tube clamped yet another derivation for the cantilevered tube is presented with the system considered to be quasi closed where all flow induced effects are incorporated through the virtual work as if they were external forces all three sets of equations are found to be identical these equations are then compared with those obtained more simply by the newtonian force balance approach some differences between them are found to exist the principal of which are associated with the follower or other tensile forces these are discussed at some length and the equations of motion obtained here are compared to those obtained by other researchers for timoshenko beams subjected to follower or tensile forces

on the construction of the solution of an equation describing an axially moving string in this paper an initial boundary value problem for a linear nonhomogeneous axially moving string equation will be considered the velocity of the string is assumed to be constant and the nonhomogeneous terms in the string equation are due to external forces acting on the string the laplace transform method will be used to construct the solution of the problem it will turn out that the method has considerable computational advantages compared to the usually applied method of modal analysis based on eigenfunction expansions

efficient erasure correcting codes we introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete time random process as a result we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability by carefully designing these graphs we can construct for any given rate r and any given real number spl epsiv a family of linear codes of rate r which can be encoded in time proportional to ln 1 spl epsiv times their block length n furthermore a codeword can be recovered with high probability from a portion of its entries of length 1 spl epsiv rn or more the recovery algorithm also runs in time proportional to n ln 1 spl epsiv our algorithms have been implemented and work well in practice various implementation issues are discussed

a periodically forced piecewise linear oscillator a single degree of freedom non linear oscillator is considered the non linearity is in the restoring force and is piecewise linear with a single change in slope such oscillators provide models for mechanical systems in which components make intermittent contact a limiting case in which one slope approaches infinity an impact oscillator is also considered harmonic subharmonic and chaotic motions are found to exist and the bifurcations leading to them are analyzed

dynamic response of a constrained axially loaded beam a dynamic beam system loaded harmonically in the axial direction and constrained in the transverse direction is modelled using different theoretical descriptions results from an experimental set up are compared to calculations using bernoulli as well as timoshenko beam theories some results from investigations of this beam system unveiling its chaotic nature have earlier been presented but here the refining of timoshenko theory is done in order to get a better understanding of the influence of the impacts on the beam motion the free motion of the beam is described as a finite sum of modes while at impact an infinite number of modes is considered albeit approximately these ideas were also used for the bernoulli beam but modifications will be made here to account for the modal equations of fourth order in time for the timoshenko beam the investigation is complemented with new experiments

application of the transfer matrix method to non conservative systems involving fluid flow in curved pipes abstract the application of the transfer matrix method to problems of fluid flow in planar curved pipes is presented also a presentation is given of how to deal with the stability of non conservative problems when using the dynamic method in the method proposed account is taken of the effect of the initial state of stress on the dynamic behaviour of the pipe three well known problems are solved to verify the convergence and applicability of the transfer matrix formulation to non conservative problems involving fluid flow

hodge integrals and tau symmetric integrable hierarchies of hamiltonian evolutionary pdes for an arbitrary semisimple frobenius manifold we construct hodge integrable hierarchy of hamiltonian partial differential equations in the particular case of quantum cohomology the tau function of a solution to the hierarchy generates the intersection numbers of the gromov witten classes and their descendents along with the characteristic classes of hodge bundles on the moduli spaces of stable maps for the one dimensional frobenius manifold the hodge hierarchy is a deformation of the korteweg de vries hierarchy depending on an infinite number of parameters conjecturally this hierarchy is a universal object in the class of scalar hamiltonian integrable hierarchies possessing tau functions mathematics subject classication 2010 primary 53d45 secondary 37k10

new fluid velocity expression in an extensible semi circular pipe conveying fluid a new expression for fluid velocity is presented for a fluid conveying semi circular pipe with an extensible centreline the proposed fluid velocity expression is obtained from the material derivative while the previous velocity expressions are from love s kinematical relations in order to show that the new fluid velocity expression is more reasonable than the previous velocity expressions the equations of in plane motion derived with the new expression are compared to the equations derived with the previous expressions furthermore the equilibrium positions natural frequencies and mode shapes obtained with both the new and previous expressions are analysed and discussed

computation of open gromov witten invariants for toric calabi yau 3 folds by topological recursion a proof of the bkmp conjecture the bkmp conjecture 2006 2008 proposed a new method to compute closed and open gromov witten invariants for every toric calabi yau 3 folds through a topological recursion based on mirror symmetry so far this conjecture has been verified to low genus for several toric cy3folds and proved to all genus only for mathbb c 3 in this article we prove the general case our proof is based on the fact that both sides of the conjecture can be naturally written in terms of combinatorial sums of weighted graphs on the a model side this is the localization formula and on the b model side the graphs encode the recursive algorithm of the topological recursion

