an approximation to δ couplings on graphs we discuss a general parametrization for vertices of quantum graphs and show in particular how the s and couplings at an n edge vertex can be approximated by means of n 1 couplings of the type provided the latter are properly scaled

generalized point interactions in one dimensional quantum mechanics there is a four parameter family of point interactions in one dimensional quantum mechanics they represent all possible self adjoint extensions of the kinetic energy operator if time reversal invariance is imposed the number of parameters is reduced to three one of these point interactions is the familiar function potential but the other generalized ones do not seem to be widely known we present a pedestrian approach to this subject and comment on a recent controversy in the literature concerning the so called interaction we emphasize that there is little resemblance between the interaction and what its name suggests

the quantum nonlinear schrodinger model with point like defect we establish a family of point like impurities which preserve the quantum integrability of the nonlinear schrodinger model in 1 1 spacetime dimensions we briefly describe the construction of the exact second quantized solution of this model in terms of an appropriate reflection transmission algebra the basic physical properties of the solution including the spacetime symmetry of the bulk scattering matrix are also discussed

energy dependent point interactions in one dimension we consider a new type of point interaction in one dimensional quantum mechanics it is characterized by a boundary condition at the origin that involves the second and or higher order derivatives of the wavefunction the interaction is effectively energy dependent it leads to a unitary s matrix for the transmission reflection problem the energy dependence of the interaction can be chosen such that any given unitary s matrix or the transmission and reflection coefficients can be reproduced at all energies generalization of the results to coupled channel cases is discussed

fundamental solution of the heat and schrodinger equations with point interaction abstract we find explicit formulae for the fundamental solution for the heat and time dependent schrodinger equations with point interaction in dimension n 3 we discuss in detail the small time asymptotics of these fundamental solutions the case n 2 has the peculiarity of involving logarithmic terms in the expansion

the generalized star product and the factorization of scattering matrices on graphs in this article we continue our analysis of schrodinger operators on arbitrary graphs given as certain laplace operators in the present article we give the proof of the composition rule for the scattering matrices this composition rule gives the scattering matrix of a graph as a generalized star product of the scattering matrices corresponding to its subgraphs we perform a detailed analysis of the generalized star product for arbitrary unitary matrices the relation to the theory of transfer matrices is also discussed

conjugate gradient method for the robin inverse problem associated with the laplace equation this paper studies a non linear inverse problem associated with the laplace equation of identifying the robin coefficient from boundary measurements a variational formulation of the problem is suggested thereby transforming it into an optimization problem mathematical properties relevant to its numerical computation are established the optimization problem is solved using the conjugate gradient method in conjunction with the discrepancy principle and the algorithm is implemented using the boundary element method numerical results are presented for several benchmark problems with both exact and noisy data and the convergence of the algorithm with respect to mesh refinement and decreasing the amount of noise in the data is investigated copyright 2006 john wiley sons ltd

mathematical models for the apparent masses of standing subjects exposed to vertical whole body vibration linear lumped parameter models of the apparent masses of human subjects in standing positions when exposed to vertical whole body vibration have been developed simple models with a single degree of freedom d o f and with two d o f were considered for practical use model parameters were optimised using both the mean apparent mass of 12 male subjects and the apparent masses of individual subjects measured in a previous study the calculated responses of two d o f models with a massless support structure showed best agreement with the measured apparent mass and phase with errors less than 0 1 in the normalised apparent mass i e corresponding to errors less than 10 of the static mass and errors less than 5 in the phase for a normal standing posture the model parameters obtained with the mean measured apparent masses of the 12 subjects were similar to the means of the 12 sets of parameters obtained when fitting to the individual apparent masses it was found that the effects of vibration magnitude and postural changes on the measured apparent mass could be represented by changes to the stiffness and damping in the two d o f models

a remark on krein s resolvent formula and boundary conditions we prove an analogue of krein s resolvent formula expressing the resolvents of self adjoint extensions in terms of boundary conditions applications to quantum graphs and systems with point interactions are discussed

many body system with a four parameter family of point interactions in one dimension we consider a four parameter family of point interactions in one dimension this family is a generalization of the usual function potential we examine a system consisting of many particles of equal masses that are interacting pairwise through such a generalized point interaction we follow mcguire who obtained exact solutions for the system when the interaction is the function potential we find exact bound states with the four parameter family for the scattering problem however we have not been so successful this is because as we point out the condition of no diffraction that is crucial in mcguire s method is not satisfied except when the four parameter family is essentially reduced to the function potential

