probabilistic metrization of fuzzy uniformities abstract modifying the structure of fuzzy uniform spaces introduced by lowen 5 we propose a further concept of fuzzy uniformities so called fuzzy t

stability of elastic rods with self contact abstract in this paper we study the numerical stability of equilibrium configurations of an elastic rod with unilateral frictionless self contact we use a finite element method with penalty and augmented lagrangian approaches to account for the self penetration constraint the numerical solution is carried out using the arclength continuation method in the case where the energy expression satisfies some hypotheses we have proved that any isolated minimum of the continuous self contact problem is the strong limit of a sequence of local minima of the discrete problem our stability analysis is based on detecting the zeros of the determinant of a symmetrized version of the stiffness matrix and whether there is a sign change of the determinant or not

on the minimum ropelength of knots and links the ropelength of a knot is the quotient of its length by its thickness the radius of the largest embedded normal tube around the knot we prove existence and regularity for ropelength minimizers in any knot or link type these are c 1 1 curves but need not be smoother we improve the lower bound for the ropelength of a nontrivial knot and establish new ropelength bounds for small knots and links including some which are sharp

a hybrid simplex search and particle swarm optimization for unconstrained optimization this paper proposes the hybrid nm pso algorithm based on the nelder mead nm simplex search method and particle swarm optimization pso for unconstrained optimization nm pso is very easy to implement in practice since it does not require gradient computation the modification of both the nelder mead simplex search method and particle swarm optimization intends to produce faster and more accurate convergence the main purpose of the paper is to demonstrate how the standard particle swarm optimizers can be improved by incorporating a hybridization strategy in a suite of 20 test function problems taken from the literature computational results via a comprehensive experimental study preceded by the investigation of parameter selection show that the hybrid nm pso approach outperforms other three relevant search techniques i e the original nm simplex search method the original pso and the guaranteed convergence particle swarm optimization gcpso in terms of solution quality and convergence rate in a later part of the comparative experiment the nm pso algorithm is compared to various most up to date cooperative pso cpso procedures appearing in the literature the comparison report still largely favors the nm pso algorithm in the performance of accuracy robustness and function evaluation as evidenced by the overall assessment based on two kinds of computational experience the new algorithm has demonstrated to be extremely effective and efficient at locating best practice optimal solutions for unconstrained optimization

path integral calculation of the writhe for circular semiflexible polymers earlier obtained numerical and analytical non path integral results for the writhe of a circular polymer are reproduced exactly employing the available path integral models for the semiflexible chains it is confirmed analytically that the average writhe scales with the root of the chain length we also briefly discuss related topological problems e g knotting of circular polymers which could be formulated and solved with the use of path integrals

an insertion theorem for continuous valued functions and its consequences spaces in which open sets take values in the l interval i l are investigated we prove a theorem concerning the insertion of a continuous function with values in i l with l a complete lattice we establish certain factorizations of the functors i l and i l with l a hypercontinuous lattice the latter result and the insertion theorem provide a partial answer to a recent open question related to insertion of lattice valued functions as another application of the insertion theorem we establish a relation between complete regularity in the categories of l topological and i l topological spaces with l a frame

the direct link model for polymer rings using topological field theory and the second topological moment in dense systems polymer rings in solution are either permanently entangled or are not permanent topological restrictions give rise to additional entropic interactions apart from the ones arising due to mere chain flexibility or excluded volume conversely entangled polymer rings systems may be formed by closing randomly entangled flexible linear chains the dependence of linking numbers between randomly entangled rings on the chain length more specifically the second topological moment n2 i e the average squared linking number may be determined in this paper an approach recently discussed in mathematical physics and called abelian bf theory is presented which allows one to express the linking constraint in its simplest form the gauss integral in terms of two gauge fields the model of brereton and shah for a single ring entangled with many other surrounding rings is rederived the latter model is finally used to calculate the second topological moment in agreement with a recent result by ferrari kleinert and lazzizzera obtained using n component 4 theory for the limit n 0

a piecewise linear chaotic map and sequential quadratic programming based robust hybrid particle swarm optimization this paper presents a novel robust hybrid particle swarm optimization rhpso based on piecewise linear chaotic map pwlcm and sequential quadratic programming sqp the aim of the present research is to develop a new single objective optimization approach which requires no adjustment of its parameters for both unconstrained and constrained optimization problems this novel algorithm makes the best of ergodicity of pwlcm to help pso with the global search while employing the sqp to accelerate the local search five unconstrained benchmarks eighteen constrained benchmarks and three engineering optimization problems from the literature are solved by using the proposed hybrid approach the simulation results compared with other state of art methods demonstrate the effectiveness and robustness of the proposed rhpso for both unconstrained and constrained problems of different dimensions