efficient encoding of low density parity check codes low density parity check ldpc codes can be considered serious competitors to turbo codes in terms of performance and complexity and they are based on a similar philosophy constrained random code ensembles and iterative decoding algorithms we consider the encoding problem for ldpc codes more generally we consider the encoding problem for codes specified by sparse parity check matrices we show how to exploit the sparseness of the parity check matrix to obtain efficient encoders for the 3 6 regular ldpc code for example the complexity of encoding is essentially quadratic in the block length however we show that the associated coefficient can be made quite small so that encoding codes even of length n spl sime 100000 is still quite practical more importantly we show that optimized codes actually admit linear time encoding

a hybrid approach for the modal analysis of continuous systems with discrete piecewise linear constraints abstract the analysis of continuous systems with piecewise linear constraints in their domains have previously been limited to either numerical approaches or analytical methods that are constrained in the parameter space boundary conditions or order of the system the present analysis develops a robust method for studying continuous systems with arbitrary boundary conditions and discrete piecewise linear constraints a superposition method is used to generate homogeneous boundary conditions and modal analysis is used to find the displacement of the system in each state of the piecewise linear constraint in order to develop a mapping across each slope discontinuity in the piecewise linear force deflection profile a variational calculus approach is taken that minimizes the l2 energy norm between the previous and current states an approach for calculating the finite time lyapunov exponents is presented in order to determine chaotic regimes to illustrate this method two examples are presented a pinned pinned beam with a deadband constraint and a leaf spring coupled with a connector pin immersed in a viscous fluid the pinned pinned beam example illustrates the method for a non operator based analysis results are used to show that the present method does not necessitate the need of a large number of basis functions to adequately map the displacement and velocity of the system across states in the second example the leaf spring is modeled as a clamped free beam the interaction between the beam and the connector pin is modeled with a preload and a penalty stiffness several experiments are conducted in order to validate aspects of the leaf spring model from the results of the convergence and parameter studies a high correlation between the finite time lyapunov exponents and the contact time per period of the excitation is observed the parameter studies also indicate that when the system s parameters are changed in order to reduce the magnitude of the impact velocity between the leaf spring and the connector pin the extent of the regions over which a chaotic response is observed increases

expander codes using expander graphs we construct a new family of asymptotically good linear error correcting codes these codes have linear time sequential decoding algorithms and logarithmic time parallel decoding algorithms that use a linear number of processors we present both randomized and explicit constructions of these codes experimental results demonstrate the good performance of the randomly chosen codes

joint unitary triangularization for gaussian multi user mimo networks the problem of transmitting a common message to multiple users over the gaussian multiple input multiple output broadcast channel is considered where each user is equipped with an arbitrary number of antennas a closed loop scenario is assumed for which a practical capacity approaching scheme is developed by applying judiciously chosen unitary operations at the transmit and receive nodes the channel matrices are triangularized so that the resulting matrices have equal diagonals up to a possible multiplicative scalar factor this along with the utilization of successive interference cancellation reduces the coding and decoding tasks to those of coding and decoding over the single antenna additive white gaussian noise channel over the resulting effective channel any off the shelf code may be used for the two user case it was recently shown that such joint unitary triangularization is always possible in this paper it is shown that for more than two users it is necessary to carry out the unitary linear processing jointly over multiple channel uses i e space time processing is employed it is further shown that exact triangularization where all resulting diagonals are equal is still not always possible and appropriate conditions for the existence of such are established for certain cases when exact triangularization is not possible an asymptotic construction is proposed that achieves the desired property of equal diagonals up to edge effects that can be made arbitrarily small at the price of processing a sufficiently large number of channel uses together

analysis of sum product decoding of low density parity check codes using a gaussian approximation density evolution is an algorithm for computing the capacity of low density parity check ldpc codes under message passing decoding for memoryless binary input continuous output additive white gaussian noise awgn channels and sum product decoders we use a gaussian approximation for message densities under density evolution to simplify the analysis of the decoding algorithm we convert the infinite dimensional problem of iteratively calculating message densities which is needed to find the exact threshold to a one dimensional problem of updating the means of the gaussian densities this simplification not only allows us to calculate the threshold quickly and to understand the behavior of the decoder better but also makes it easier to design good irregular ldpc codes for awgn channels for various regular ldpc codes we have examined thresholds can be estimated within 0 1 db of the exact value for rates between 0 5 and 0 9 codes designed using the gaussian approximation perform within 0 02 db of the best performing codes found so far by using density evolution when the maximum variable degree is 10 we show that by using the gaussian approximation we can visualize the sum product decoding algorithm we also show that the optimization of degree distributions can be understood and done graphically using the visualization

