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The specific objective of this study is to analyze the dynamics of functionally graded carbon nanotubes (FGCNT) reinforced double plates. Connected via an elastic layer, the plates have simply supported boundary conditions. In the current study, three carbon nanotubes functionally graded patterns, varying in the thickness direction are considered, including uniformly distributed, functionally graded O-pattern, and functionally graded X-pattern. Following the development of the coupled equations of motion using the Hamilton principle while considering the influences of the elastic layer, the equations are subsequently solved utilizing a two-spatial-variable modal decomposition method. For verification purposes, the equations developed are compared to simplified configurations provided in the existing studies. The solution methodology is verified through comparing against numerical results of simplified configurations of plates obtained from the development of the finite element method and existing studies. Both verifications have shown very good agreement. Influences of plates' dimensions, carbon nanotubes reinforcement, and the stiffness of elastic layer are analyzed and provided in this study. The transverse-motion natural frequencies of the double plates are also identified, and they follow a decreasing trend as the aspect ratio increases for all the cases. The fundamental lateral-motion and axial-motion natural frequency also follows a similar trend as the aspect ratio increases. The reinforcement effect of carbon nanotubes on the transverse-motion natural frequencies is less obvious for thinner plates. An increase in the elastic layer stiffness increases the second series transverse-motion natural frequencies of the double-plate system. Among the considered functionally graded patterns, the functionally graded X-pattern reinforcement provides the largest increase in the transverse-motion natural frequencies. [ABSTRACT FROM AUTHOR]

In this work, the nonlinear vibrations of functionally graded (FG) porous circular plates under hygro-thermal loading is studied utilizing a numerical approach. Hygroscopic stresses generated due to the nonlinear rise in moisture concentration, even and uneven porosity distributions, and temperature dependency of material properties are all taken into account. Modified Voigt's rule of mixture is applied to obtain the hygro-thermo-mechanical properties of the FG circular plate. All material properties are assumed to be temperature-dependent using the Touloukian formula. In order to obtain the equations of motion, the first-order shear deformation theory, von-Kármán geometrical non-linearity assumption, and hygro-thermal strains are considered concurrently. After deriving the equations of motion using Hamilton's principle, the differential quadrature method and the Newmark-beta time integration scheme are employed in conjunction with an iterative approach to solve the set of nonlinear governing differential equations of motion. The effects of various parameters including temperature distribution, plate's thickness, porosity volume fraction, moisture concentration, and FG index are studied on plate's maximum non-dimensional lateral deflection. [ABSTRACT FROM AUTHOR]

In this article, dynamic analysis of viscoelastic beam, which is made of porous functionally graded materials (FGM), is investigated by using the generalised differential quadrature method (GDQM). The material properties for FG beam are supposed to be graded in the thickness direction by two types of porosities and estimated using a modified power-law form. The surrounding visco-Pasternak foundation is made of viscous layer symbolised by dashpots, parallel springs and a shear layer. The governing equations achieved by Hamilton's principle are solved implementing GDQM. Afterwards, the effects of types of porosity distribution and its pattern, foundation type, power-law index, slenderness ratio, structural damping coefficient and boundary conditions on the damping frequency of the present viscoelastic FG beams are explored. [ABSTRACT FROM AUTHOR]

This study presents a novel SBFEM to model the horizontal layered bounded domain with side face load. In order to overcome the limit of original SBFEM in modelling horizontal layered domain, a novel semi-analytical technique which named as the modified SBFEM is proposed. The novel type of local coordinate system makes the original scaling centre replace by scaling line. It is more suitable for the horizontal layered model analysis. The coordinate transformation is greatly reduced by using scaling line. Basing on the principle of virtual work, the modified SBFEM displacement equation is derived. Firstly, the displacement differential equation is transformed into state equation in Hamilton system. The displacement and stress of layered bounded domain can be obtained by one time. As well as making the modified SBFEM more accessible, a new technique for the treatment of side face load is provided. Furthermore, basing on the novel side face load formulation, the displacement and stress expressions for layered bounded domain can be built. The paper fully develops the new formulations, and provides numerical examples to illustrate the accuracy and efficiency of the modified SBEFM. More importantly, the complex side face form and anisotropic material are considered. It significantly extends the application field of the modified SBFEM in solving elastostatic problem. [ABSTRACT FROM AUTHOR]