self contact for rods on cylinders we study self contact phenomena in elastic rods that are constrained to lie on a cylinder by choosing a particular set of variables to describe the rod centerline the variational setting is made particularly simple the strain energy is a second order functional of a single scalar variable and the self contact constraint is written as an integral inequality using techniques from ordinary differential equation theory comparison principles and variational calculus cut and paste arguments we fully characterize the structure of constrained minimizers an important auxiliary result states that the set of self contact points is continuous a result that contrasts with known examples from contact problems in free rods

the static deformation of a twisted elastic rod constrained to lie on a cylinder the cosserat director theory is used to formulate the problem of a long thin weightless rod constrained by suitable distributed forces to lie on a cylinder while being held by end tension and twisting moment applications of this problem are found for instance in the buckling of drill strings inside a cylindrical hole in the case of a rod of isotropic cross section the equilibrium equations can be reduced to those of a one degree of freedom oscillator in terms of the angle that the local tangent to the rod makes with the axis of the cylinder depending on the radius of the cylinder and the applied load the oscillator has several fixed points each of which corresponds to a different helical solution of the rod more complicated shapes are also possible and special attention is given to localized configurations described by homoclinic orbits of the oscillator heteroclinic saddle connections are found to play an important role in the post buckling behaviour by defining critical loads at which a straight rod may coil up into a helix

automatic classification of protein structure by using gauss integrals we introduce a method of looking at analyzing and comparing protein structures the topology of a protein is captured by 30 numbers inspired by vassiliev knot invariants to illustrate the simplicity and power of this topological approach we construct a measure scaled gauss metric sgm of similarity of protein shapes under this metric protein chains naturally separate into fold clusters we use sgm to construct an automatic classification procedure for the cath2 4 database the method is very fast because it requires neither alignment of the chains nor any chain chain comparison it also has only one adjustable parameter we assign 95 51 of the chains into the proper c class a architecture t topology and h homologous superfamily fold find all new folds and detect no false geometric positives using the sgm we display a map of the space of folds projected onto two dimensions show the relative locations of the major structural classes and zoom into the space of proteins to show architecture topology and fold clusters the existence of a simple measure of a protein fold computed from the chain path will have a major impact on automatic fold classification

improving particle swarm optimization using multi layer searching strategy abstract in recent years particle swarm optimization pso algorithm has been used to solve global optimization problems this algorithm is widely used as an effective optimization tool in various applications however traditional pso consists of only two searching layers and thus often results in premature convergence into the local minima thus multi layer particle swarm optimization mlpso is proposed in this paper to improve the performance of traditional pso by increasing the two layers of swarms to multiple layers the mlpso strategy increases the diversity of searching swarms to improve its performance when solving complex problems the experiment indicates that the novel approach improves the final results and the convergence speed

elastic stability of dna configurations i general theory results are presented in the theory of the elastic rod model for dna among which are criteria enabling one to determine whether a calculated equilibrium configuration of a dna segment is stable in the sense that it gives a local minimum to the sum of the segment s elastic energy and the potential of forces acting on it the derived stability criteria are applicable to plasmids and to linear segments subject to strong anchoring end conditions their utility is illustrated with an example from the theory of configurations of the extranucleosomal loop of a dna miniplasmid in a mononucleosome with emphasis placed on the influence that nicking and ligation on one hand and changes in the ratio of elastic coefficients on the other have on the stability of equilibrium configurations in that example the configurations studied are calculated using an extension of the method of explicit solutions to cases in which the elastic rod modeling a dna segment is considered impenetrable and hence excluded volume effects and forces arising from self contact are taken into account

euler lagrange equations for nonlinearly elastic rods with self contact we derive the euler lagrange equations for nonlinearly elastic rods with self contact the excluded volume constraint is formulated in terms of an upper bound on the global curvature of the centre line this condition is shown to guarantee the global injectivity of the deformation of the elastic rod topological constraints such as a prescribed knot and link class to model knotting and supercoiling phenomena as observed e g in dna molecules are included by using the notion of isotopy and gaussian linking number the bound on the global curvature as a nonsmooth side condition requires the use of clarke s generalized gradients to obtain the explicit structure of the contact forces which appear naturally as lagrange multipliers in the euler lagrange equations transversality conditions are discussed and higher regularity for the strains moments the centre line and the directors is shown

