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A class of left bialgebroids whose underlying algebra A ♯ H is a smash product of a bialgebra H with a braided commutative Yetter–Drinfeld H -algebra A has recently been studied in relation to models of field theories on noncommutative spaces. In Borowiec and Pachoł (2017 J. Phys. A: Math. Theor. 50 055205) a proof has been presented that the bialgebroid A F ♯ H F where HF and AF are the twists of H and A by a Drinfeld 2-cocycle F = ∑ F 1 ⊗ F 2 is isomorphic to the twist of bialgebroid A ♯ H by the bialgebroid 2-cocycle ∑ 1 ♯ F 1 ⊗ 1 ♯ F 2 induced by F. They assume H is quasitriangular, which is reasonable for many physical applications. However the proof and the entire paper take for granted that the coaction and the prebraiding are both given by special formulas involving the R-matrix. There are counterexamples of Yetter–Drinfeld modules over quasitriangular Hopf algebras which are not of this special form. Nevertheless, the main result essentially survives. We present a proof with a general coaction and the correct prebraiding, and even without the assumption of quasitriangularity. [ABSTRACT FROM AUTHOR]

The authors replies to the comment made by Yang and Zhou (2024 J. Phys. A: Math. Theor.) on his 2015 paper entitled 'Critical points of Potts and O(N) models from eigenvalue identities in periodic Temperley–Lieb algebras' (Jacobsen 2015 J. Phys. A: Math. Theor. 48 454003). [ABSTRACT FROM AUTHOR]

In 1989 Mason and Newman (Commun. Math. Phys. 121 659–68) proved that there is a 1-1-correspondence between self-dual metrics satisfying Einstein vacuum equation (in complex case or in neutral signature) and pairs of commuting parameter depending vector fields X 1 (λ) , X 2 (λ) which are divergence free with respect to some volume form. Earlier Plebański (1975 J. Math. Phys. 16 2395–402) showed instances of such vector fields depending of one function of four variables satisfying the so-called I or II Plebański heavenly PDEs. Other PDEs leading to Mason–Newman vector fields are also known in the literature: Park (1992 Int. J. Mod. Phys. A 7 1415), Husain (1994 Phys. Rev. Lett. 72 800), Grant (1993 Phys. Rev. D 48 2606–12), Schief (Phys. Lett. A 223 55–62). In this paper we discuss these matters in the context of the web theory, i.e. theory of collections of foliations on a manifold, understood from the point of view of Nijenhuis operators. In particular we show how to apply this theory for constructing new 'heavenly' PDEs based on different normal forms of Nijenhuis operators in 4D, which are integrable similarly to their predecessors. Relation with the Hirota dispersionless systems of PDEs and the corresponding Veronese webs, which was recently observed by Konopelchenko–Schief–Szereszewski, is established in all the cases. We also discuss some higher dimensional generalizations of the 'heavenly' PDEs and the existence of related vacuum Einstein metrics in 4D-case. [ABSTRACT FROM AUTHOR]

In the paper, we are concerned with the nonlinear Cauchy problem on the Vlasov–Poisson–Landau/Boltzmann system around global Maxwellians in a torus or a finite channel. The main goal is to establish the global existence and large time behaviour of small amplitude solutions for a class of low regularity initial data. The molecular interaction type is restricted to the case of hard potentials for two classical collision operators because of the effect of the self-consistent forces. The result extends the one by Duan–Liu–Sakamoto-Strain (Duan et al 2021 Commun. Pure Appl. Math. 74 932–1020) for the pure Landau/Boltzmann equation to the case of the VPL and VPB systems. [ABSTRACT FROM AUTHOR]

In this paper, we present the construction of all nonstandard integrable systems in magnetic fields whose integrals have leading order structure corresponding to the case (i) of theorem 1 in Marchesiello and Šnobl (2022 J. Phys. A: Math. Theor. 55 145203). We find that the resulting systems can be written as one family with several parameters. For certain limits of these parameters the system belongs to intersections with already known standard systems separating in Cartesian and / or cylindrical coordinates and the number of independent integrals of motion increases, thus the system becomes minimally superintegrable. These results generalize the particular example presented in section 3 of Marchesiello and Šnobl (2022 J. Phys. A: Math. Theor. 55 145203). [ABSTRACT FROM AUTHOR]