In this article, an accurate mixed zigzag theory (HZZTM) is proposed for free vibration analysis of laminated composite and sandwich plates. In-plane displacements in the proposed zigzag theory nonlinearly distribute through the thickness and exhibit an abrupt discontinuity of slope at interfaces, which coincide with three-dimensional analysis. In order to obtain the accurate transverse shear stresses, a preprocessing approach based on the three-dimensional (3D) equilibrium equations and the Reissner mixed variational theorem (RMVT) is used. It is significant that the second-order derivatives of in-plane displacement variables have been removed from the transverse shear stress fields, such that the finite element implementation is greatly simplified. Thus, based on the proposed zigzag model, a computationally efficient C0-type three-node triangular plate element with linear interpolation function is proposed for free vibration analysis of thick laminated composite and sandwich plates. Moreover, the accurate transverse shear stresses are introduced in the dynamic equilibrium equation by employing the Hamilton's principle, which can actively improve the accuracy of natural frequencies of the laminated composite plates with different thickness and material properties at each ply. Performance of the proposed model is assessed by comparing with several benchmark solutions. Agreement between the present results and the reference solutions is very good, and the proposed model only includes the seven displacement variables which can demonstrate the accuracy and effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, imperfect multi-item production inventory models are considered over a finite time horizon with known dynamic demands. The production rates are functions of time which are taken as control variables. In the production process, reliability plays an important role to improve the quality of products and to decrease the defective rate. The said defective units are partially or fully reworked. The unit production cost is a function of production rate and also dependent on raw material cost, development cost due to reliability and wear-tear cost. There is a constraint on the total production cost termed as budget constraint which is crisp/imprecise/random in nature. The objective of the present investigation is to fix the optimum reliabilities of the production system to have maximum return. Thus, the models are formulated as optimal control problems for the maximisation of profit and solved using Hamiltonian (Pontryagin’s Maximum Principle), fixed-final time and free-final state system, Kuhn–Tucker conditions and Generalised Reduced Gradient Method. Several particular cases are derived from the general model. The models are illustrated numerically and graphically and some managerial decisions are derived. [ABSTRACT FROM PUBLISHER]

We consider the perturbed sine-Gordon equation θ t t − θ x x + sin ⁡ θ = ε 2 f (ε x) , where the external perturbation ε 2 f (ε x) is small and slowly varying. We show that the initial value problem with an appropriate initial state close enough to the solitary manifold has a unique solution, which follows up to time 1 / ε and errors of order ε 3 / 4 a trajectory on the solitary manifold. The trajectory on the solitary manifold is described by ODEs, which agree up to errors of order ε 3 with Hamilton equations for the restricted to the solitary manifold sine-Gordon Hamiltonian. [ABSTRACT FROM AUTHOR]

This paper analyses the properties of the solutions of the generalized continuous algebraic Riccati equation from a geometric perspective. This analysis reveals the presence of a subspace that may provide an appropriate degree of freedom to stabilize the system in the related optimal control problem even in cases where the Riccati equation does not admit a stabilizing solution. [ABSTRACT FROM AUTHOR]

In the present paper, nonlocal couple stress theory is developed to investigate free vibration characteristics of functionally graded (FG) nanobeams considering exact position of neutral axis. The theory introduces two parameters based on nonlocal elasticity theory and modified couple stress theory to capture the size effects much accurately. Therefore, a nonlocal stress field parameter and a material length scale parameter are used to involve both stiffness-softening and stiffness-hardening effects on responses of FG nanobeams. The FG nanobeam is modeled via a higher-order refined beam theory in which shear deformation effect is verified needless of shear correction factor. A power-law distribution is used to describe the graded material properties. The governing equations and the related boundary conditions are derived by Hamilton's principle and they are solved applying Galerkin's method, which satisfies various boundary conditions. A comparison study is performed to verify the present formulation with the provided data in the literature and a good agreement is observed. The parametric study covered in this paper includes several parameters, such as nonlocal and length scale parameters, power-law exponent, slenderness ratio, shear deformation, and various boundary conditions on natural frequencies of FG nanobeams in detail. [ABSTRACT FROM AUTHOR]

This article focuses on the coupled vibration characteristics of a spinning and axially moving composite thin-walled beam. Dynamic equations of the coupled vibration problem are built by Hamilton's principle. Galerkin's method is employed to solve the equations. The combined effects of spinning angular speeds and axial speeds on natural frequencies of the beam are studied specifically. Some interesting conclusions about the critical axial speed and critical spinning angular speed are proposed. Numerical simulations are performed to discuss the influences of spinning angular speeds, axial speeds, length- and thickness-to-radius ratios and fiber orientation angles on vibration characteristics of the beam. [ABSTRACT FROM AUTHOR]