all dimension neighborhood based particle swarm optimization with randomly selected neighbors particle swarm optimization pso is widely used for solving various optimization problems since it has few parameters and is easy to implement however canonical pso generally suffers from premature convergence because it usually loses diversity too rapidly during the evolutionary process to improve the performance of pso on complex problems an all dimension neighborhood based pso with randomly selected neighbors learning strategy adn rsn pso is proposed in this study the randomly selected neighbors rsn learning strategy is adopted in the early stage of pso to enhance the swarm diversity while the all dimension neighborhood adn strategy is utilized in the later stage to accelerate the convergence rate the adn strategy enhances the local search capability around the global best solution in a dimension by dimension manner and the search distance is adapted by shrinking and random expansion operators experimental results show that adn pso can improve the exploitation capability of the global version of pso to test the performance of the proposed adn rsn pso comparison tests on the cec2013 test suite are carried out the comparison results reveal that adn rsn pso outperforms other peer pso variants in the end the proposed adn rsn pso is applied to the radar system design problem to demonstrate its potential in real life applications

stability results for constrained calculus of variations problems an analysis of the twisted elastic loop problems with a variational structure are ubiquitous throughout the physical sciences and have a distinguished scientific history constrained variational problems have been much less studied particularly the theory of stability which determines which solutions are physically realizable in this paper we develop stability exchange results appropriate for parameter dependent calculus of variations problems with two particular features either the parameter appears in the boundary conditions or there are isoperimetric constraints in particular we identify an associated distinguished bifurcation diagram which encodes the direction of stability exchange at folds we apply the theory to a twisted elastic loop which can naturally be formulated as a calculus of variations problem with both isoperimetric constraints and parameter dependent boundary conditions in combination with a perturbation expansion that classifies certain pitchfork bifurcations as sub or super critical the distinguished diagram for the twisted loop provides a classification of the stability properties of all equilibria in particular an unanticipated sensitive dependence of stability properties on the ratio of twisting to bending stiffness is revealed

an intelligent augmentation of particle swarm optimization with multiple adaptive methods over the last two decades the newly developed optimization technique particle swarm optimization pso has attracted great attention two common criticisms exist first most existing psos are designed for a specific search space thus an algorithm performing well on a diverse set of problems is lacking secondly pso suffers premature convergence to address the first issue we propose to augment pso via the fusion of multiple search methods an intelligent selection mechanism is developed based on an effectiveness index to trigger appropriate search methods in this research two search techniques are studied a non uniform mutation based method and an adaptive sub gradient method we further improve the proposed pso using adaptive cauchy mutation to prevent premature convergence as a result an augmented pso with multiple adaptive methods pso mam is proposed the performance of pso mam is tested on 43 functions uni modal multi modal non separable shifted rotated noisy and mis scaled functions the results are compared in terms of solution quality and convergence speed with 10 published pso methods the experimental results demonstrate pso mam outperforms the comparison algorithms on 36 out of 43 functions we conclude while promising there is still room for improving pso mam on complex multi modal functions e g rotated multi modal functions

stability and folds it is known that when one branch of a simple fold in a bifurcation diagram represents linearly stable solutions the other branch represents unstable solutions the theory developed here can predict instability of some branches close to folds without knowledge of stability of the adjacent branch provided that the underlying problem has a variational structure first one particular bifurcation diagram is identified as playing a special role the relevant diagram being specified by the choice of functional plotted as ordinate the results are then stated in terms of the shape of the solution branch in this distinguished bifurcation diagram in many problems arising in elasticity the preferred bifurcation diagram is the loaddisplacement graph the theory is particularly useful in applications where a solution branch has a succession of folds

a theory of fuzzy uniformities with applications to the fuzzy real lines abstract for each completely distributive lattice l with order reversing involution the fuzzy real line r l is uniformizable by a uniformity which both generates the canonical fuzzy topology and induces a pseudometric generating the canonical topology if l is also a chain the usual addition and multiplication defined on r r 0 1 extend jointly fuzzy continuously to and on r l three fundamental questions in fuzzy sets until now are question a if l 1 l 2 is r l 1 uniformly isomorphic to r l 2 in some sense question b for each chain l is jointly uniformly continuous in a sense which guarantees its joint continuity on r l question c is r l a complete pseudometric space in some sense we construct categories qu and u using the quasi uniformities of b hutton which enable us to answer these questions in the affirmative these results enhance the canonical standing of the fuzzy real lines and so give additional justification for answering in the affirmative question d does fuzzy topology have deep specific canonical examples