raptor codes on binary memoryless symmetric channels in this paper we will investigate the performance of raptor codes on arbitrary binary input memoryless symmetric channels bimscs in doing so we generalize some of the results that were proved before for the erasure channel we will generalize the stability condition to the class of raptor codes this generalization gives a lower bound on the fraction of output nodes of degree 2 of a raptor code if the error probability of the belief propagation decoder converges to zero using information theoretic arguments we will show that if a sequence of output degree distributions is to achieve the capacity of the underlying channel then the fraction of nodes of degree 2 in these degree distributions has to converge to a certain quantity depending on the channel for the class of erasure channels this quantity is independent of the erasure probability of the channel but for many other classes of bimscs this fraction depends on the particular channel chosen this result has implications on the universality of raptor codes for classes other than the class of erasure channels in a sense that will be made more precise in the paper we will also investigate the performance of specific raptor codes which are optimized using a more exact version of the gaussian approximation technique

nonlinear vibration analysis of axially moving strings based on gyroscopic modes decoupling abstract a novel idea that applies the multiple scale analysis to a discretized decoupled system of gyroscopic continua is introduced and an axial moving string is treated as an example first the invariant manifold method is applied to the discretized ordinary differential equations of the axially moving string complex gyroscopic mode functions that agree well with true analytical results are obtained the gyroscopic modes are subsequently used for the discretized ordinary differential equations with gyroscopic and nonlinear coupling terms that yield a gyroscopically decoupled system further the method of multiple scales is used to obtain the equations at a slow scale this novel procedure is compared to solutions obtained by directly applying the classical multiple scale analysis to the gyroscopically coupled system without decoupling the modal decoupled system analysis yields better frequency with comparing to the classic method the proposed methodology provides a novel alternative for nonlinear dynamic analysis of gyroscopic continua

hodge gue correspondence and the discrete kdv equation we prove the conjectural relationship recently proposed in dubrovin and yang commun number theory phys 11 311 336 2017 between certain special cubic hodge integrals of the gopakumar marino vafa type gopakumar and vafa in adv theor math phys 5 1415 1443 1999 marino and vafa in contemp math 310 185 204 2002 and gue correlators and the conjecture proposed in dubrovin et al adv math 293 382 435 2016 that the partition function of these hodge integrals is a tau function of the discrete kdv hierarchy

rateless lossy compression via the extremes we begin by presenting a simple lossy compressor operating at near zero rate the encoder merely describes the indices of the few maximal source components while the decoder s reconstruction is a natural estimate of the source components based on this information this scheme turns out to be near optimal for the memoryless gaussian source in the sense of achieving the zero rate slope of its distortion rate function motivated by this finding we then propose a scheme comprised of iterating the above lossy compressor on an appropriately transformed version of the difference between the source and its reconstruction from the previous iteration the proposed scheme achieves the rate distortion function of the gaussian memoryless source under squared error distortion when employed on any finite variance ergodic source it further possesses desirable properties and we respectively refer to as infinitesimal successive refinability ratelessness and complete separability its storage and computation requirements are of order no more than n 2 log beta n per source symbol for beta 0 at both the encoder and the decoder though the details of its derivation construction and analysis differ considerably we discuss similarities between the proposed scheme and the recently introduced sparse regression codes of venkataramanan et al

remodeling the b model we propose a complete new formalism to compute unambiguously b model open and closed amplitudes in local calabi yau geometries including the mirrors of toric manifolds the formalism is based on the recursive solution of matrix models recently proposed by eynard and orantin the resulting amplitudes are non perturbative in both the closed and the open moduli the formalism can then be used to study stringy phase transitions in the open closed moduli space at large radius this formalism may be seen as a mirror formalism to the topological vertex but it is also valid in other phases in the moduli space we develop the formalism in general and provide an extensive number of checks including a test at the orbifold point of ap fibrations where the amplitudes compute the t hooft expansion of vevs of wilson loops in chern simons theory on lens spaces we also use our formalism to predict the disk amplitude for the orbifold mathbb c 3 mathbb z 3

the vibration and stability of a friction guided translating string abstract eyelets capstans and cylindrical surfaces are often used in thread fiber and paper handling machinery to guide the axially moving element in addition to providing positional control these guides introduce dry friction forces that alter the vibration and stability characteristics of the system this paper examines the lateral response of a string that slides through an elastically supported dry friction guide exact expressions are derived for the linear response under free and forced conditions solutions for the eigenvalue spectrum exhibit unusual features including multiple divergence instabilities regions of flutter instability and regions of curve veering associated with mode localization a second order perturbation solution is derived to examine the behavior of the eigenvalue spectrum in regions of flutter instability and curve veering the analysis highlights the common features of these two phenomena and suggests ways to minimize vibration by adjusting various design variables the analysis also demonstrates that the eigenvalue loci in regions of flutter instability and curve veering are naturally described by a local hyperbolic approximation

the mapping dynamics of periodic motions for a three piecewise linear system under a periodic excitation in this paper the mapping dynamics of periodic motions for a three piecewise linear system under a periodic excitation is developed and the mapping structures for specified periodic motions are constructed based on the mapping structures an analytical prediction of all possible stable and unstable periodic motions is given the symmetry for the stable asymmetrical periodic motions of such a system is observed however the unstable periodic motions do not have such symmetry the methodology presented in this paper is applicable to other non smooth systems such as friction induced vibration impact oscillator and power control systems in addition the mapping dynamics provides a useful and efficient tool for the co existence of periodic motions and or chaotic motions in nonlinear dynamical systems