Stan is a flexible probabilistic programming language providing full Bayesian inference through Hamiltonian Monte Carlo algorithms. The benefits of Hamiltonian Monte Carlo include improved efficiency and faster inference, when compared to other MCMC software implementations. Users can interface with Stan through a variety of computing environments, including R, Python, MATLAB, Stata, and Mathematica. Programs written in Stan are portable across these interfaces, encouraging collaboration and transparency. These benefits, and others, offer several advantages for measurement practitioners; this review uses a simple example of Stan for a two-parameter logistic IRT model to illustrate the utility of Stan and its relevant features. [ABSTRACT FROM AUTHOR]

In this paper we prove the persistence of lower dimensional invariant tori for a class of reversible systems without any non-degeneracy condition. In the proof, we use the special nature that the dimension of the frequency ω is 2 and the modified KAM iteration to prove the persistence of lower dimensional hyperbolic invariant tori, but the frequency has some small shifts from small perturbations. [ABSTRACT FROM PUBLISHER]

In this paper, we study the algebraic connectivity of a Hamiltonian graph, and determine all Hamiltonian graphs whose algebraic connectivity attain the minimum among all Hamiltonian graphs onnvertices. [ABSTRACT FROM AUTHOR]

Within the framework of the scattering matrix formalism, the nonlinear Kubo theory for electron transport in the metal with a tunnel barrier has been considered. A general expression for the mean electrical current was obtained. It significantly simplifies the calculation of nonlinear contributions to the conductivity of various hybrid structures. In the model of the tunnel Hamiltonian, all linear and nonlinear contributions to a mean electrical current are evaluated. The linear approximation agrees with results of other theories. For effective barrier transmission, the ballistic transport is realised with a value of the Landauer conductivity equal to. [ABSTRACT FROM PUBLISHER]

This paper explores an efficient energy-preserving scheme for the coupled nonlinear Schrödinger system with emphasis on preserving the Hamiltonian structure based on the weak formulation of the system. First, the Schrödinger system is discretized in spatial direction by the Galerkin spectral element method, and the resulting semi-discrete system is rewritten as a finite-dimensional canonical Hamiltonian system. Second, we apply the energy method to discretize the resulting ordinary differential equations in time direction and obtain an efficient conservative scheme. Using the energy method, an error estimate without any restriction on the grid ratio is derived, and the new scheme is convergent with the orderin the discrete-norm, whereτandhdenote the time and the space steps, respectively. Finally, comprehensive numerical results including comparisons with the semi-explicit multi-symplectic Euler-box and the Crank–Nicolson finite difference method are given to illustrate the superiority of the proposed energy-preserving scheme. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal decision problems for a class of dynamic joint promotions in the distribution channel. Here, the evolution of brand goodwill is allowed to be influenced by vertical joint promotions (VJP) and horizontal joint promotions (HJP). By applying the Hamilton-Jacobi-Bellman (HJB) equation, the optimal VJP and HJP strategies, the wholesale prices and the VJP participation rates are obtained under the Decentralized-Decentralized (DD) and Decentralized-Centralized (DC) channel structures, respectively. The comparison between the two channel structures shows that channel members are inclined to take the DC channel structure when HJP's impact factor θ is no less than a given constant. Finally, two numerical examples are given to show the changes of manufacturers' and retailers' profits with η under the different channel structures. [ABSTRACT FROM AUTHOR]

The static-dynamic-static multi-state multi-reference second-order perturbation theory (SDS-MS-MRPT2 or SDSPT2 in short), which employs a multi-partitioned (state-dependent) Møller–Plesset-like diagonal operator for the zeroth-order Hamiltonian and individual configuration state functions for the perturbers, is reconsidered by making use of the state-universal Dyall Hamiltonian for the zeroth-order Hamiltonian and the union of spin-adapted, internally contracted basis functions generated from all the reference functions for the perturbers. The graphical unitary group approach along with particle–hole correspondence is employed in the evaluation of Hamiltonian matrix elements. This particular variant of SDSPT2 can also be regarded as an extension of the spin-adapted, partially contracted variant of NEVPT2 (n-electron valence state second-order perturbation theory). The performance of SDSPT2 is examined by taking C2, LiF, and Fe(C5H5)2as examples. The results show that the low-lying states of the systems can be obtained very accurately. [ABSTRACT FROM PUBLISHER]