It is well-known that any Lennard–Jones type potential energy must have a periodic ground state given by a triangular lattice in dimension 2. In this paper, we describe a computer-assisted method that rigorously shows such global minimality result among 2-dimensional lattices once the exponents of the potential have been fixed. The method is applied to the widely used classical (12 , 6) Lennard–Jones potential, which is the main result of this work. Furthermore, a new bound on the inverse density (i.e. the co-volume) for which the triangular lattice is minimal is derived, improving those found in (Bétermin and Zhang 2015 Commun. Contemp. Math. 17 1450049) and (Bétermin 2016 SIAM J. Math. Anal. 48 3236–3269). The same results are also shown to hold for other exponents as additional examples and a new conjecture implying the global optimality of a triangular lattice for any parameters is stated. [ABSTRACT FROM AUTHOR]

In this paper, the initial-boundary value problem of the one-dimensional full compressible Navier–Stokes equations with positive constant viscosity but with zero heat conductivity is considered. Global well-posedness is established for any H1 initial data. The initial density is assumed only to be nonnegative, and, thus, is not necessary to be uniformly away from vacuum. Comparing with the well-known result of Kazhikhov and Shelukhin (1977 J. Appl. Math. Mech. 41 273–282), the heat conductive coefficient is zero in this paper, and the initial vacuum is allowed. [ABSTRACT FROM AUTHOR]

In this paper, we consider a Levenbergâ€"Marquardt method with general regularization terms that are uniformly convex on bounded sets to solve the ill-posed inverse problems in Banach spaces, where the forward mapping might not Gâteaux differentiable and the image space is unnecessarily reflexive. The method therefore extends the one proposed by Jin and Yang in (2016 Numer. Math. 133 655â€"684) for smooth inverse problem setting with globally uniformly convex regularization terms. We prove a novel convergence analysis of the proposed method under some standing assumptions, in particular, the generalized tangential cone condition and a compactness assumption. All these assumptions are fulfilled when investigating the identification of the heat source for semilinear elliptic boundary-value problems with a Robin boundary condition, a heat source acting on the boundary, and a possibly non-smooth nonlinearity. Therein, the Clarke subdifferential of the non-smooth nonlinearity is employed to construct the family of bounded operators that is a replacement for the non-existing Gâteaux derivative of the forward mapping. The efficiency of the proposed method is illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

Let us say that a three-qubit state u 000|000âź© + u 001|001âź© + â‹Ż + u 111|111âź© is real if all its amplitudes u rst are real numbers. We will prove that for every real three-qubit state | Ď• âź©, there exist three angles θ 0, θ 1 and θ 2 such that R y (θ 2) ⊗ R y (θ 1) ⊗ R y (θ 0)| Ď• âź© is a three-qubit of the form λ 1|000âź© + λ 2|011âź© + λ 3|101âź© + λ 4|110âź© + λ 5|111âź© with the λ i real numbers. In contrast with the general case, the case of three-qubits with complex amplitudes, we proved that for three qubit states, the dimension of the real entanglement space (the space obtained by identifying real qubit states with local orthogonal gates, instead of local unitary gates) is 4 and in this paper we find four linearly independent polynomial invariants of degree 4 which are not possible to find for the different Schmidt representations of three qubit states. See (AcĂ-n et al 2000 Phys. Rev. Lett. 85 1560; AcĂ-n et al 2001 J. Phys. A: Math. Gen. 34 6725; Carteret et al 2000 J. Math. Phys. 41 7932; Sudbery 2001 J. Phys. A: Math. Gen. 34 643). [ABSTRACT FROM AUTHOR]

This paper studies the conductance on the universal homology covering space Z of 2D orbifolds in a strong magnetic field, thereby removing the rationality constraint on the magnetic field in earlier works (Avron et al 1994 Phys. Rev. Lett. 73 3255–3257; Mathai and Wilkin 2019 Lett. Math. Phys. 109 2473–2484; Prieto 2006 Commun. Math. Phys. 265 373–396) in the literature. We consider a natural Landau Hamiltonian on Z and study its spectrum which we prove consists of a finite number of low-lying isolated points and calculate the von Neumann degree of the associated holomorphic spectral orbibundles when the magnetic field B is large, and obtain fractional quantum numbers as the conductance. [ABSTRACT FROM AUTHOR]