on the solution of an inverse natural convection problem using various conjugate gradient methods the inverse problem of determining the time varying strength of a heat source which causes natural convection in a two dimensional cavity is considered the boussinesq equation is used to model the natural convection induced by the heat source the inverse natural convection problem is solved through the minimization of a performance function utilizing the conjugate gradient method the gradient of the performance function needed in the minimization procedure of the conjugate gradient method is obtained by employing either the adjoint variable method or the direct differentiation method the accuracy and efficiency of these two methods are compared and a new method is suggested that exploits the advantageous aspects of both methods while avoiding the shortcomings of them copyright 2000 john wiley sons ltd

four parameter point interaction in 1d quantum systems the author constructs a four parameter point interaction for a nonrelativistic particle moving on a line as the limit of a short range interaction with a range tending toward zero for particular choices of the parameters one can obtain a delta interaction or the so called delta interaction the hamiltonian corresponding to the four parameter point interaction is shown to correspond to the four parameter self adjoint hamiltonian of the free particle moving on the line with the origin excluded

investigations on boundary temperature control analysis considering a moving body based on the adjoint variable and the fictitious domain finite element methods summary this paper presents an examination of moving boundary temperature control problems with a moving boundary problem a finite element mesh is generated at each time step to express the position of the boundary on the other hand if an overlapped domain that is comprising foreground and background meshes is prepared the moving boundary problem can be solved without mesh generation at each time step by using the fictitious domain method in this study boundary temperature control problems with a moving boundary are formulated using the finite element the adjoint variable and the fictitious domain methods and several numerical experiments are carried out copyright 2015 john wiley sons ltd

smooth approximation of singular perturbations abstract we consider a certain subclass of self adjoint extensions of the symmetric operator c 0 r s where s r that correspond formally to perturbations of the laplacian by potentials involving the potential we show that these extensions can be approximated in the strong resolvent sense by smooth perturbations of the laplacian when s is both a finite and infinite subset of r also we show that the operator in the finitely many potential case approaches the operator in the infinitely many potential case as the number of potentials approaches infinity these results extend and unify what has previously been known about smooth approximations of point interactions in one dimension

theoretical foundation methods and criteria for calibrating human vibration models using frequency response functions while simulations of the measured biodynamic responses of the whole human body or body segments to vibration are conventionally interpreted as summaries of biodynamic measurements and the resulting models are considered quantitative this study looked at these simulations from a different angle model calibration the specific aims of this study are to review and clarify the theoretical basis for model calibration to help formulate the criteria for calibration validation and to help appropriately select and apply calibration methods in addition to established vibration theory a novel theorem of mechanical vibration is also used to enhance the understanding of the mathematical and physical principles of the calibration based on this enhanced understanding a set of criteria was proposed and used to systematically examine the calibration methods besides theoretical analyses a numerical testing method is also used in the examination this study identified the basic requirements for each calibration method to obtain a unique calibration solution this study also confirmed that the solution becomes more robust if more than sufficient calibration references are provided practically however as more references are used more inconsistencies can arise among the measured data for representing the biodynamic properties to help account for the relative reliabilities of the references a baseline weighting scheme is proposed the analyses suggest that the best choice of calibration method depends on the modeling purpose the model structure and the availability and reliability of representative reference data

mathematical models for the apparent mass of the seated human body exposed to vertical vibration alternative mathematical models of the vertical apparent mass of the seated human body are developed the optimum parameters of four models two single degree of freedom models and two two degree of freedom models are derived from the mean measured apparent masses of 60 subjects 24 men 24 women 12 children previously reported the best fits were obtained by fitting the phase data with single degree of freedom and two degree of freedom models having rigid support structures for these two models curve fitting was performed on each of the 60 subjects so as to obtain optimum model parameters for each subject for the averages of each of the three groups of subjects and for the entire group of subjects the values obtained are tabulated use of a two degree of freedom model provided a better fit to the phase of the apparent mass at frequencies greater than about 8 hz and an improved fit to the modulus of the apparent mass at frequencies around 5 hz it is concluded that the two degree of freedom model provides an apparent mass similar to that of the human body but this does not imply that the body moves in the same manner as the masses in this optimized two degree of freedom model