hybrid harmony search particle swarm optimization with global dimension selection this study presents a hybrid harmony search particle swarm optimization with global dimension selection hhspso gds for improving the performance of particle swarm optimization pso in hhspso gds a new global velocity updating strategy is introduced to enhance the neighborhood region search of the current best solution and to get a better trade off between convergence rate and robustness additionally a dynamic non linear decreased inertia weight is utilized to balance the global exploration and local exploitation moreover the best worst improvisation mechanism of harmony search hs is implanted in the hhspso gds algorithm and a global dimension selection is employed in the improvisation process which can effectively accelerate convergence global best information sharing strategy is developed to link the two layer exploration frames pso and hs finally a comprehensive experimental study is conducted on a large number of benchmark functions the experimental results reveal that hhspso gds performs better in terms of the quality of solution convergence rate robustness and scalability compared to various state of the art psos and other meta heuristic search algorithms

nelder mead simplex modifications for simulation optimization when the nelder mead method is used to optimize the expected response of a stochastic system e g an output of a discrete event simulation model the simplex resizing steps of the method introduce risks of inappropriate termination we give analytical and empirical results describing the performance of nelder mead when it is applied to a response function that incorporates an additive white noise error and we use these results to develop new modifications of nelder mead that yield improved estimates of the optimal expected response compared to nelder mead the best performance was obtained by a modified method rs s9 in which a the best point in the simplex is reevaluated at each shrink step and b the simplex is reduced by 10 rather than 50 at each shrink step in a suite of 18 test problems that were adapted from the minpack collection of netlib the expected response at the estimated optimal point obtained by rs s9 had errors that averaged 15 less than at the original method s estimated optimal point at an average cost of three times as many function evaluations two well known existing modifications for stochastic responses the n 3 rule and the next to worst rule were found to be inferior to the new modification rs s9

lock on to tape like behaviour in the torsional buckling of anisotropic rods abstract through nonlinear normal form analysis of the equilibrium equations developed in a neighbourhood of the straight rod solution we show the existence of a phase transition from mildly anisotropic to full tape like buckling in non symmetric rods subject to terminal loads provided the material has a sufficiently low poisson s ratio for a solid elliptical rod with a poisson s ratio of 0 2 the critical point is found to occur at a cross sectional aspect ratio of just over 3 for larger aspect ratios the rod locks on to a one twist per wave buckling mode with no internal twist in the mildly anisotropic regime there turn out to be two physically distinct pairs of symmetric so called primary localised buckling modes differing in the phase of the internal twist these four modes homoclinic orbits remain of the full circle of localised buckling modes existing in the symmetric case after breaking of the circular symmetry of the rod s cross section in the strongly anisotropic regime only the energetically favourable pair of flat buckling modes survives

entanglement complexity of self avoiding walks self avoiding walks on three dimensional lattices are flexible linear objects which can be self entangled the authors discuss several ways to measure entanglement complexity for n step walks and prove that these complexity measures tend to infinity with n for small n they use monte carlo methods to estimate and compare the n dependence of two of these complexity measures

particle swarm optimization hybridization perspectives and experimental illustrations metaheuristic optimization algorithms have become popular choice for solving complex and intricate problems which are otherwise difficult to solve by traditional methods in the present study an attempt is made to review the hybrid optimization techniques in which one main algorithm is a well known metaheuristic particle swarm optimization or pso hybridization is a method of combining two or more techniques in a judicious manner such that the resulting algorithm contains the positive features of both or all the algorithms depending on the algorithm s used we made three classifications as i hybridization of pso and genetic algorithms ii hybridization of pso with differential evolution and iii hybridization of pso with other techniques where other techniques include various local and global search methods besides giving the review we also show a comparison of three hybrid pso algorithms hybrid differential evolution particle swarm optimization de pso adaptive mutation particle swarm optimization ampso and hybrid genetic algorithm particle swarm optimization ga pso on a test suite of nine conventional benchmark problems

supercoiling transitions of closed dna conformations of closed dna molecules are considered within a simple elastic model the interplay of elastic energies of bending and twisting can lead to supercoiling induced by variations of the linking difference these shape transformations are studied in the limit of a large length to thickness ratio of the molecule stationary shapes and energy diagrams are obtained by solving shape equations for closed rings four different families of stationary shapes can be distinguished i planar circles ii nonplanar rings iii self interacting rings and iv interwound configurations they all occur as shapes of minimal energy in the phase diagram of supercoiling the transitions between the different regions in this phase diagram can be either continuous or discontinuous the sequence of shape transitions turns out to be sensitive to the precise values of the elastic parameters the buckling instability of the circle changes within the range of physically accessible values from continuous to discontinuous behavior

restricted quadratic forms inertia theorems and the schur complement the starting point of this investigation is the properties of restricted quadratic forms x ax x s rm where a is an m m real symmetric matrix and s is a subspace the index theory of hestenes 1951 and maddocks 1985 that treats the more general hilbert space version of this problem is first specialized to the finite dimensional context and appropriate extensions valid only in finite dimensions are made the theory is then applied to obtain various inertia theorems for matrices and positivity tests for quadratic forms expressions for the inertias of divers symmetrically partitioned matrices are described in particular an inertia theorem for the generalized schur complement is given the investigation recovers links and extends several formerly disparate results in the general area of inertia theorems