In this paper, we propose an averaged vector field Legendre spectral element (AVFLSE) method for the nonlinear Schrödinger (NLS) equation. The key idea is to rewrite the NLS equation as an infinite-dimensional Hamiltonian PDE and discrete the Hamiltonian PDE by using the Legendre spectral element (LSE) method in space and an averaged vector field (AVF) method in time. We show that applying a Galerkin method to Hamiltonian PDEs in space can lead to a semi-discrete system which can be cast into Hamiltonian ODEs. For the NLS equation, the concrete canonical form of the resulting Hamiltonian ODEs is presented. This methodology can ensure that the structure matrix of the resulting Hamiltonian ODEs is sparse and the full discrete scheme for the Hamiltonian PDEs is an energy-preserving, unconditionally linearly stable and symmetric method. With the aid of cut-off technique, we also derive the error estimate and the new method turns out to be convergent with the convergence order ofin the discrete-norm with the exact solution, whereNis the order of the Legendre cardinal basis functions. Numerical experiments are provided to demonstrate the energy-preserving property and the convergence behaviour of the method. [ABSTRACT FROM AUTHOR]

We consider in the whole plane the following Hamiltonian coupling of Schrödinger equationswhereV0>0,f,ghave critical growth in the sense of Moser. We prove that the (nonempty) setSof ground-state solutions is compact inup to translations. Moreover, for each (u,v)∈S, one has thatu,vare uniformly bounded inand uniformly decaying at infinity. Then we prove that actually the ground state is positive and radially symmetric. We apply those results to prove the existence of semiclassical ground-state solutions to the singularly perturbed systemwhereV∈𝒞(ℝ2) is a Schrödinger potential bounded away from zero. Namely, as the adimensionalized Planck constant𝜀→0, we prove the existence of minimal energy solutions which concentrate around the closest local minima of the potential with some precise asymptotic rate. [ABSTRACT FROM AUTHOR]

The travelling salesman problem (TSP) asks for a shortest tour through all vertices of a graph with respect to the weights of the edges. The symmetric quadratic travelling salesman problem (SQTSP) associates a weight with every three vertices traversed in succession. If these weights correspond to the turning angles of the tour, we speak of the angular-metric travelling salesman problem (Angle TSP). In this paper, we first consider the SQTSP from a computational point of view. In particular, we apply a rather basic algorithmic idea and perform the separation of the classical subtour elimination constraints on integral solutions only. Surprisingly, it turns out that this approach is faster than the standard fractional separation procedure known from the literature. We also test the combination with strengthened subtour elimination constraints for both variants, but these turn out to slow down the computation. Secondly, we provide a completely different, mathematically interesting MILP linearization for the Angle TSP that needs only a linear number of additional variables while the standard linearization requires a cubic one. For medium-sized instances of a variant of the Angle TSP, this formulation yields reduced running times. However, for larger instances or pure Angle TSP instances, the new formulation takes more time to solve than the known standard model. Finally, we introduce MaxSQTSP, the maximization version of the quadratic travelling salesman problem. Here, it turns out that using some of the stronger subtour elimination constraints helps. For the special case of the MaxAngle TSP, we can observe an interesting geometric property if the number of vertices is odd. We show that the sum of inner turning angles in an optimal solution always equals. This implies that the problem can be solved by the standard ILP model without producing any integral subtours. Moreover, we give a simple constructive polynomial time algorithm to find such an optimal solution. If the number of vertices is even, the optimal value lies between 0 andand these two bounds are tight, which can be shown by an analytic solution for a regularn-gon. [ABSTRACT FROM AUTHOR]

The spin-Hamiltonian parameters (g-factorsg//,g⊥and hyperfine structure constantsA//,A⊥) of the square-planar CuS6 −4clusters in Cu(II)–bis [4-ethoxphenyl-O-alkyl]-dithiophosphonate complexes are computed with the high-order perturbation formulas based on the two-mechanism model. The model includes the contributions to spin-Hamiltonian parameters from the vastly-utilised crystal-field (CF) mechanism concerning the CF excited states and the generally-omitted charge-transfer (CT) mechanism due to CT excited states. The energy levels of CF and CT excited states needed in the calculation are obtained from the observed optical spectra. The calculated results are in rational accordance with the experimental values. The signs of constantsA//andA⊥are suggested and the reasons of the very smallg-shifts |∆gi| (= |gi−ge|, wherege≈ 2.0023 andi= // or ⊥) are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we establish some sufficient conditions for a graph to be Hamilton-connected in terms of the edge number, the spectral radius and the signless Laplacian spectral radius of the graph. Furthermore, we also give some sufficient conditions for a graph to be traceable from every vertex in terms of the edge number, the spectral radius and the signless Laplacian spectral radius. [ABSTRACT FROM PUBLISHER]