In this paper we prove that, after an appropriate rescaling, the sum of moments of an N × N Hermitian matrix H sampled according to the generalized Cauchy (also known as Hua–Pickrell) ensemble with parameter s > 0 is a continuous-Hahn polynomial in the variable k. This completes the picture of the investigation that began in (Cunden et al 2019 Commun. Math. Phys. 369 1091–45) where analogous results were obtained for the other three classical ensembles of random matrices, the Gaussian, the Laguerre and Jacobi. Our strategy of proof is somewhat different from the one in (Cunden et al 2019 Commun. Math. Phys. 369 1091–45) due to the fact that the generalized Cauchy is the only classical ensemble which has a finite number of integer moments. Our arguments also apply, with straightforward modifications, to the other three cases studied in (Cunden et al 2019 Commun. Math. Phys. 369 1091–45) as well. We finally obtain a differential equation for the one-point density function of the eigenvalue distribution of this ensemble and establish the large N asymptotics of the moments. [ABSTRACT FROM AUTHOR]

We consider the Sasa–Satsuma (SS) and nonlinear Schrödinger (NLS) equations posed along the line, in 1 + 1 dimensions. Both equations are canonical integrable U(1) models, with solitons, multi-solitons and breather solutions Yang (2010 SIAM Mathematical Modeling and Computation). For these two equations, we recognize four distinct localized breather modes: the Sasa–Satsuma for SS, and for NLS the Satsuma–Yajima, Kuznetsov–Ma and Peregrine breathers. Very little is known about the stability of these solutions, mainly because of their complex structure, which does not fit into the classical soliton behavior Grillakis et al (1987 J. Funct. Anal. 74 160–97). In this paper we find the natural H2 variational characterization for each of them. This seems to be the first known variational characterization for these solutions; in particular, the first one obtained for the famous Peregrine breather. We also prove that Sasa–Satsuma breathers are H2 nonlinearly stable, improving the linear stability property previously proved by Pelinovsky and Yang (2005 Chaos 15 037115). Moreover, in the SS case, we provide an alternative understanding of the SS solution as a breather, and not only as an embedded soliton. The method of proof is based in the use of a H2 based Lyapunov functional, in the spirit of Alejo and Muńoz (2013 Commun. Math. Phys. 324 233–62), extended this time to the vector-valued case. We also provide another rigorous justification of the instability of the remaining three nonlinear modes (Satsuma–Yajima, Peregrine and Kuznetsov–Ma), based in the study of their corresponding linear variational structure (as critical points of a suitable Lyapunov functional), and complementing the instability results recently proved e.g. in Muńoz (2017 Proyecciones (Antofagasta) 36 653–83). [ABSTRACT FROM AUTHOR]

Godrčche, in Comment on 'Fluctuation dominated phase ordering at a mixed order transition' [2021 J. Phys. A: Math. Theor. 54 038001], has commented on our recent paper Fluctuation dominated phase ordering at a mixed order transition (2019 J. Phys. A: Math. Theor. 52 254001). This comment concerns the prefactor of the cusp-like small-argument singularity of the scaled spin-spin correlation function at criticality. We remark that the approach used in our paper is adequate for computing the cusp exponent, which is what is really needed to establish fluctuation-dominated phase ordering. Computing the precise value of the prefactor of the cusp singularity is irrelevant for this purpose, or for the physics behind the relation between the mixed order phase transition and the fluctuation-dominated phase ordering—the understanding of which was the main purpose of our paper. [ABSTRACT FROM AUTHOR]

In this paper, we consider a compressible–incompressible two-velocity hydrodynamic system studied by Bresch et al (2015 J. Math. Pure Appl. 104 762–800) and Lions (1996 Mathematical Topics in Fluid Mechanics (Oxford: OUP)). When the density ρ is a small perturbation of a constant, we establish a priori estimates by using some delicate structure of the nonlinear terms and Hardy space. By using these a priori estimates, we prove the existence of global strong solutions and weak solutions. Our results do not require any constraint between the viscosity and the conductivity and improve the results of Bresch et al (2015) and Lions (1996) in the two-dimensional case. As an application of our results we also establish global strong solutions and weak solutions for a model of gaseous mixture and the ghost effect system. [ABSTRACT FROM AUTHOR]

