universality class of trails in two dimensions a trail is a walk on a lattice that may visit a site more than once but a bond at most once we have carried out transfer matrix studies of trails on the square lattice and of hybrid walks that interpolate between self avoiding walks and trails the results are in agreement with the same universal exponents as self avoiding walks however the finite size corrections are much larger than for self avoiding walks an explanation in terms of an irrelevant variable with scaling index is given

on the controllability of linear juggling mechanical systems this paper deals with the controllability of a class of nonsmooth complementarity mechanical systems due to their particular structure they can be decomposed into an object and a robot consequently they are named juggling systems it is shown that the accessibility of the object can be characterized by nonlinear constrained equations or generalized equations examples are presented including a simple model of backlash the main focus of the work is about linear jugglers 2005 elsevier b v all rights reserved

critical behaviour of the two dimensional potts model with a continuous number of states a finite size scaling analysis we investigate the critical behaviour of the two dimensional q state potts model using finite size scaling and transfer matrix methods for the continuous transition range 0 these results for continuous q were obtained from a transfer matrix constructed for a generalized whitney polynomial representing the potts models an effective algorithm to compute the dominant eigenvalues of this essentially nonsymmetric transfer matrix is developed

self avoiding path walks on lattices a new universality class the trails problem self avoiding path walks is reconsidered by the conventional series expansion approach an exact enumeration on the square triangular and simple cubic lattices is done by computer up to 18 12 and 11 steps respectively the more self consistent and refined results between the connective constant and the corresponding critical exponent indicate the possibility of there being a different universality class from that of the self avoiding walk an average approach based on stolz s theorem is proposed which often appears to be smoother and better than the traditional one

new exact exponents for two dimensional self avoiding walks the author establishes using standard coulomb gas methods the values of a new set of geometrical exponents that have been previously conjectured these exponents give for any p the number of configurations of p two dimensional self avoiding walks of the same length l which are attached by their ends

lattice trails i exact results considers the problem of lattice trails introduced by malakis 1975 1976 the author proves the existence of a finite connective constant and establishes a result for the growth of n step trails tn analogous to the best known result for self avoiding walks tn lambda n expt o n for the honeycomb d 2 and lave s lattice d 3 the author establishes a counting theorem from which one can deduce the exact value of the connective constant lambda for the honeycomb lattice lambda 2 2 square root 2 further it follows that the trail problem is in the same universality class as the self avoiding walk problem for those lattices an exact amplitude relation between trails and self avoiding walks and between dumb bells and trails and self avoiding walks is established the non existence of a counting theorem for arbitrary lattices is established an inequality for the triangular lattice connective constant is proved a high density expansion for lambda for the d dimensional hybercubic lattice is also obtained the author argues that contrary to recent suggestions the model is in the same universality class as the self avoiding walk model

remarks on the time varying h riccati equations in this paper we establish some useful properties of three riccati equations appearing in the standard h control problems for continuous and discrete time time varying systems we then give necessary and sufficient conditions for the existence of a suboptimal controller by three conditions involving two independent riccati equations with a coupling inequality

follow the bouncing ball global results on tracking and state estimation with impacts in this paper we formulate tracking and state estimation problems of a translating mass in a polyhedral billiard as a stabilization problem for a suitable set due to the discontinuous trajectories arising from the impacts we use hybrid systems stability analysis tools to establish the results using a novel concept of mirrored images of the target mass we prove that 1 a tracking control algorithm and 2 an observer algorithm guarantee global exponential stability results for specific classes of polyhedral billiards including rectangles moreover we combine these two algorithms within dynamic controllers that guarantee global output feedback tracking the results are illustrated via simulations

velocity observers for linear mechanical systems subject to single non smooth impacts abstract in this paper we consider the problem of the velocity estimation from position measurement for linear mechanical systems with multiple degrees of freedom subject to single non smooth impacts both elastic and inelastic i e with coefficient of restitution e 1 and e 0 1 respectively through a simple example it is shown that a classical luenberger observer is not able to reproduce instantaneously the jumps in the mass velocities since it recovers the error induced by such jumps only asymptotically an infinite sequence of impacts can prevent the estimation error to asymptotically go to zero a new observer structure is proposed for linear mechanical systems subject to single unilateral constraints that guarantees that the corresponding error dynamics are exponentially stable also in presence of an infinite sequence of non smooth impacts the observer that we propose switches at the impact times that can be recognized by position measurements only to validate the proposed observer both simulation and experimental tests have been carried out and are briefly reported pointing out the drawbacks and advantages of the observer