large amplitude non linear normal modes of piecewise linear systems a numerical method for constructing non linear normal modes nnms for piecewise linear autonomous systems is presented these nnms are based on the concept of invariant manifolds and are obtained using a galerkin based solution of the invariant manifold s non linear partial differential equations the accuracy of the constructed non linear modes is checked by the comparison of the motion on the invariant manifold to the exact solution in both time and frequency domains it is found that this construction approach can accurately capture the nnms over a wide range of amplitudes including those with strong non linear effects several interesting dynamic characteristics of the non linear modal motion are found and compared to those of linear modes a two degree of freedom example is used to illustrate the technique the existence stability and bifurcations of the nnms for this example are investigated

optimization design and asymptotic analysis of systematic luby transform codes over biawgn channels in this paper we study systematic luby transform slt codes over binary input additive white gaussian noise biawgn channels to improve the bit error rate ber performance of slt codes on the biawgn channel this paper presents a novel optimization design of degree distributions first we apply the gaussian approximation ga to analyze the asymptotic ber performance of slt codes and calculate overhead thresholds for successful decoding second we derive an approximate closed form expression for lower bound on ber by applying the ga and further simplify the expression in low and high signal to noise ratio regimes respectively third we adopt the conventional linear programming clp constrained by the ga to optimize the degree distribution of slt codes the objective of clp is to minimize the average degree of the degree distribution that may result in bad error floor to improve the error floor caused by clp we put forth a novel optimization model constrained by the lower bound on ber and using the model we can design the degree distribution more flexibly with any desired ber simulation results show that the proposed degree distribution can provide better ber performance of slt codes over the biawgn channel

topological open strings on orbifolds we use the remodeling approach to the b model topological string in terms of recursion relations to study open string amplitudes at orbifold points to this end we clarify modular properties of the open amplitudes and rewrite them in a form that makes their transformation properties under the modular group manifest we exemplify this procedure for the mathbb c 3 mathbb z 3 orbifold point of local mathbb p 2 where we present results for topological string amplitudes for genus zero and up to three holes and for the one holed torus these amplitudes can be understood as generating functions for either open orbifold gromov witten invariants of mathbb c 3 mathbb z 3 or correlation functions in the orbifold cft involving insertions of both bulk and boundary operators

intersection theory on the moduli space of curves and the matrix airy function we show that two natural approaches to quantum gravity coincide this identity is nontrivial and relies on the equivalence of each approach to kdv equations we also investigate related mathematical problems

the topological vertex we construct a cubic field theory which provides all genus amplitudes of the topological a model for all non compact toric calabi yau threefolds the topology of a given feynman diagram encodes the topology of a fixed calabi yau with schwinger parameters playing the role of kahler classes of the threefold we interpret this result as an operatorial computation of the amplitudes in the b model mirror which is the quantum kodaira spencer theory the only degree of freedom of this theory is an unconventional chiral scalar on a riemann surface in this setup we identify the b branes on the mirror riemann surface as fermions related to the chiral boson by bosonization

in plane and out of plane motions of an extensible semi circular pipe conveying fluid abstract in plane and out of plane motions of a semi circular pipe conveying fluid are analyzed in this paper assuming that the centerline of the semi circular pipe is extensible nonlinear equations of in plane and out of plane motions are derived according to the extended hamilton principle the lagrange nonlinear strain theory and the euler bernoulli beam theory are used to derive the equations the derived equations of motion are discretized by applying the galerkin method linearized equations around the equilibrium position are obtained from the discretized equations and then the dynamic characteristics of the pipe are investigated in addition some modelling issues which are related to the nonlinearity of the circumferential strain and stress are discussed this study finds that a semi circular pipe conveying fluid does not lose stability even at a high fluid velocity although a model using the lagrange nonlinear strain and the corresponding nonlinear stress yields the most accurate computational results of the natural frequencies a model using the lagrange strain and a linearized stress is recommended to compute the natural frequencies efficiently while still maintaining accuracy

on the energy delay tradeoff in streaming data finite blocklength analysis this paper investigates basic trade offs between energy and delay in wireless communication systems using finite blocklength theory we first assume that data arrive in constant stream of bits which are put into packets and transmitted over a communications link our results show that depending on exactly how energy is measured in general energy depends on sqrt d 1 or sqrt d 1 log d where d is the delay this means that the energy decreases quite slowly with increasing delay furthermore to approach the absolute minimum of 1 59 db on energy bandwidth has to increase very rapidly much more than what is predicted by infinite blocklength theory we then consider the scenario when data arrive stochastically in packets and can be queued we devise a scheduling algorithm based on finite blocklength theory and develop bounds for the energy delay performance our results again show that the energy decreases quite slowly with increasing delay