Asymmetric lemon billiards was introduced in Chen et al (2013 Chaos 23 043137), where the billiard table Q(r, b, R) is the intersection of two round disks with radii r ⩽ R, respectively, and b measures the distance between the two centres. It is conjectured Bunimovich et al (2016 Commun. Math. Phys. 341 781–803) that the asymmetric lemon billiards is hyperbolic when the arc Γr is a major arc and R is large. In this paper we prove this conjecture for sufficiently large R. [ABSTRACT FROM AUTHOR]

In this paper we develop the mathematics required in order to provide a description of the observables for quantum fields on low-regularity spacetimes. In particular we consider the case of a massless scalar field ϕ on a globally hyperbolic spacetime M with C1,1 metric g. This first entails showing that the (classical) Cauchy problem for the wave equation is well-posed for initial data and sources in Sobolev spaces and then constructing low-regularity advanced and retarded Green operators as maps between suitable function spaces. In specifying the relevant function spaces we need to control the norms of both ϕ and □gϕ in order to ensure that □g◦G± and G±◦□g are the identity maps on those spaces. The causal propagator G = G+ − G− is then used to define a symplectic form ω on a normed space V(M) which is shown to be isomorphic to ker(□g). This enables one to provide a locally covariant description of the quantum fields in terms of the elements of quasi-local C*-algebras. [ABSTRACT FROM AUTHOR]

This paper aims to provide a robust model for the well-known phenomenon of Kármán vortex street arising in fluid mechanics. The first theoretical attempt to model this pattern was given by von Kármán (1991 Göttinger Nachr., Math. Phys. Kl. 509–17); von Kármán (1912 Göttinger Nachr., Math. Phys. Kl. 547–56). He considered two parallel staggered rows of point vortices, with opposite strength, that translate at the same speed. Following the ideas of Saffman and Schatzman (1981 SIAM J. Sci. Stat. Comput. 2 285–95), we propose to study this phenomenon in the Euler equations by considering two infinite arrows of vortex patches. The key idea is to desingularize the point vortex model proposed by von Kármán. Our construction is flexible and can be extended to more general incompressible models. [ABSTRACT FROM AUTHOR]

In this paper we consider the slightly L2-supercritical gKdV equations , with the nonlinearity and . In the previous work of the author, we know that there exists a stable self-similar blow-up dynamics for slightly L2-supercritical gKdV equations. Such solutions can be viewed as solutions with a single blow-up point. In this paper we will prove the existence of solutions with multiple blow-up points, and give a description of the formation of the singularity near the blow-up time. [ABSTRACT FROM AUTHOR]

The damped and parametrically driven nonlinear Dirac equation with arbitrary nonlinearity parameter is analyzed, when the external force is periodic in space and given by , both numerically and in a variational approximation using five collective coordinates (time dependent shape parameters of the wave function). Our variational approximation satisfies exactly the low-order moment equations. Because of competition between the spatial period of the external force , and the soliton width ls, which is a function of the nonlinearity as well as the initial frequency of the solitary wave, there is a transition (at fixed ) from trapped to unbound behavior of the soliton, which depends on the parameters r and K of the external force and the nonlinearity parameter . We previously studied this phenomena when (Quintero et al 2019 J. Phys. A: Math. Theor. 52 285201) where we showed that for the soliton oscillates in an effective potential, while for it moves uniformly as a free particle. In this paper we focus on the dependence of the transition from oscillatory to particle behavior and explicitly compare the curves of the transition regime found in the collective coordinate approximation as a function of r and K when at fixed value of the frequency . Since the solitary wave gets narrower for fixed as a function of , we expect and indeed find that the regime where the solitary wave is trapped is extended as we increase . [ABSTRACT FROM AUTHOR]

We complete the derivation of the sausage model NLIE by giving a proof of the crucial relation (3.24) of the original paper based on the analytic properties of Q and . [ABSTRACT FROM AUTHOR]