green function approach for general quantum graphs we present a recursive prescription to calculate the exact green function for general quantum graphs for the closed case the expression for the poles of g which gives the individual eigenstates has the structure of a semiclassical formula where the sum over the periodic orbit is already performed as applications we discuss eigenstate localization for a three arm closed star and filter like mechanisms for transmission throughout an open trident graph

unveiling and exemplifying the unitary equivalence of discrete time quantum walk models the two major discrete time formulations for quantum walks coined and scattering are unitarily equivalent for arbitrary position dependent transition amplitudes and any topology andrade et al 2009 phys rev a 80 052301 although the proof explicitly describes the mapping obtention its high technicality may hinder relevant physical aspects involved in the equivalence discussing concrete examples the most general constructions for the line square and honeycomb lattices here we unveil the similarities and differences of these two versions of quantum walks we moreover show how to derive the dynamics of one from the other by means of proper projections we perform calculations for different probability amplitudes such as hadamard grover discrete fourier transform and the uncommon in the area but interesting discrete hartley transform comparing the evolutions our study illustrates the models interplay an important issue for implementations and applications of such systems

boundary conditions in path integrals from point interactions for the path integral of the one dimensional dirac particle a proposal is given of how to implement point interactions and boundary conditions in the path integral the starting point is a path integral formulation of a dirac particle in one dimension the implementation of a point interaction yields by means of a perturbation expansion the corresponding green function for a relativistic particle in the non relativistic limit several cases can be distinguished depending on which of the four possibilities of the point interaction has been chosen by a proper combination of the various possibilities of implementing the point interaction the whole range of the four parameter family of boundary conditions for point interactions can be exploited in the relativistic case as well as in the non relativistic limit in addition making the strength of the point interaction infinitely repulsive yields boundary conditions at finite points on the real line in particular dirichlet and neumann boundary conditions emerge the method is illustrated with some examples

single point interactions quantization by parts and boundary conditions traditionally point interaction problems in quantum mechanics are treated in the physics literature by solving the schrodinger equation containing an appropriate potential term in this paper we discuss a systematic quantization scheme known as the method of quantization by parts which provides a general method for dealing with single point interactions in one dimension namely by reducing the problem to boundary conditions our method can also be applied to superconducting systems like those concerning josephson and the recently discovered junctions and single electron circuit systems

empirical reduction of modes for the shape identification problems of heat conduction systems abstract the karhunen loeve galerkin procedure is a type of galerkin method that employs as basis functions the empirical eigenfunctions of the karhunen loeve decomposition and proved to be a powerful tool for reducing the degree of freedom of partial differential equations int j numer methods engrg 41 1998 1131 comput methods appl mech engrg 188 2000 165 in the present investigation we extend the applicability of the karhunen loeve galerkin procedure to systems of variable domains and apply it to the shape identification problems of heat conduction systems where the unknown boundary shape is estimated from temperature measurements on the other boundary the efficiency and accuracy of the present technique are assessed as compared to the traditional technique employing the original partial differential equation

shape identification for natural convection problems using the adjoint variable method an inverse geometry problem is investigated to identify the boundary shape of a domain from temperature measurements on the other boundary where the temperature field is dominated by natural convection the potential applications of the present investigation are the determination of a phase change isotherm in the bridgman crystal growth or the thermal tomography which detects flaws in materials nondestructively the inverse problem is posed as a minimization problem of the performance function which is the sum of square residuals between calculated and observed temperature by means of a conjugate gradient method employing the adjoint variable method the present method is found to identify the domains reasonably accurately even with noisy temperature measurements

the identification of a robin coefficient by a conjugate gradient method this paper investigates a non linear inverse problem associated with the heat conduction problem of identifying a robin coefficient from boundary temperature measurement the variational formulation of the problem is given the conjugate gradient method combining with the discrepancy principle for choosing the suitable stop step are proposed for solving the optimization problem in which the finite difference method is used to solve the direct problems the performance of the method is verified by simulating four examples the convergence with respect to the grid refinement and the amount of noise in the data is also investigated copyright 2008 john wiley sons ltd