non linear real and complex modes of conewise linear systems abstract conewise piecewise linear non gyroscopic and gyroscopic autonomous systems are studied in detail first the general properties of such systems are examined then the non linear real and complex modes are obtained for both non gyroscopic and gyroscopic cases by means of analytical or numerical tools several interesting characteristics of non linear modes are found and compared to those of linear modes accurate analytical estimates of non linear mode periods are formulated for both non gyroscopic and gyroscopic systems the validity of such estimates is discussed in relation to a non linear mode bifurcation phenomenon which is located by using both characteristic multipliers and poincare mapping

new non linear modelling for vibration analysis of a straight pipe conveying fluid abstract a new non linear model of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends using the euler bernoulli beam theory and the non linear lagrange strain theory from the extended hamilton s principle the coupled non linear equations of motion for the longitudinal and transverse displacements are derived these equations of motion are discretized by using the galerkin method after the discretized equations are linearized in the neighbourhood of the equilibrium position the natural frequencies are computed from the linearized equations on the other hand the time histories for the displacements are also obtained by applying the generalized time integration method to the non linear discretized equations the validity of the new modelling is provided by comparing results from the proposed non linear equations with those from the equations proposed by paidoussis

rateless codes for avc models the arbitrarily varying channel avc is a channel model whose state is selected maliciously by an adversary fixed blocklength coding assumes a worst case bound on the adversary s capabilities which leads to pessimistic results this paper defines a variable length perspective on this problem for which achievable rates are shown that depend on the realized actions of the adversary specifically rateless codes are constructed which require a limited amount of common randomness these codes are constructed for two kinds of avc models in the first the channel state cannot depend on the channel input and in the second it can as a by product the randomized coding capacity of the avc with state depending on the transmitted codeword is found and shown to be achievable with a small amount of common randomness the results for this model are proved using a randomized strategy based on list decoding

a more accurate one dimensional analysis and design of irregular ldpc codes we introduce a new one dimensional 1 d analysis of low density parity check ldpc codes on additive white gaussian noise channels which is significantly more accurate than similar 1 d methods our method assumes a gaussian distribution in message passing decoding only for messages from variable nodes to check nodes compared to existing work which makes a gaussian assumption both for messages from check nodes and from variable nodes our method offers a significantly more accurate estimate of convergence behavior and threshold of convergence similar to previous work the problem of designing irregular ldpc codes reduces to a linear programming problem however our method allows irregular code design in a wider range of rates without any limit on the maximum variable node degree we use our method to design irregular ldpc codes with rates greater than 1 4 that perform within a few hundredths of a decibel from the shannon limit the designed codes perform almost as well as codes designed by density evolution

linear time encodable and decodable error correcting codes we present a new class of asymptotically good linear error correcting codes these codes can be both encoded and decoded in linear time they can also be encoded by logarithmic depth circuits of linear size and decoded by logarithmic depth circuits of size o nlogn we present both randomized and explicit constructions of these codes

raptor codes in the low snr regime in this paper we revisit the design of raptor codes for binary input additive white gaussian noise channels where we are interested in very low signal to noise ratios snrs a linear programming degree distribution optimization problem is defined for raptor codes in the low snr regime through several approximations we also provide an exact expression for the polynomial representation of the degree distribution with infinite maximum output node degree in the low snr regime which enables us to calculate the exact value of the fractions of output nodes of small degrees a more practical degree distribution design is also proposed for raptor codes in the low snr regime where we include the rate efficiency and the decoding complexity in the optimization problem and an upper bound on the maximum rate efficiency is derived for given design parameters simulation results show that the raptor code with the designed degree distributions can approach rate efficiencies larger than 0 95 in the low snr regime

clearance effects on bilinear normal mode frequencies abstract the effects of a clearance or interference on the normal mode frequencies of a n dof system with bilinear stiffness and without damping are investigated through various modifications of the bilinear frequency relation first the exact penetration distances and bilinear natural frequencies of a single degree of freedom system are analytically obtained in terms of the amount of clearance and the strength of non linearity and an equivalent linear system is derived these results are in turn used to construct three methods which approximate the bilinear frequencies for the n dof system the specific example of a two dof system is studied in which the resulting approximate frequencies are compared with those obtained from numerical simulations in order to determine the most accurate approximation technique the results demonstrate how these bilinear normal mode frequencies vary with the magnitude of the clearance interference and thus point toward the need of including such effects in methods which utilize the bilinear frequency relation

a proof of a conjecture of marino vafa on hodge integrals where i c1 li is the first chern class of li and j cj e is the j th chern class of the hodge bundle hodge integrals arise in the calculations of gromov witten invariants by localization techniques 14 7 the explicit evaluation of hodge integrals is a difficult problem the hodge integrals involving only classes can be computed recursively by witten s conjecture 26 proven by kontsevich 13 algorithms of computing hodge integrals are described in 2 in 23 m marino and c vafa obtained a closed formula for a generating function of certain open gromov witten invariants some of which has been reduced to hodge integrals by localization techniques which are not fully clarified mathematically this leads to a conjectural formula of hodge integrals to state this formula we introduce some notation following 28 let