In this article we use the Lagrange multiplier method, which is well-known in constrained optimization theory, to derive several different Hamiltonian counterparts to Lagrangian systems described by partial differential equations in a variational setting. The main observation is the fact that unconstrained, infinite-dimensional systems can be formulated as constrained variational problems, where the constraints are used to hide some or all derivative variables appearing in the Lagrangian. Depending on the chosen derivative variables that are affected by this approach, different representations of the same dynamical system can be achieved. These theoretical investigations will be applied to a demonstrative example from mechanics. [ABSTRACT FROM PUBLISHER]

We prove that suspended robust heterodimensional cycles and suspended robust homoclinic tangencies can be found arbitrarily close to any non-degenerate bifocal homoclinic orbit of a Hamiltonian vector field. In order to achieve this result, we show that any diffeomorphism with a saddle-node periodic point, which has both quasi-transversal and tangential strong homoclinic intersections, can be approximated by diffeomorphisms with both, robust homoclinic tangencies and a robust heterodimensional cycles. As explained in the paper, Hamiltonian vector fields with non-degenerate bifocal homoclinic orbits are exhibited in the limit family of any generic unfolding of a four-dimensional nilpotent singularity of codimension four. Supported by the achieved results, we conjecture that suspended robust cycles can be generically unfolded from such singularities. [ABSTRACT FROM PUBLISHER]

An ongoing challenge in the analysis of document collections is how to summarize content in terms of a set of inferredthemesthat can be interpreted substantively in terms of topics. The current practice of parameterizing the themes in terms of most frequent words limits interpretability by ignoring the differential use of words across topics. Here, we show that words that are both frequent and exclusive to a theme are more effective at characterizing topical content, and we propose a regularization scheme that leads to better estimates of these quantities. We consider a supervised setting where professional editors have annotated documents to topic categories, organized into a tree, in which leaf-nodes correspond to more specific topics. Each document is annotated to multiple categories, at different levels of the tree. We introduce a hierarchical Poisson convolution model to analyze these annotated documents. A parallelized Hamiltonian Monte Carlo sampler allows the inference to scale to millions of documents. The model leverages the structure among categories defined by professional editors to infer a clear semantic description for each topic in terms of words that are both frequent and exclusive. In this supervised setting, we validate the efficacy of word frequency and exclusivity at characterizing topical content on two very large collections of documents, fromReutersand theNew York Times. In an unsupervised setting, we then consider a simplified version of the model that shares the same regularization scheme with the previous model. We carry out a large randomized experiment on Amazon Mechanical Turk to demonstrate that topic summaries based on frequency and exclusivity, estimated using the proposed regularization scheme, are more interpretable than currently established frequency-based summaries, and that the proposed model produces more efficient estimates of exclusivity than the currently established models. [ABSTRACT FROM AUTHOR]

We consider a one-parameter family of nonlinear coherent states by replacing the factorial in coefficientsof the canonical coherent states by a specific generalized factorial,These states are superposition of eigenstates of the Hamiltonian with a symmetric Pöschl–Teller potential depending on a parameter. The associated Bargmann-type transform is defined for. Some results on the infinite square well potential are also derived. For some different values ofγ, we discuss two sets of orthogonal polynomials that are naturally attached to these coherent states. [ABSTRACT FROM PUBLISHER]

The study investigated the influence of square electric-field pulses with random fluctuation on the state dynamics of InAs/GaAs double quantum dots (DQDs) charge qubits. The DQDs were proposed as a charge qubit under operation by a finite number of sequent square pulses of electric field, whose amplitude varied from −0.3 to 0.3 [mV/A°] with random fluctuation at various frequencies. Moreover, for a fixed period of a single pulse, the operation time can also have fluctuation. The state dynamics were analyzed by modelling the DQDs as a two-level quantum system with the effective Hamiltonian and solving the time-dependent Schrödinger equation with the fourth-order Runge-Kutta method using modelling parameters obtained by interpolating results from the tight-binding calculation. Without fluctuation, the state dynamics depicted on the Bloch sphere showed that the states can have different phases, while the probability profiles remain roughly the same with varying electric field strength. When the square pulses were added with uniform random fluctuations in amplitude of the electric field, it was found that the mean state dynamics remained close to that without fluctuation, and the standard deviation of the occupancy probability profiles was proportional to that of the random fluctuation. For fluctuations in operation time, such proportionality does not exist, and the effects on the standard deviation were more pronounced. By comparing the occupancy probability profiles with that without fluctuation, the accuracy of the averaged probability profiles is not monotonic, depending on the fluctuation strength, but there exist some moments in operation time when the profiles are close to the mean dynamics, for both types of fluctuations. [ABSTRACT FROM PUBLISHER]