on internal characterizations of completelyl regular spaces abstract complete l regularity is internally characterized in terms of separating chains of open l sets a possible characterization in terms of normal and separating families of closed l sets is discussed and it is shown that spaces admitting such families are completely l regular the question of whether the converse holds true remains open some partial solutions are however given e g in the class of countably compact spaces

eulerian formulation of elastic rods in numerous biological medical and engineering applications elastic rods are constrained to deform inside or around tube like surfaces to solve efficiently this class of problems the equations governing the deflection of elastic rods are reformulated within the eulerian framework of this generic tubular constraint defined as a perfectly stiff normal ringed surface this reformulation hinges on describing the rod deformed configuration by means of its relative position with respect to a reference curve defined as the axis or spine curve of the constraint and on restating the rod local equilibrium in terms of the curvilinear coordinate parametrizing this curve associated with a segmentation strategy which partitions the global problem into a sequence of rod segments either in continuous contact with the constraint or free of contact except for their extremities this re parametrization not only trivializes the detection of new contacts but also transforms these free boundary problems into classic two points boundary value problems and suppresses the isoperimetric constraints resulting from the imposition of the rod position at the extremities of each rod segment

magnetic fields and brownian motion on the 2 sphere using constrained path integrals the authors study some statistical properties of brownian paths on the two dimensional sphere a generalized levy law for the probability p a that a closed brownian path encloses an algebraic area a is obtained distributions of scaled variables related to the winding of paths around some fixed point are recovered in the asymptotic regime t to infinity

on l tychonoff spaces topics of this paper include 1 basic terminology and auxiliary observations 2 pointfree characterizations of completely l regular spaces 3 embedding spaces of prescribed weight applications to l tychonoff and l to spaces 4 remarks on liu s characterizations of complete l regularity involving points 5 extending continuous l real functions from h compact subspaces 6 conditional completeness of c x r l 7 remarks on the compactification of liu and luo 8 l creg l creg and l tych l tych 9 lower order axioms for the l line a new coherent system of separation axioms for l topological spaces 10 open questions

knots in self avoiding walks discusses the existence of knots in random self avoiding walks on a lattice using kesten s 1963 pattern theorem it is shown that almost all sufficiently long self avoiding walks on the three dimensional simple cubic lattice contain a knot

the energy spectrum of a twisted flexible string under elastic relaxation a full investigation of the energy spectrum of a twisted flexible string under elastic relaxation is presented and discussed in detail for the first time new polynomial expressions for critical energy states are derived and the whole spectrum of critical states minima maxima and inflexion points of the elastic energy is found and discussed in relation to superhelicity and elastic characteristics of the string the study is carried out in the context of the theory of linear elasticity and the thin rod approximation the relaxation mechanism is studied by using conservation of linking difference by the formula delta lk wr delta tw we show how specific geometric quantities such as pitch angle writhe and twist contributions as well as physical quantities such as torsional and bending energy depend on superhelicity given by the specific linking difference and elastic characteristics of the string given by bending and torsional rigidity these quantities expressed per unit length are examined and compared at each critical energy state starting from a supertwisted configuration we show that the string relaxes by twist reduction through two different intermediate helical states which correspond to different local minima to reach the lowest minimum energy state in a supercoiled configuration the case of a generic kink formation and consequent passage through an inflexional configuration is then examined and new expressions for the energy change in the vicinity of the inflexion point are derived

conformations of closed dna we examine the conformations of a model for a short segment of closed dna the molecule is represented as a cylindrically symmetric elastic rod with a constraint corresponding to a specification of the linking number we obtain analytic expressions leading to the spatial configuration of a family of solutions representing distortions that interpolate between the circular form of dna and a figure eight form that represents the onset of interwinding we are also able to generate knotted loops we suggest ways to use our approach to produce other configurations relevant to studies of dna structure the stability of the distorted configurations is assessed along with the effects of fluctuations on the free energy of the various configurations

modeling and numerical treatment of elastic rods with frictionless self contact in this paper we present a hyperelastic rod model that takes into account self contact forces the model is based on cosserat rod theory that incorporates shear elongation flexure and twist deformations the problem of avoiding self penetration of parts of the rod is handled by the introduction of a contact distance function and the incorporation of associated contact forces we present a penalty method for the treatment of the multi valued and non differentiable contact law we also describe an augmented lagrangian formulation of this problem we then give the details of the finite element discretization of the elastic rod self contact problem as well as some numerical examples