modal analysis of a continuous gyroscopic second order system with nonlinear constraints abstract a method for the modal analysis of continuous gyroscopic systems with nonlinear constraints is developed this method assumes that the nonlinear constraint can be expressed as a piecewise linear force deflection profile located at an arbitrary position within the domain using this assumption the mode shapes and natural frequencies are first found for each state then a mapping method based on the inner product of the mode shapes is developed to map the displacement of the system between the in contact and out of contact states to illustrate this method a model for the vibration of a traveling string in contact with a piecewise linear constraint is developed as an analog of the interaction between magnetic tape and a guide in data storage systems five design parameters of the guide are considered flange clearance flange stiffness symmetry of the force deflection profile in terms of flange stiffness and offset and the guide s position along the length of the string there are critical bifurcation thresholds below which the system exhibits no chaotic behavior and is dominated by period one symmetric behavior and above which the system contains asymmetric higher periodic motion with windows of chaotic behavior these bifurcation thresholds are particularly pronounced for the transport speed flange clearance symmetry of the force deflection profile and guide position the stability of the system is sensitive to the system s velocity and compared to stationary systems more mode shapes are needed to accurately model the dynamics of the system

steady state forced response of a mechanical oscillator with combined parametric excitation and clearance type non linearity a mechanical system exhibiting combined parametric excitation and clearance type non linearity is examined analytically and experimentally in an effort to explain complex behavior that is commonly observed in the steady state forced response of rotating machines the specific case of a preloaded mechanical oscillator having a periodically time varying stiffness function and subject to a symmetric backlash condition is considered a generalized solution methodology is proposed based on the harmonic balance method the resulting non linear algebraic equations are solved by using a direct newton raphson technique in which a closed form jacobian matrix is computed using frequency domain methods analytical solutions are validated by comparison with numerical integration results and experimental measurements obtained from a gear dynamics test rig

simple maps hurwitz numbers and topological recursion we introduce the notion of fully simple maps which are maps with non self intersecting disjoint boundaries in contrast maps where such a restriction is not imposed are called ordinary we study in detail the combinatorics of fully simple maps with topology of a disk or a cylinder we show that the generating series of simple disks is given by the functional inversion of the generating series of ordinary disks we also obtain an elegant formula for cylinders these relations reproduce the relation between moments and higher order free cumulants established by collins et al 22 and implement the symplectic transformation x leftrightarrow y on the spectral curve in the context of topological recursion we conjecture that the generating series of fully simple maps are computed by the topological recursion after exchange of x and y we propose an argument to prove this statement conditionally to a mild version of the symplectic invariance for the 1 hermitian matrix model which is believed to be true but has not been proved yet our conjecture can be considered as a combinatorial interpretation of the property of symplectic invariance of the topological recursion our argument relies on an unconditional matrix model interpretation of fully simple maps via the formal hermitian matrix model with external field we also deduce a universal relation between generating series of fully simple maps and of ordinary maps which involves double monotone hurwitz numbers in particular ordinary maps without internal faces which are generated by the gaussian unitary ensemble and with boundary perimeters lambda 1 ldots lambda n are strictly monotone double hurwitz numbers with ramifications lambda above infty and 2 ldots 2 above 0 combining with a recent result of dubrovin et al 24 this implies an elsv like formula for these hurwitz numbers

dynamical behaviors of a fluid conveying curved pipe subjected to motion constraints and harmonic excitation this paper investigates the nonlinear dynamics of a fluid conveying curved pipe subjected to motion constraints and harmonic excitation at first the background theory for curved pipes conveying fluid with motion constraints is presented then emphasis is placed on the possible nonlinear dynamic behaviors of a constrained curved pipe subject to a harmonic excitation for such a forced dynamical system calculations of bifurcation diagrams phase plane portraits time responses power spectrum diagrams and poincare maps of the oscillations clearly establish the existence of the chaotic motions and quasi periodic motions moreover it is found that the route to chaos is through a sequence of period doubling bifurcations finally the difference in the nonlinear dynamics between the self vibration system and forced system is further discussed

cross flow induced chaotic vibrations of heat exchanger tubes impacting on loose supports abstract the chaotic dynamics of heat exchanger tubes impacting on the generally loose baffle plates is studied using an analytic model that involves delay differential equations the critical flow velocity for the local instability of the flexible cylinder near the static equilibrium position is obtained by assuming a harmonic solution in the discretized linearized model and solving the resulting algebraic equations numerical solutions show that with increasing flow beyond the critical the amplitude of motion grows until impacting with the loose support occurs more complex motions then arise leading to chaos for a sufficiently high flow velocity a lyapunov exponent technique is developed for delay differential equations and is applied to the present model showing definitely and unequivocally for the first time for this system that chaotic motions do occur to understand the system behaviour better a one degree of freedom forced negatively damped impact oscillator is studied the response is quite complex and results in chaos in certain parameter regions the analysis is performed by finding periodic solutions and determining their stability and bifurcations with the poincare map technique