The use of beams and similar structural elements is finding increasing application in many areas including micro and nanotechnology devices. For the purpose of buckling analysis and control, it is essential to account for nonlinear terms in the strains while modelling these flexible structures. Further, the Poisson’s effect can be accounted in modelling by the use of a two-dimensional stress–strain relationship. This paper studies the buckling effect for a slender, vertical beam (in the clamped-free configuration) with horizontal actuation at the fixed end and a tip-mass at the free end. Including also the inextensibility constraint of the beam, the equations of motion are derived. A preliminary modal analysis of the system has been carried out to describe candidate post-buckling configurations and study the stability properties of these equilibria. The vertical configuration of the beam under the action of gravity is without loss of generality, since the objective is to model a potential field that determines the equilibria. Neglecting the inextensibility constraint, the equations of motion are then casted in port-Hamiltonian form with appropriately defined flows and efforts as a basis for structure-preserving discretization and simulation. Finally, the finite-dimensional model is simulated to obtain the time response of the tip-mass for different loading conditions. [ABSTRACT FROM AUTHOR]

A salient feature of de Broglie-Bohm (dBB) quantum theory is that particles have determinate positions at all times and in all physical contexts. Hence, the trajectory of a particle is a well-defined concept. One then may expect that the closely related notion of inertial trajectory is also unproblematically defined. I show that this expectation is not met. I provide a framework that deploys six different ways in which dBB theory can be interpreted, and I state that only in the canonical interpretation the concept of inertial trajectory is the customary one. However, in this interpretation the description of the dynamical interaction between the pilot-wave and the particles, which is crucial to distinguish inertial from non-inertial trajectories, is affected by serious difficulties, so other readings of the theory intend to avoid them. I show that in the alternative interpretations the concept at issue gets either drastically altered, or plainly undefined. I also spell out further conceptual difficulties that are associated to the redefinitions of inertial trajectories, or to the absence of the concept. [ABSTRACT FROM AUTHOR]

The accurate estimation of the excess free energy due to an interface between coexisting phases of a model system by computer simulation often is a challenging task. We review here two methods, which rely on constructing paths between a system containing a ‘slab’ of one phase separated by two planar interfaces from the other phase, and a system (with the same total volume) without interfaces. Studying such a system with a slab geometry, it is natural to choose a rectangular geometry(indimensions), whereis the direction perpendicular to the interfaces, and periodic boundary conditions are applied throughout. Since interfaces exhibit large-scale fluctuations, a careful analysis of finite-size effects is mandatory. In the ensemble switch method, an intermediate Hamiltonian is constructed, adding the Hamiltonian of a system with interfaces, multiplied by a fraction, to an equivalent system without interfaces, with fraction. Addingto the state variables of the system, a thermodynamic integration fromtoyields the desired interfacial free energy. While intermediate states (with) lack immediate physical meaning, the alternative method discussed here relies on sampling the probability distribution, whereis a suitable physical order parameter distinguishing the phases. Advantages and disadvantages of both methods are discussed, using Ising models, Lennard-Jones fluids and the solid-to-liquid transition of the hard sphere model as examples. [ABSTRACT FROM AUTHOR]

A treatment of a chemical reaction network theory is given from the perspective of nonlinear network dynamics, in particular of consensus dynamics. By starting from the complex-balanced assumption, the reaction dynamics governed by mass action kinetics can be rewritten into a form which allows for a very simple derivation of a number of key results in the chemical reaction network theory, and which directly relates to the thermodynamics and port-Hamiltonian formulation of the system. Central in this formulation is the definition of a balanced Laplacian matrix on the graph of chemical complexes together with a resulting fundamental inequality. This immediately leads to the characterisation of the set of equilibria and their stability. Furthermore, the assumption of complex balancedness is revisited from the point of view of Kirchhoff's matrix tree theorem. Both the form of the dynamics and the deduced behaviour are very similar to consensus dynamics, and provide additional perspectives to the latter. Finally, using the classical idea of extending the graph of chemical complexes by a ‘zero’ complex, a complete steady-state stability analysis of mass action kinetics reaction networks with constant inflows and mass action kinetics outflows is given, and a unified framework is provided for structure-preserving model reduction of this important class of open reaction networks. [ABSTRACT FROM AUTHOR]