The purpose of this paper is to give a characterization of the structure of non-autonomous attractors of the problem when the parameter varies. Also, we answer a question proposed in Carvalho et al (2012 Proc. Am. Math. Soc. 140 2357–73), concerning the complete description of the structure of the pullback attractor of the problem when and, more generally, for , . We construct global bounded solutions, ‘non-autonomous equilibria’, connections between the trivial solution and these ‘non-autonomous equilibria’ and characterize the -limit and -limit set of global bounded solutions. As a consequence, we show that the global attractor of the associated skew-product flow has a gradient structure. The structure of the related pullback an uniform attractors are derived from that. [ABSTRACT FROM AUTHOR]

In this paper, we study a large time behavior of the global spherically or cylindrically symmetric solutions in H1 for the compressible viscous radiative and reactive gas in multi-dimension with large initial data. Precisely, if the initial data are spherically symmetric or cylindrically symmetric, the smallness of initial data is not needed. The main concern of the present paper is to investigate the exponential stability of a solution toward the stationary solution as time goes to infinity. We obtain the uniform positive lower and upper bounds of the density by using different methods. [ABSTRACT FROM AUTHOR]

The topological entropy of upper recurrent, lower recurrent points and Birkhoff regularity were considered in Tian (2016 Adv. Math. 288 464–526) but Banach upper recurrence points are not considered. In this paper we mainly consider whether the points that are Banach upper recurrent but not upper recurrent can carry full topological entropy. Moreover, we use statistical -limit sets to obtain entropy results on the refined orbit distribution of Banach recurrence. In this process, we strengthen Pfister and Sullivan’s result of Pfister and Sullivan (2007 Ergod. Theor. Dynam. Syst. 27 929–56) from saturated property to transitively-saturated property (and from single-saturated property to transitively-convex-saturated property). We also establish an abstract framework on the combination of Banach recurrence and multifractal analysis of general observable functions and in particular, how these results can be applied in the combination of Banach recurrence Lyapunov regularity to obtain a generalized and refined theory of Barreira and Doutor (2009 J. Math. Pures Appl. 92 1–17); Barreira and Gelfert (2006 Commun. Math. Phys. 267 393–418); Barreira and Saussol (2001 Trans. Am. Math. Soc. 353 3919–44); Feng and Huang (2010 Commun. Math. Phys. 297 1–43); Feng (2003 J. Math. 138 353–76); Feng (2009 Israel J. Math. 170 355–94); Feng and Lau (2002 Math. Res. Lett. 9 363–78) etc, on mixed Lyapunov multifractal analysis such as irregular sets and level sets of Lyapunov exponents. [ABSTRACT FROM AUTHOR]

This paper is the first part of a series which provides a systematic treatment of the space-filling curves of self-similar sets. In the present paper, we introduce a notion of linear graph-directed IFS (linear GIFS in short). We show that to construct a space-filling curve of a self-similar set, it amounts to exploring its linear GIFS structures. Compared to the previous methods, such as the L-system or recurrent set method, the linear GIFS approach is simpler, more rigorous and leads to further studies on this topic. We also propose a new algorithm for the beautiful visualization of space-filling curves. In a series of papers Dai et al (2015 arXiv:1511.05411 [math.GN]), Rao and Zhang (2015) and Rao and Zhang (2015), we investigate for a given self-similar set how to get ‘substitution rules’ for constructing space-filling curves, which was obscure in the literature. We solve the problem for self-similar sets of finite type, which covers most of the known results on constructions of space-filling curves. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the global well-posedness and time-asymptotic decay of the Vlasov–Fokker–Planck equation with local alignment forces. The equation can be formally derived from an agent-based model for self-organized dynamics called the Motsch–Tadmor model with noises. We present the global existence and uniqueness of classical solutions to the equation around the global Maxwellian in the whole space. For the large-time behavior, we show the algebraic decay rate of solutions towards the equilibrium under suitable assumptions on the initial data. We also remark that the rate of convergence is exponential when the spatial domain is periodic. The main methods used in this paper are the classical energy estimates combined with hyperbolic–parabolic dissipation arguments. [ABSTRACT FROM AUTHOR]