state estimation of otherwise unobservable linear mechanical systems through the use of non smooth impacts in this paper we consider a particular mechanism constituted by a pair of infinitely rigid mating gears subject to backlash where only the position of the actuated gear is measured so that the system is unobservable if the impacts between the teeth of the gears are ignored under the assumption that there is an infinite sequence of non smooth impacts which assumption is generally satisfied during a usual task e g when the mechanism is actuated by a constant torque it is possible to design an observer that asymptotically estimates also the position and the velocity of the non actuated gear simulation results are included to verify the effectiveness of the proposed observer

on the control of finite dimensional mechanical systems with unilateral constraints this paper focuses on the problem of the control of a class of mechanical systems with a finite number of degrees of freedom subject to unilateral constraints on the position roughly speaking those systems are described by a set of ordinary differential equations that represent smooth dynamics together with an algebraic inequality condition f q spl ges 0 where q is the vector of generalized coordinates and an impact rule relating the interaction impulse and the velocity nonsmooth dynamics is at the core of the study of such systems this implies that one can suitably define solutions and stability concepts that fit with the considered model we then discuss the closed loop control problem and analyze various switching control strategies

critical behaviour and conformal anomaly of the o n model on the square lattice finite size scaling and transfer matrix techniques are used to determine the conformal anomaly and critical exponents of o n models on the square lattice these calculations were performed on five branches of critical points parametrised by n the results for two of the branches agree with the known universal properties of the o n model as derived for the honeycomb lattice finite size convergence is poor for most of the third branch so that in this case the classification in terms of known models is uncertain the authors data show that the fourth branch can be interpreted in terms of a combination of a low temperature o n and a critical ising model finally the numerical results for the o n model on the remaining branch agree accurately with the known results for the low temperature o n 1 model they prove this equivalence by means of an exact mapping

modeling and control of impact in mechanical systems theory and experimental results considers the equations of motion of mechanical systems subject to inequality constraints which can be obtained by looking for the stationary value of the action integral two different methods are used to take into account the inequality constraints in the computation of the stationary value of the action integral the valentine variables method and the penalty functions method the equations of motion resulting from the application of the valentine variables method which introduces the concept of nonsmooth impacts constitute the exact model of the constrained mechanical system such a model is suitable to be employed when the impacting parts of the actual mechanical system are very stiff the equations of motion resulting from the application of the penalty functions method which introduces the concept of smooth impacts constitute an approximate model of the constrained mechanical system such a model is suitable to be employed when the impacting parts of the actual mechanical system show some flexibility various feedback control laws from the natural outputs and from their time derivatives are studied with reference to both models of impact the closed loop systems resulting from the application of the same control law to both models show pretty much the same global asymptotic stability properties the proposed control laws are only concerned with regulation problems in the presence of possible contacts and impacts among parts of the mechanical system or with the external environment the effectiveness of the proposed control structure has been tested experimentally with reference to a single link robot arm showing a valuable behavior

phenomenological renormalisation of the self avoiding walk in two dimensions phenomenological renormalisation is used to calculate the exponent v and the connective constant of the self avoiding walk problem on a square lattice a transfer matrix technique is developed for the polymer problem the results indicate that flory s value v 0 75 is true in two dimensions to extremely high accuracy

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

velocity observers for non linear mechanical systems subject to non smooth impacts this paper is concerned with the estimation of the velocity variables when the position variables are the measured outputs for non linear mechanical systems subject to non smooth impacts both elastic and inelastic i e with coefficient of restitution e 1 and e 0 1 respectively a reduced order observer is proposed which guarantees that the corresponding error system despite the possible presence of an infinite sequence of non smooth impacts is locally exponentially stable an estimate of the basin of attraction is also given

algebraic techniques for enumerating self avoiding walks on the square lattice the authors describe a new algebraic technique for enumerating self avoiding walks on the rectangular lattice the computational complexity of enumerating walks of n steps is of order 3n 4 times a polynomial in n and so the approach is greatly superior to direct counting techniques they have enumerated walks of up to 39 steps as a consequence they are able to accurately estimate the critical point critical exponent and critical amplitude

h sub 2 and h sub spl infin control for infinite dimensional systems with jumps we consider a semigroup model with jumps in the state that covers distributed parameter systems with impulse control or sampled data distributed parameter systems with control realized through zero order or first order hold we then introduce the h sub 2 and h sub spl infin problems for this system and give the solutions in terms of the solutions of riccati equations with jumps

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

the size and number of rings on the square lattice the authors have calculated the number of self avoiding polygons on the square lattice to 56 steps and the caliper size to 54 steps analysis of the generating function permits estimates of the connective constant mu 2 638 1585 or 10 6 and the critical exponents alpha 0 500 06 or 0 000 06 and v 0 753 or 0 007 the singularity structure of the polygon generating function is found to be consistent with a correction to the scaling exponent delta 1 5 as predicted by nienhuis 1982 1984 the confluent part however maps into the additive analytic term due to the value of the exponent alpha