non linear forced vibrations of plates by an asymptotic numerical method abstract non linear forced vibrations of thin elastic plates have been investigated by an asymptotic numerical method anm various types of harmonic excitation forces such as distributed and concentrated are considered using the harmonic balance method and hamilton s principle the equation of motion is converted into an operational formulation based on the finite element method a starting point corresponding to a non linear solution associated to a given frequency and amplitude of excitation is computed applying perturbation techniques in the vicinity of this solution the non linear governing equation obtained is transformed into a sequence of linear problems having the same stiffness matrix employing one matrix inversion a large number of terms of the perturbation series of the displacement and frequency can be easily computed with a small computation time iterations of this method lead to a powerful path following technique comprehensive numerical tests for forced vibrations of plates subjected to time harmonic lateral excitations are reported

an asymptotic numerical method for large amplitude free vibrations of thin elastic plates abstract an asymptotic numerical method has been developed for large amplitude free vibrations of thin elastic plates it is based on the perturbation method and the finite element method this method eliminates the major difficulties of the classical perturbation methods namely the complexity of the right hand sides and the limitation of the validity of the solution obtained the applicability of this method to non linear vibrations of plates is clearly presented based on the von karman theory and the harmonic balance method a cubic non linear operational formulation has been obtained by using the mixed stress displacement hellinger reissner principle a quadratic formulation is given the displacement and frequency are expanded into power series with respect to a control parameter the non linear governing equation is then transformed into a sequence of linear problems having the same stiffness matrix which can be solved by a classical fem needing one matrix inversion a large number of terms of the series can be easily computed with a small computation time the non linear mode and frequency are then obtained up to the radius of convergence taking the starting point in the zone of validity the method is reapplied in order to determine a further part of the non linear solution iteration of this method leads to a powerful incremental method in order to increase the validity of the perturbed solution another technique called pade approximants is shrewdly incorporated the solutions obtained by these two concepts coincide perfectly in a very large part of the backbone curve comprehensive numerical tests for non linear free vibrations of circular square rectangular and annular plates with various boundary conditions are reported and discussed

periodic solutions of a multi dof beam system with impact the steady state behaviour is analyzed of a periodically driven multi dof beam system which has an elastic stop at its middle the elastic stop is modelled in a continuous way by using the contact law of hertz the beam is modelled by using finite elements and subsequently reduced by using a component mode synthesis method the steady state behaviour of the system reduced to one two and four dof s is investigated by calculating periodic solutions at varying excitation frequency periodic solutions are calculated by solving two point boundary value problems by the multiple shooting method in combination with a path following technique it is shown that models with more than one dof are required for a good assessment of the long term behaviour of the system

definition and properties of lagrangian coherent structures from finite time lyapunov exponents in two dimensional aperiodic flows this paper develops the theory and computation of lagrangian coherent structures lcs which are defined as ridges of finite time lyapunov exponent ftle fields these ridges can be seen as finite time mixing templates such a framework is common in dynamical systems theory for autonomous and time periodic systems in which examples of lcs are stable and unstable manifolds of fixed points and periodic orbits the concepts defined in this paper remain applicable to flows with arbitrary time dependence and in particular to flows that are only defined computed or measured over a finite interval of time previous work has demonstrated the usefulness of ftle fields and the associated lcss for revealing the lagrangian behavior of systems with general time dependence however ridges of the ftle field need not be exactly advected with the flow the main result of this paper is an estimate for the flux across an lcs which shows that the flux is small and in most cases negligible for well defined lcss or those that rotate at a speed comparable to the local eulerian velocity field and are computed from ftle fields with a sufficiently long integration time under these hypotheses the structures represent nearly invariant manifolds even in systems with arbitrary time dependence the results are illustrated on three examples the first is a simplified dynamical model of a double gyre flow the second is surface current data collected by high frequency radar stations along the coast of florida and the third is unsteady separation over an airfoil in all cases the existence of lcss governs the transport and it is verified numerically that the flux of particles through these distinguished lines is indeed negligible

virasoro symmetries of the extended toda hierarchy we prove that the extended toda hierarchy of 1 admits a nonabelian lie algebra of infinitesimal symmetries isomorphic to half of the virasoro algebra the generators lm m 1 of the lie algebra act by linear differential operators onto the tau function of the hierarchy we also prove that the tau function of a generic solution to the extended toda hierarchy is annihilated by a combination of the virasoro operators and the flows of the hierarchy as an application we show that the validity of the virasoro constraints for the cp1 gromov witten invariants and their descendents implies that their generating function is the logarithm of a particular tau function of the extended toda hierarchy