isoperimetric conjugate points with application to the stability of dna minicircles a conjugate point test determining an index of the constrained second variation in one dimensional isoperimetric calculus of variations problems is described the test is then implemented numerically to determine stability properties of equilibria within a continuum mechanics model of dna minicircles

confinement of semiflexible polymers a variational framework is developed to examine the equilibrium states of a semiflexible polymer that is constrained to lie on a fixed surface as an application the confinement of a closed polymer loop of fixed length 2 r within a spherical cavity of smaller radius r 0 is considered it is shown that an infinite number of distinct periodic completely attached equilibrium states exist labeled by two integers n 2 3 4 and p 1 2 3 the number of periods of the polar and azimuthal angles respectively small loops oscillate about a geodesic circle n 2 p 1 is the stable ground state states with higher n exhibit instabilities if r 2r 0 new states appear as oscillations about a doubly covered geodesic circle the state n 3 p 2 replaces the twofold as the ground state in a finite band of values of r with increasing r loop states make a transition from oscillatory and orbital behavior on crossing the poles returning to oscillation upon collapse to a multiple cover of a geodesic circle signaled respectively by an increase in p and an increase in n the force transmitted to the surface does not increase monotonically with loop size but does asymptotically it behaves discontinuously where n changes the contribution to energy from geodesic curvature is bounded in large loops the energy becomes dominated by a state independent contribution proportional to the loop size the energy gap between the ground state and excited states disappears

on the asymmetric elasticity of twisted dsdna abstract we present an analytical based proof for the consistency of two asymmetric elastic models of the double stranded dna in the regime around the b form we derive the shape equations in terms of euler angles for a uniform ribbon with noncircular cross section and spontaneous torsion we study the conditions to form a helical ribbon for the model and find that the euler angle must be either 0 or 2 we find that the helix is always stable or at least metastable for the model and there is either a continuous or discontinuous transition of extension from a twisted straight ribbon to a helical ribbon an over collapse phenomena of extension is observed for the ribbon under twisting the stability of the helix and the intrinsic asymmetric elasticity under twisting are also studied

nonlinear dynamics and loop formation in kirchhoff rods with implications to the mechanics of dna and cables the paper contributes a general dynamical formulation and numerical solution procedure for studying nonlinear and three dimensional dynamics of kirchhoff rods target applications include the dynamic formation of dna loops and supercoils as well as loops hockles in marine cables the formulation accommodates non homogeneous and non isotropic inextensible rods both with and without coupling of tension and torsion the utility of this formulation is illustrated by studying the dynamics and quasi static response of a clamped clamped rod subject to compression and or twist for slow loading rates the computed quasi static responses converge to published equilibrium solutions for a benchmark problem as loading rates increase new behaviors are observed including hysteresis in the neighborhood of equilibrium bifurcations the addition of chirality in the form of tension torsion coupling has a pronounced influence on the computed looped geometries this finding has implications for dna loops formed by dna protein binding as well as loop formation in helically wound wire and synthetic cables

knot complexity and related observables from path integrals for semiflexible polymers we analyse earlier obtained numerical results for the knot complexity and the topological persistence length i e the minimal number of steps on the lattice needed for the knot to be formed with help of well known path integrals for semiflexible chains in addition we provide an estimate for the number of different knots having knot diagrams with exactly n crossings analytical results obtained are in satisfactory agreement with the available numerical data

numerical solution of a bending torsion model for elastic rods aiming at simulating elastic rods we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods after reviewing this model and discussing topological effects of periodic rods we prove convergence of the discretized functionals and stability of a corresponding discrete flow our experiments numerically confirm thresholds e g for michell s instability and indicate a complex energy landscape in particular in the presence of impermeability

on the stability of elastic annular rods abstract the stability of equilibrium of non linearly elastic rods whose deformations obey the classical kirchhoff s equations is considered a variational formulation of the equilibrium problem is given and the equilibrium equations for infinitesimal deformations superimposed to a finite transformation of a rod are deduced the stability of annular rings in which the twisting strain is non null is investigated by study of the second variation of the energy functional

solving bi level linear programming problem through hybrid of immune genetic algorithm and particle swarm optimization algorithm bi level linear programming consisting of upper level and lower level objectives is a technique for modeling decentralized decision this study presents a hybrid of immune genetic algorithm and vector controlled particle swarm optimization igvpso to solve the bi level linear programming problem blpp it is applied to a supply chain model that is a blpp using four problems from the literature and the supply chain distribution models the computational results indicate that the proposed method is superior to some algorithms

some questions in fuzzy topology the purpose of this paper is to discuss some basic questions related mainly to hutton s l fuzzy unit interval some of those questions are stated here for the first time while some of them are long standing related results are surveyed in some cases