quantification of changes in modal parameters due to the presence of passive people on a slender structure abstract this work proposes a method to predict changes in modal parameters of a generic structure due to the presence of passive people the method requires to accurately know the modal model of the empty structure i e natural frequencies damping ratios and mode shapes no restriction on the number of degrees of freedom of the structure is required each passive subject on the structure is modelled through his apparent mass and is introduced locally on the empty structure to obtain a model of the joint human structure system to include the apparent mass of the subjects in the model both measurements and models available in literature were used the effect of using different models of the apparent mass was investigated and the effect of using apparent masses obtained with different levels of vibration was analysed the proposed model was validated by means of experimental tests carried out on a lightly damped staircase the empty structure was first tested to obtain its modal model in order to apply the proposed approach after performing several tests with passive people standing on the structure the experimental results showed small changes of natural frequencies increase or decrease and a high increase of damping ratios due to people s presence thus the proposed approach was used to predict the above mentioned changes the measured and predicted frequency response functions natural frequencies and damping ratios were compared in all the cases taken into consideration the predicted results fitted with the experimental evidence

development of a two dimensional dynamic model of the foot ankle system exposed to vibration abstract workers in mining mills construction and some types of manufacturing are exposed to vibration that enters the body through the feet exposure to foot transmitted vibration ftv is associated with an increased risk of developing vibration induced white foot viwft viwft is a vascular and neurological condition of the lower limb leading to blanching in the toes and numbness and tingling in the feet which can be disabling for the worker this paper presents a two dimensional dynamic model describing the response of the foot ankle system to vibration using four segments and eight kelvin voigt models the parameters of the model have been obtained by minimizing the quadratic reconstruction error between the experimental and numerical curves of the transmissibility and the apparent mass of participants standing in a neutral position the average transmissibility at five locations on the foot has been optimized by minimizing the difference between experimental data and the model prediction between 10 and 100 hz the same procedure has been repeated to fit the apparent mass measured at the driving point in a frequency range between 2 and 20 hz monte carlo simulations were used to assess how the variability of the mass stiffness and damping matrices affect the overall data dispersion results showed that the 7 of freedom model correctly described the transmissibility the average transmissibility modulus error was 0 1 the error increased when fitting the transmissibility and apparent mass curves the average modulus error was 0 3 however the obtained values were reasonable with respect to the average inter participant variability experimentally estimated at 0 52 for the modulus study results can contribute to the development of materials and equipment to attenuate ftv and consequently lower the risk of developing viwft

proper incorporation of the self adjoint extension method to the green function formalism one dimensional function potential case the one dimensional function potential is discussed in the framework of the green function formalism without invoking perturbation expansion it is shown that the energy dependent green function for this case is crucially dependent on the boundary conditions which are provided by the self adjoint extension method the most general green function which contains four real self adjoint extension parameters is constructed the relation between the bare coupling constant and the self adjoint extension parameter is also derived

boundary control of the navier stokes equation by empirical reduction of modes abstract the karhunen loeve galerkin procedure is a type of galerkin methods that employs the empirical eigenfunctions of the karhunen loeve decomposition as basis functions this technique can reduce nonlinear partial differential equations to sets of minimal number of ordinary differential equations by limiting the solution space to the smallest linear subspace that is sufficient to describe the observed phenomena previously 1 it has been shown that one dimensional burgers equation is reduced to a low dimensional model by this method which is employed to solve boundary optimal control problems very efficiently the present paper demonstrates that the karhunen loeve galerkin procedure can be extended to solve problems of the boundary optimal control of multidimensional navier stokes equations since the reduction of modes in the multidimensional case is much larger than that in the one dimensional case the present technique is found to be more powerful when applied to the control problems of the navier stokes equation than those of the burgers equation

kirchhoff s rule for quantum wires we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with n open ends and where we define the hamiltonian to be minus the laplace operator with general boundary conditions at the vertices this results in a scattering theory with n channels the corresponding on shell s matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy e 0 is given explicitly in terms of the boundary conditions and the lengths of the internal lines it is shown to be unitary which may be viewed as the quantum version of kirchhoff s law we exhibit covariance and symmetry properties it is symmetric if the boundary conditions are real also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low energy behaviour of one theory gives the high energy behaviour of the transformed theory finally we provide a composition rule by which the on shell s matrix of a graph is factorizable in terms of the s matrices of its subgraphs all proofs use only known facts from the theory of self adjoint extensions standard linear algebra complex function theory and elementary arguments from the theory of hermitian symplectic forms