In this paper, we report vibrational energy levels of some tetraphenylporphyrins and its cation radicals, i.e. Cu[TPP], Cu[TPP]+, Ni(TPP), Ni(TPP)+, ClFe(TPP) and ClFe(TPP)+using U(2) algebraic model Hamiltonian. In our study, we have used five fitting parameters which provide better comparisons between the experimental and theoretical calculations throughout the study. RMS deviation has been improved in this paper due to the inclusion of intermode couplings in algebraic model. Structure of metalloporphyrins In our work, we study the spectroscopic features of some biomolecules using Lie algebraic methods. This will be sought to be accomplished by studying the different vibrational energy levels as function of vibrational quantum numbers for certain biomolecules. Possibilities of local-to-normal transition in viable cases will be taken into consideration. In addition, new vibrational parameters for certain biomolecules will be sought to be identified for cases where Lie algebraic approach has not been initiated. The Lie algebraic study may as well be useful in interpreting the vibrational spectra of proteins and other biological systems. [ABSTRACT FROM AUTHOR]

In this paper we develop a time-independent approach for the study of the spectral shift function (SSF for short). We apply this method for the perturbed Stark Hamiltonian. We obtain a weak and a Weyl-type asymptotics with optimal remainder estimate of the SSF of the operator pair (P = P0 + V(x),P0 = − h2Δ +x1),x = (x1,…,xn) whereV(x) ∈ 𝒞∞(ℝn, ℝ) decays sufficiently fast at infinity, andhis a small positive parameter. Near a non-trapping energy λ, we give a pointwise asymptotic expansions in powers ofhof the derivative of the SSF, and we compute explicitly the two leading terms. [ABSTRACT FROM AUTHOR]

A perturbative analysis of the ground-state similarity transformed Hamiltonian and its effect on the various Fock-space coupled cluster (FSCC) sectors is presented through calculation of ionisation potential, electron affinity, excitation energies and response properties. Various truncation schemes of the effective Hamiltonian are presented with explicit form of the defining equations. Based on such a truncation, the approximate methods are labelled as FSCC(n), wherenrepresents the correlation energy of the ionised, electron attached or excited states corrected at least up tonth order within coupled cluster singles and doubles scheme (CCSD). A lower scaling CC2 type of approach (abbreviated as FS-CC2) is compared against the group of FSCC(n) methods for energies. Electric response properties have been compared and contrasted for the two lower scaling methods: FSCC(2) and FS-CC2. The various truncated methods are tested for a number of small molecules. The results obtained from a range of truncated methods are compared against full FSCCSD calculations. [ABSTRACT FROM PUBLISHER]

An examination is made of the way in which the kinetic energy operator for internal motion alone is commonly constructed in molecular quantum mechanics. It is shown that some care needs to be taken to specify the precise conditions under which the form of the operator so obtained is a valid form. Particular care is needed in constructing a reaction path Hamiltonian. [ABSTRACT FROM PUBLISHER]

The article focuses on a study on similarity between Combinatorics and Differential Geometry by mathematicians including Francis C. Motta, Patrick D. Shipman and Bethany Springer. Topics discussed includes de Bruijn sequence, Hamiltonian path, Eulerian graphs, Epicycloids and asymptomatic tangency of de Bruijn edges to Epicycloids.

The study presents a formulation on the basis of Hamilton’s principle and solution for the problem of damped vibration in hydraulic cylinders. The physical model took into consideration the energy dissipation in a vibrating cylinder as a result of external viscous damping and internal damping of viscoelastic material in beams used to construct a model of a cylinder (rheological model by Kelvin–Voigt). Constructional damping in the points of the cylinder connection with the components of the basic structure was also considered. The example computation was made for a cylinder used in a mining prop. The results of the computations concern the determination of the relationships between the first eigenvalue of transverse vibration in the cylinder and its extension length with two values of load and determination of the amplitude decay factor for the first and the second eigenvalue versus the extension length. Furthermore, the study also focused on determination of the relationships between the amplitude decay factor of the first and second mode of vibration for a particular length of the cylinder. [ABSTRACT FROM PUBLISHER]

In this addendum note we fill in the gap left in the description of 2D homogeneous solutions to the stationary Euler system initiated in the previous publication. This completes the classification of all homogeneous stationary solutions. The note includes updated classification tables. [ABSTRACT FROM AUTHOR]