l fuzzy normal spaces and tietze extension theorem abstract in this paper we prove a characterization theorem for normal l fuzzy topological spaces l is an infinitely distributive lattice with an order reversing involution in the particular case l 0 1 this theorem reduces to a known result of kat tov fund math 38 1951 85 91 and tong duke math j 19 1952 289 292 as an important application we obtain a fuzzy version of tietze extension theorem this yields an affirmative answer to a question raised in a series of papers by rodabaugh fuzzy sets and systems 11 1983 163 183

writhe and mutual entanglement combine to give the entanglement length we propose a method to estimate n e the entanglement length that incorporates both local and global topological characteristics of chains in a melt under equilibrium conditions this estimate uses the writhe of the chains the writhe of the primitive paths and the number of kinks in the chains in a melt an advantage of this method is that it works for both linear and ring chains works under all periodic boundary conditions does not require knowing the contour length of the primitive paths and does not rely on a smooth set of data we apply this method to linear finitely extendable nonlinear elastic chains and we observe that our estimates are consistent with those from other studies

elastic stability of dna configurations ii supercoiled plasmids with self contact configurations of protein free dna miniplasmids are calculated with the effects of impenetrability and self contact forces taken into account by using exact solutions of kirchhoff s equations of equilibrium for elastic rods of circular cross section bifurcation diagrams are presented as graphs of excess link ensuremath delta mathcal l versus writhe w and the stability criteria derived in paper i of this series are employed in a search for regions of such diagrams that correspond to configurations that are stable in the sense that they give local minima to elastic energy primary bifurcation branches that originate at circular configurations are composed of configurations with mathrm d m symmetry m 2 3 dots among the results obtained are the following i there are configurations with mathrm c 2 symmetry forming secondary bifurcation branches which emerge from the primary branch with m 3 and bifurcation of such secondary branches gives rise to tertiary branches of configurations without symmetry ii whether or not self contact occurs a noncircular configuration in the primary branch with m 2 called branch ensuremath alpha is stable when for it the derivative d ensuremath delta mathcal l d mathcal w computed along that branch is strictly positive iii for configurations not in ensuremath alpha the condition d ensuremath delta mathcal l d mathcal w g0 is not sufficient for stability in fact each nonplanar contact free configuration that is in a branch other than ensuremath alpha is unstable a rule relating the number of points of self contact and the occurrence of intervals of such contact to the magnitude of ensuremath delta mathcal l which in paper i was found to hold for segments of dna subject to strong anchoring end conditions is here observed to hold for computed configurations of protein free miniplasmids

fractional variational principle of herglotz for a new class of problems with dependence on the boundaries and a real parameter the fractional variational problem of herglotz type for the case where the lagrangian depends on generalized fractional derivatives the free endpoints conditions and a real parameter is studied this type of problem generalizes several problems recently studied in the literature moreover it allows us to unify conservative and non conservative dynamical processes in the same model the dependence of the lagrangian with respect to the boundaries and a free parameter is effective and transforms the standard herglotz s variational problem into a problem of a different nature

a note on teaching learning based optimization algorithm teaching learning based optimization tlbo seems to be a rising star from amongst a number of metaheuristics with relatively competitive performances it is reported that it outperforms some of the well known metaheuristics regarding constrained benchmark functions constrained mechanical design and continuous non linear numerical optimization problems such a breakthrough has steered us towards investigating the secrets of tlbo s dominance this paper reports our findings on tlbo qualitatively and quantitatively through code reviews and experiments respectively our findings have revealed three important mistakes regarding tlbo 1 at least one unreported but important step 2 incorrect formulae on a number of fitness function evaluations and 3 misconceptions about parameter less control additionally unfair experimental settings conditions were used to conduct experimental comparisons e g different stopping criteria the experimental results for constrained and unconstrained benchmark functions under fairly equal conditions failed to validate its performance supremacy the ultimate goal of this paper is to provide reminders for metaheuristics researchers and practitioners in order to avoid similar mistakes regarding both the qualitative and quantitative aspects and to allow fair comparisons of the tlbo algorithm to be made with other metaheuristic algorithms

the writhe of a self avoiding walk the writhe of a self avoiding walk in a three dimensional space is the average over all projections onto a plane of the sum of the signed crossings we compute this number using a monte carlo simulation our results suggest that the average of the absolute value of the writhe of self avoiding walks increases as nalpha where n is the length of the walks and alpha approximately 0 5 the mean crossing number of walks is also computed and found to have a power law dependence on the length of the walks in addition we consider the effects of solvent quality on the writhe and mean crossing number of walks