A recent study claimed that heavy use of equations impedes communication among biologists, as measured by the ability to attract citations from peers. It was suggested that to increase the probability of being cited one should reduce the density of equations in papers, that equations should be moved to appendices, and that math training among biologists should be improved. Here, we report a detailed study of the citation habits among physicists, a community that has traditionally strong training and dependence on mathematical formulations. Is it possible to correlate statistical citation patterns and fear of mathematics in a community whose work strongly depends on equations? By performing a systematic analysis of the citation counts of papers published in one of the leading journals in physics covering all its disciplines, we find striking similarities with distribution of citations recorded in biological sciences. However, based on the standard deviations in citation data of both communities, biologists and physicists, we argue that trends in statistical indicators are not reliable to unambiguously blame mathematics for the existence or lack of citations. We digress briefly about other statistical trends that apparently would also enhance citation success. [ABSTRACT FROM AUTHOR]

We study the Laurent property, the irreducibility and co-primeness of discrete integrable and non-integrable equations. First we study a discrete integrable equation related to the Somos-4 sequence, and also a non-integrable equation as a comparison. We prove that the conditions of irreducibility and co-primeness hold only in the integrable case. Next, we generalize our previous results on the singularities of the discrete Korteweg–de Vries (dKdV) equation. In our previous paper (Kanki et al 2014 J. Phys. A: Math. Theor.47 065201) we described the singularity confinement test (one of the integrability criteria) using the Laurent property, and the irreducibility, and co-primeness of the terms in the bilinear dKdV equation, in which we only considered simplified boundary conditions. This restriction was needed to obtain simple (monomial) relations between the bilinear form and the nonlinear form of the dKdV equation. In this paper, we prove the co-primeness of the terms in the nonlinear dKdV equation for general initial conditions and boundary conditions, by using the localization of Laurent rings and the interchange of the axes. We assert that co-primeness of the terms can be used as a new integrability criterion, which is a mathematical re-interpretation of the confinement of singularities in the case of discrete equations. [ABSTRACT FROM AUTHOR]

In Bergweiler and Eremenko (2016 Proc. Am. Math. Soc. 144 2911–22), Bergweiler and Eremenko computed the number of critical points of the Green’s function on a torus by investigating the dynamics of a certain family of antiholomorphic meromorphic functions on tori. They also observed that hyperbolic maps are dense in this family of meromorphic functions in a rather trivial way. In this paper, we study the parameter space of this family of meromorphic functions, which can be written as antiholomorphic perturbations of Weierstrass Zeta functions. On the one hand, we give a complete topological description of the hyperbolic components and their boundaries, and on the other hand, we show that these sets admit natural parametrizations by associated dynamical invariants. This settles a conjecture, made in Lin and Wang (2010 Ann. Math. 172 911–54), on the topology of the regions in the upper half plane where the number of critical points of the Green’s function remains constant. [ABSTRACT FROM AUTHOR]

The pedagogical aim of the present paper, thought for an undergraduate audience, is to help students to appreciate how the development of elementary models based on physics first principles is a fundamental and necessary preliminary step for the behaviour of complex real systems to be grasped with minimal amounts of math. In some particularly fortunate cases, such models also show reasonably good results when are compared to reality. The speed behaviour of the Space Shuttle during its first two minutes of flight from liftoff is here analysed from such a didactical point of view. Only the momentum conservation law is employed to develop the model, which is eventually applied to quantitatively interpret the telemetry of the 2011 last launches of Shuttle Discovery and Shuttle Endeavour. [ABSTRACT FROM AUTHOR]

Inertial microfluidics systems carry a great importance for particle focusing and separation due to their simple configurations, robust structures, and precise high-throughput cell manipulation ability. In this paper, a novel microchannel geometry, called Sunflower, which is developed by superimposing two microchannel geometries, is presented. An empirical formula for normalized focus quality, which enables the quantitative comparison of particle focusing abilities of different microchannel geometries via fluorescent images, is introduced. In particle focusing experiments, focus quality enhancements ranging from 14% at 0.9 ml min−1 to 487% at 0.3 ml min−1 is observed. Besides, 99.57% of the 9.9 µm polystyrene particles are collected at a flow rate of 2.5 ml min−1 from a 60 µm wide outlet section, whose location within the microchannel width is specifically tailored. A clear, stable and narrow particle focus line is observed not only at an optimum flow rate, but also in a great range of flow rates between 0.3 ml min−1 and 2.5 ml min−1, offering great levels of flexibility and robustness against disturbances. Moreover, the novel microchannel geometry is tested with HL-60 cancer cell lines, and similar results are obtained in a great flow rate range without an observed effect on the cell’s viability. [ABSTRACT FROM AUTHOR]