The Complex Absorbing Potential (CAP) method is widely used to compute resonances in quantum chemistry, both for nonrelativistic and relativistic Hamiltonians. In the semiclassical limit ℏ → 0 we consider resonances near the real axis and we establish the CAP method rigorously for the perturbed Dirac operator by proving that individual resonances are perturbed eigenvalues of the nonselfadjoint CAP Hamiltonian, and vice versa. The proofs are based on pseudodifferential operator theory and microlocal analysis. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish existence and uniqueness of time almost periodic viscosity solutions to first-order evolution equations in Carnot groups. [ABSTRACT FROM AUTHOR]

Based on the higher order shear deformation theory and the Hamilton principle, this article derives the equations to govern the displacement and electric potential of smart functionally graded (FG) circular cylindrical panels with surface embedded on actuator and sensor layers. The analytical solution considering simply supported boundary conditions is based on the Navier solution procedure. Negative velocity feedback control is used. Numerical results show the influence of (a) different volume fractions of FG material layer, (b) different temperature change of inner surface, (c) different central angle of circular cylindrical panels, (d) different piezoelectric material (PZT-4, BaTiO3, PZT-5A), on the vibration characteristics of smart FG circular cylindrical panels in thermal environmental. [ABSTRACT FROM PUBLISHER]

A semi-analytical solution based on the modified H-R (Hellinger-Reissner) variational principle and a nonlinear spring-layer model is presented to analyze the free vibration problem of laminates with a delamination in the Hamilton system. This nonlinear spring-layer model between the upper and lower sub-laminates ensures the exact continuous transverse stresses and displacements in the un-delaminated region by specifying the infinite values of springs and avoids the possibility of penetration phenomenon in the delaminated region. As an application of this method, the influence of the delamination size, depth, and boundary conditions on the first three natural frequencies of delaminated composite laminates is investigated. [ABSTRACT FROM PUBLISHER]

Quaternions, objects consisting of a scalar and a vector, sound like a mysterious concept from the past. In the nineteenth century, the theory of quaternions was praised as one of the most brilliant achievements in mathematical physics. The originator of this theory, Hamilton, surely one of the greatest scientists in that area, spent about 18 years in discussing all kinds of algebraic and geometric properties of quaternions. His research was communicated to the Philosophical Magazine in three series of papers comprising a total of 29 contributions. In this commentary, these three series of papers are revisited concentrating primarily on the algebraic properties of quaternions. [ABSTRACT FROM PUBLISHER]

Variational non-relativistic calculations are performed for the four lowest Rydberg2Fstates (1s2nf,n= 4, … , 7) of the main isotope of the lithium atom (7Li). The finite-nuclear-mass approach is employed and the wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian function. A total of 140 Gaussians are used for each state. The calculated relative energy of the two lowest states is compared with the experimental value, which is the only value available in the literature. The two results agree within a few wavenumbers. [ABSTRACT FROM AUTHOR]

The recently developed method designed to perform calculations for the double electron attached (DEA) states has been applied to study potential energy curves (PECs) for the ground and excited states of the NaLi molecule. The method is based on the multireference coupled cluster scheme formulated in the Fock space (FS) formalism for the (2,0) sector. To avoid the intruder state problems, the FS approach is realised within the framework of the intermediate Hamiltonian which generates an efficient size-extensive computational scheme. The DEA calculations can be applied to the double ionised system and then they provide results describing the neutral molecule. This is particularly advantageous in the studies of the PECs for the cases when the closed-shell molecule dissociates into open-shell fragments, but its double positive ion generates closed-shell parts. We used this strategy in the current work to generate the PECs for the ground and excited states of the NaLi molecule. In all cases, we were able to compute the smooth PECs for the whole range of interatomic distances from the equilibrium to the dissociation limit. In addition, spectroscopic characteristics of various electronic states are presented. [ABSTRACT FROM AUTHOR]

In this contribution, we pay tribute to the scientific achievements of Professor Rodney J. Bartlett on account of his seminal contributions to the many-body electron correlation problem. We are here concerned with strongly correlated situations as met in the theory of superconductivity. In condensed matter physics, one often makes use of the famous Bardeen–Cooper–Schrieffer (BCS) formulation, while quantum chemists often instigate an approach that originates in Yang's concept of off-diagonal long-range order (ODLRO), and the Coleman–Sasaki extreme state. Our aim is to demonstrate that both approaches are essentially equivalent by deriving the BCS gap equation from the assumption of the presence of ODLRO. [ABSTRACT FROM AUTHOR]

The article offers information on proving that a Hamiltonian cycle on the faces of an Archimedean solid is twisting free. Topics include exploring a continuous analogue on the unit sphere, defining an Archimedean solid as a vertex transitive three-dimensional polyhedron whose faces are regular polygons and use of the Gauss-Bonnet theorem for the proof.