a variational rod model with a singular nonlocal potential the classical theory of elastic rods does not account for the possibility that large deformations may involve distinct points along the rod occupying the same physical space we develop an elastic rod model with a pairwise repulsive potential such that if two non adjacent points along the rod are close in physical space there is an energy barrier which prevents contact while for points nearby along the rod the potential is describable classically this framework is developed to prove the existence of minimizers within each homotopy class where the idea of topological homotopy of a curve is generalized to elastic rods as framed curves finally the relevant first order optimality conditions are derived and used to investigate the regularity of minimizers

conformations of linear dna we examine the conformations of a model for underwound and overwound dna the molecule is represented as a cylindrically symmetric elastic string subjected to a stretching force and to constraints corresponding to a specification of the link number we derive a fundamental relation between the euler angles that describe the curve and the topological linking number analytical expressions for the spatial configurations of the molecule in the infinite length limit are obtained a unique configuration minimizes the energy for a given set of physical conditions an elastic model incorporating thermal fluctuations provides excellent agreement with experimental results on the plectonemic transition

writhe formulas and antipodal points in plectonemic dna configurations the linking and writhing numbers are key quantities when characterizing the structure of a piece of supercoiled dna defined as double integrals over the shape of the double helix these numbers are not always straightforward to compute though a simplified formula was established in a theorem by fuller proc natl acad sci u s a 75 3557 1978 we examine the range of applicability of this widely used simplified formula and show that it cannot be employed for plectonemic dna we show that inapplicability is due to a hypothesis of fuller theorem that is not met the hypothesis seems to have been overlooked in many works

the nonlinear dynamics of elastic tubes conveying a fluid abstract the kirchhoff equations for elastic tubes are modified to include the effect of fluid flow using the techniques of linear and nonlinear analysis specially developed for the kirchhoff equations the effect of the fluid flow on the basic twist to writhe instability is investigated the results suggest an intriguing modification of the bifurcation threshold due to the flow beyond threshold the buckled tube acquires a slight curvature which modifies the flow rate and results in a correction to nonlinearity of the amplitude equation governing the deformation dynamics

the writhe of a self avoiding polygon we discuss the writhe of a self avoiding polygon on a lattice as a geometrical measure of its entanglement complexity we prove a rigorous result about the dependence of the absolute value of the writhe on the number n of edges in the polygon and use monte carlo methods to estimate the distribution of the writhe both for all polygons with n edges and for the subset of polygons that are trefoils

the statistical mechanics of a melt of polymer rings topological restrictions are introduced into a melt of flexible polymer rings by specifying the linking number between each pair of rings attention is focused on the configurational properties of a single ring in the melt where the winding number between each pair of rings is zero the configurations of all the other chains are averaged out in the partition sum the effect of the topological constraint on the remaining chain is expressed as a product of two configurational weighting factors which involve unusual geometrical properties of the configuration one is a phase factor depending on the torsion of the configuration and the other is a boltzmann like factor with the self inductance of the configuration in the role of the interaction energy the term based on the torsion has the remarkable property of transforming random walk like configurations into those of stiff rods while the inductance term promotes a transition to a completely collapsed state our preliminary results suggest that the actual configuration of the loop is a non trivial balance between these opposing tendencies with the size r of the loop scaling with the length as r2 approximately l1 1 3 pi approximately l0 89

solving the boundary value problem for finite kirchhoff rods the kirchhoff model describes the statics and dynamics of thin rods within the approximations of the linear elasticity theory in this paper we develop a method based on a shooting technique to find equilibrium configurations of finite rods subjected to boundary conditions and given load parameters the method consists in making a series of small changes on a trial solution satisfying the kirchhoff equations but not necessarily the boundary conditions by linearizing the differential equations around the trial solution we are able to push its end point to the desired position step by step the method is also useful to obtain configurations of rods with fixed end points but different mechanical parameters such as tension components of the moment or inhomogeneities

niching particle swarm optimization with local search for multi modal optimization multimodal optimization is still one of the most challenging tasks for evolutionary computation in recent years many evolutionary multi modal optimization algorithms have been developed all these algorithms must tackle two issues in order to successfully solve a multi modal problem how to identify multiple global local optima and how to maintain the identified optima till the end of the search for most of the multi modal optimization algorithms the fine local search capabilities are not effective if the required accuracy is high these algorithms fail to find the desired optima even after converging near them to overcome this problem this paper integrates a novel local search technique with some existing pso based multimodal optimization algorithms to enhance their local search ability the algorithms are tested on 14 commonly used multi modal optimization problems and the experimental results suggest that the proposed technique not only increases the probability of finding both global and local optima but also reduces the average number of function evaluations