This paper investigates the phenomenon of three-pulse photon echo in thick rare-earth ions doped crystal whose thickness is far larger than 0.002 cm which is adopted in previous works. The influence of thickness on the three-pulse photon echo’s amplitude and efficiency is analyzed with the Maxwell–Bloch equations solved by finite-difference time-domain method. We demonstrate that the amplitude of three-pulse echo will increase with the increasing of thickness and the optimum thickness to generate three-pulse photon echo is 0.3 cm for Tm:YAG when the attenuation of the input pulse is taken into account. Meanwhile, we find the expression , which is previously employed to describe the relationship between echo’s efficiency and thickness, should be modified as with the propagation of echo considered. [ABSTRACT FROM AUTHOR]

This paper presents calculation results for the photoassociation of a NaK molecule with a two-color modulated laser and gives a detailed analysis about them. For the two-step photoassociation process in intense fields, the effect of two-color modulated laser parameters, such as relative phase, envelope period, and laser intensity, on the population of the molecular electronic state can be obtained by solving the time-dependent Schrödinger equation through the quantum wave packet method. The numerical simulation shows not only that the influence of laser parameters on the vibrational distribution presents some regularity, but also that a higher population in the ground electronic state can be realized through adjusting these laser parameters. [ABSTRACT FROM AUTHOR]

In this paper, the control problem of distributed parameter systems is investigated by using wireless sensor and actuator networks with the observer-based method. Firstly, a centralized observer which makes use of the measurement information provided by the fixed sensors is designed to estimate the distributed parameter systems. The mobile agents, each of which is affixed with a controller and an actuator, can provide the observer-based control for the target systems. By using Lyapunov stability arguments, the stability for the estimation error system and distributed parameter control system is proved, meanwhile a guidance scheme for each mobile actuator is provided to improve the control performance. A numerical example is finally used to demonstrate the effectiveness and the advantages of the proposed approaches. [ABSTRACT FROM AUTHOR]

The performance analysis of the generalized Carlson iterating process, which can realize the rational approximation of fractional operator with arbitrary order, is presented in this paper. The reasons why the generalized Carlson iterating function possesses more excellent properties such as self-similarity and exponential symmetry are also explained. K-index, P-index, O-index, and complexity index are introduced to contribute to performance analysis. Considering nine different operational orders and choosing an appropriate rational initial impedance for a certain operational order, these rational approximation impedance functions calculated by the iterating function meet computational rationality, positive reality, and operational validity. Then they are capable of having the operational performance of fractional operators and being physical realization. The approximation performance of the impedance function to the ideal fractional operator and the circuit network complexity are also exhibited. [ABSTRACT FROM AUTHOR]

Based on the fundamental equations of piezoelasticity of quasicrystal material, we investigated the interaction between a screw dislocation and a wedge-shaped crack in the piezoelectricity of one-dimensional hexagonal quasicrystals. Explicit analytical solutions are obtained for stress and electric displacement intensity factors of the crack, as well as the force on dislocation. The derivation is based on the conformal mapping method and the perturbation technique. The influences of the wedge angle and dislocation location on the image force are also discussed. The results obtained in this paper can be fully reduced to some special cases already available or deriving new ones. [ABSTRACT FROM AUTHOR]

Recently, bidirectional quantum teleportation has attracted a great deal of research attention. However, existing bidirectional teleportation schemes are normally discussed on the basis of perfect quantum environments. In this paper, we first put forward a bidirectional teleportation scheme to transport three-qubit Greenberger–Horne–Zeilinger (GHZ) states based on controled-not (CNOT) operation and single-qubit measurement. Then, we generalize it to the teleportation of multi-qubit GHZ states. Further, we discuss the influence of quantum noise on our scheme by the example of an amplitude damping channel, then we obtain the fidelity of the teleportation. Finally, we utilize the weak measurement and the corresponding reversing measurement to protect the quantum entanglement, which shows an effective enhancement of the teleportation fidelity. [ABSTRACT FROM AUTHOR]