an efficient method of solving the navier stokes equations for flow control a new method of solving the navier stokes equations efficiently by reducing their number of modes is proposed in the present paper it is based on the karhunen loeve decomposition which is a technique of obtaining empirical eigenfunctions from the experimental or numerical data of a system employing these empirical eigenfunctions as basis functions of a galerkin procedure one can a priori limit the function space considered to the smallest linear subspace that is sufficient to describe the observed phenomena and consequently reduce the navier stokes equation defined on a complicated geometry to a set of ordinary differential equations with a minimum degree of freedom the present algorithm is well suited for the problems of flow control or optimization where one has to compute the flow field repeatedly using the navier stokes equation but one can also estimate the approximate solution space of the flow field based on the range of control variables the low dimensional dynamic model of viscous fluid flow derived by the present method is shown to produce accurate flow fields at a drastically reduced computational cost when compared with the finite difference solution of the navier stokes equation 1998 john wiley sons ltd

smooth approximation of finitely many relativistic point interactions the purpose of this paper is to show that finitely many relativistic point interactions may be approximated in the strong resolvent sense by sequences of operators with smooth potentials we consider the entire family of relativistic point interactions and determine those for which renormalization of the coupling constant occurs when the corresponding potentials are approximated by finitely many local short range perturbations of the free dirac operator

generalized local interactions in 1d solutions of quantum many body systems describing distinguishable particles as is well known there exists a four parameter family of local interactions in 1d we interpret these parameters as coupling constants of delta type interactions which include different kinds of momentum dependent terms and determine all cases leading to many body systems of distinguishable particles which are exactly solvable by the coordinate bethe ansatz we find two such families of systems one with two independent coupling constants deforming the well known delta interaction model to non identical particles and the other with a particular one parameter combination of the delta and the so called delta prime interaction we also find that the model of non identical particles gives rise to a somewhat unusual solution of the yang baxter relations for the other model we write down explicit formulae for all eigenfunctions

time dependent propagator with point interaction we compute the time dependent schrodinger propagator with a point interaction in dimension n or 3 including the new cases of n 2 and the most general interaction supported by a point for n 1 we also give the small time asymptotics for n or 3 the case n 2 has the peculiarity of involving logarithmic terms in the expansion

exact form of green functions for segmented potentials we derive the exact green functions for segmented potentials i e for potentials of the form where each has compact support the expressions depend explicitly on the wavefunctions quantum amplitudes e g transmission and reflection coefficients for the individual s we also show that the exact green functions are in fact generalizations of the usual semiclassical formula finally the possibility of applying the method to a general potential is briefly discussed

classifying the general family of 1d point interactions a scattering approach we propose a classification scheme for the complete family of 1d point interactions to do so we first review the solutions of the wavefunctions and green functions of the problem second we derive the exact time dependent propagators in such a way that we can write the expressions for the k s in a very compact form as they should such expressions do reduce to the known results in the literature according to the potential parameter values then we analyse in general terms how the different point interactions scatter off arbitrary initially localized wave packets finally we show that the physical features associated with the scattering process can be used to establish a classification procedure moreover these physical characteristics are directly related to the potential parameters leading to the many formulae for the k s as an application we present numerical calculations for gaussian wave packets

identification of the thermal conductivity and heat capacity in unsteady nonlinear heat conduction problems using the boundary element method in this study the inverse problem of the identification of temperature dependent thermal properties of a heat conducting body is investigated the solution of the corresponding direct problem is obtained using a time marching boundary element method bem which allows without any need of interpolation and solution domain discretisation efficient and accurate evaluation of the temperature everywhere inside the space time dependent domain since the inverse problem which requires the determination of the thermal conductivity and heat capacity from a finite set of temperature measurements taken inside the body possesses poor uniqueness features additional information is achieved by assuming that the thermal properties belong to a set of polynomials thus the inverse problem reduces to a parameter system estimation problem which is solved using the nonlinear least squares method convergent and stable numerical results are obtained for the finite set of parameters which characterise the thermal properties for various test examples once the thermal properties are accurately obtained then the bem determines automatically the temperature inside the solution domain and the remaining unspecified boundary values and the numerically obtained results show good agreement with the corresponding analytical solutions

reconstruction of heat transfer coefficients using the boundary element method this paper describes the reconstruction of the heat transfer coefficient space problem i or time dependent problem ii in one dimensional transient inverse heat conduction problems from surface temperature or average temperature measurements since the inverse problem posed does not involve internal temperature measurements this means that non destructive testing of materials can be performed in the formulation convective boundary conditions relate the boundary temperature to the heat flux numerical results obtained using the boundary element method are presented and discussed