dynamic stability of a semi circular pipe conveying harmonically oscillating fluid the dynamic stability of a semi circular pipe conveying harmonically oscillating fluid is investigated in this study for analysis harmonically oscillating flow is regarded as a parametrically excited system with time varying coefficients considering the extensibility and nonlinearity of the semi circular pipe the equations of motion and the associated boundary conditions are obtained by using the extended hamilton principle applying floquet theory to the derived equations the stability of the pipe is analyzed for variations of the amplitude and oscillating frequency of the fluid velocity the effects of the mean value for the fluid velocity on the stability are also analyzed it is found that the semi circular pipe may become unstable when the fluctuation frequency approaches some multiples or sum of the out of plane natural frequencies furthermore it is observed that the instability regions increase with the mean value of the velocity the results obtained via the stability analysis are verified by time responses computed by using a direct time integration method

application of non smooth modelling techniques to the dynamics of a flexible impacting beam non smooth modelling techniques have been successfully applied to lumped mass type structures for modelling phenomena such as vibro impact and friction oscillators in this paper the application of these techniques to continuous elements using the example of a cantilever beam is considered employing a galerkin reduction to form an n degree of freedom modal model a technique for modelling impact phenomena using a non smooth dynamics approach is demonstrated numerical simulations computed using the non smooth model are compared with experimentally recorded data for a flexible beam constrained to impact on one side a method for dealing with sticking motions when numerically simulating the beam motion is presented in addition choosing the dimension of the model based on power spectra of experimentally recorded time series is discussed

the euler characteristic of the moduli space of curves let fg 1 g 1 be the mapping class group consisting of all isotopy classes of base point and orientation preserving homeomorphisms of a closed oriented surface f of genus g let 1 be its euler characteristic in the sense of wall that is z f i fgl f l z e f where f is any torsion free subgroup of finite index in f 1 and e is a contractible space on which f acts freely and properly discontinuously an example of such a space is the teichmiiller space 1 and g f can be interpreted as the orbifold euler characteristic of f i join the moduli space of curves of genus g with base point the purpose of this paper is to prove the following formula for f i

modelling localized nonlinearities in continuous systems via the method of augmentation by non smooth basis functions existing solutions for continuous systems with localized non smooth nonlinearities such as impacts focus on exact methods for satisfying the nonlinear constitutive equations exact methods often

a formula of two partition hodge integrals jmg n where tpi ci l is the first chern class of l and xj cj e is the j th chern class of the hodge bundle the study of hodge integrals is an important part of intersection theory on mg n hodge integrals also naturally arise when one computes gromov witten invariants by localization techniques for example the following generating series of hodge integrals arises when one computes local invariants of a toric fano surface in a calabi yau 3 fold by virtual localization 33

rateless coding for gaussian channels a rateless code i e a rate compatible family of codes has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones a perfect family of such codes is one in which each of the codes in the family is capacity achieving we show by construction that perfect rateless codes with low complexity decoding algorithms exist for additive white gaussian noise channels our construction involves the use of layered encoding and successive decoding together with repetition using time varying layer weights as an illustration of our framework we design a practical three rate code family we further construct rich sets of near perfect rateless codes within our architecture that require either significantly fewer layers or lower complexity than their perfect counterparts variations of the basic construction are also developed including one for time varying channels in which there is no a priori stochastic model

nonlinear model reduction of von karman plates under quasi steady fluid flow a reduced order model for von karman plates using a method of quadratic components is presented in this paper the method of quadratic components postulates the full kinematics of the plate as consisting of a combination of linear and quadratic components this reduced model is then discretized in space with a galerkin approximation and in time with an implicit integration scheme the plate is coupled with a fluid flowing over it at a supersonic speed using a quasi steady pressure model commonly referred to as piston theory a static loading example is used to validate the model reduction of the plate with respect to other numerical and approximate solutions the limit cycles of the plate coupled with piston theory are calculated via a cyclic method and the results from parameter studies are compared to classical results a previously unexplored regime of the limit cycle amplitudes is investigated a second coexisting limit cycle is found that yields a discontinuity in the limit cycle amplitudes at a critical dynamic pressure

improved low density parity check codes using irregular graphs we construct new families of error correcting codes based on gallager s 1973 low density parity check codes we improve on gallager s results by introducing irregular parity check matrices and a new rigorous analysis of hard decision decoding of these codes we also provide efficient methods for finding good irregular structures for such decoding algorithms our rigorous analysis based on martingales our methodology for constructing good irregular codes and the demonstration that irregular structure improves performance constitute key points of our contribution we also consider irregular codes under belief propagation we report the results of experiments testing the efficacy of irregular codes on both binary symmetric and gaussian channels for example using belief propagation for rate 1 4 codes on 16000 bits over a binary symmetric channel previous low density parity check codes can correct up to approximately 16 errors while our codes correct over 17 in some cases our results come very close to reported results for turbo codes suggesting that variations of irregular low density parity check codes may be able to match or beat turbo code performance