In this paper, we propose a susceptible-infective-recovered (SIR) epidemic model to describe the geographic spread of an infectious disease in two groups/sub-populations living in a spatially continuous habitat. It is assumed that the susceptibility of individuals for infection and the infectivity of individuals are distinct between these two groups/sub-populations. It is also assumed that the infectious disease has a fixed latent period and the latent individuals may diffuse. We investigate the traveling wave solutions and obtain complete information about the existence and nonexistence of nontrivial traveling wave solutions. We prove that when the basic reproduction number at the disease free equilibrium , there exists a critical number c*  >  0 such that for each c  >  c*, the system admits a nontrivial traveling wave solution with wave speed c, and for c  <  c*, the system admits no nontrivial traveling wave solution. When , we show that there exists no nontrivial traveling wave solution. In addition, for the case and c  >  c*, we also find that the final sizes of susceptible individuals, denoted by , satisfies , which means that there is no outbreak of this the infectious disease anymore. At last, we analyze and simulate the continuous dependence of the minimal speed c* on the parameters. [ABSTRACT FROM AUTHOR]

The Witten–Dijkgraaf–Verlinde–Verlinde (or WDVV) equations, as one would expect from an integrable system, has many symmetries, both continuous and discrete. One class—the so-called Legendre transformations—were introduced by Dubrovin. They are a discrete set of symmetries between the stronger concept of a Frobenius manifold, and are generated by certain flat vector fields. In this paper this construction is generalized to the case where the vector field (called here the Legendre field) is non-flat but satisfies a certain set of defining equations. One application of this more general theory is to generate the induced symmetry between almost-dual Frobenius manifolds whose underlying Frobenius manifolds are related by a Legendre transformation. This also provides a map between rational and trigonometric solutions of the WDVV equations. [ABSTRACT FROM AUTHOR]

In this paper we produce seven new algebras as confluences of the Cherednik algebra of type and we characterise their spherical-sub-algebras. The limit of the spherical sub-algebra of the Cherednik algebra of type is the monodromy manifold of the Painlevé VI equation (Oblomkov 2004 Int. Math. Res. Not. 2004 877–912). Here we prove that by considering the limits of the spherical sub-algebras of our new confluent algebras, one obtains the monodromy manifolds of all other Painlevé differential equations. Moreover, we introduce confluent versions of the Zhedanov algebra and prove that each of them (quotiented by their Casimir) is isomorphic to the corresponding spherical sub-algebra of our new confluent Cherednik algebras. We show that in the basic representation our confluent Zhedanov algebras act as symmetries of certain elements of the q-Askey scheme, thus setting a stepping stone towards the solution of the open problem of finding the corresponding quantum algebra for each element of the q-Askey scheme. These results establish a new link between the theory of the Painlevé equations and the theory of the q-Askey scheme making a step towards the construction of a representation theoretic approach for the Painlevé theory. [ABSTRACT FROM AUTHOR]

A variational principle code which can calculate self-consistently currents on the conductors is used to assess the coupling characteristic of the EAST 4-strap ion cyclotron range of frequency (ICRF) antenna. Taking into account two layers of antenna conductors without lateral frame but with slab geometry, the antenna impedances as a function of frequency and the structure of RF field excited inside the plasma in various phasing cases are discussed in this paper. [ABSTRACT FROM AUTHOR]

It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and also scale-free (the degrees are distributed according to a power law). Moreover, these networks are very often hierarchical, as they describe the modularity of the systems that are modeled. Most of the studies for complex networks are based on stochastic methods. However, a deterministic method, with an exact determination of the main relevant parameters of the networks, has proven useful. Indeed, this approach complements and enhances the probabilistic and simulation techniques and, therefore, it provides a better understanding of the modeled systems. In this paper we find the radius, diameter, clustering coefficient and degree distribution of a generic family of deterministic hierarchical small-world scale-free networks that has been considered for modeling real-life complex systems. [ABSTRACT FROM AUTHOR]

There is growing evidence of star formation in the vicinity of supermassive black holes (SMBHs) in galactic nuclei. A viable scenario for this process assumes infall of a massive gas cloud toward the SMBH and subsequent formation of a dense accretion disk, which gives birth to the young stars. Numerical hydrodynamical models indicate that this star formation process is rather fast and precedes full circularization of the accretion flow, i.e., the new stars are born on elliptic orbits. By means of direct numerical N-body modeling, we show in this paper that the nonzero eccentricity of the stellar disks around the SMBH leads to an onset of various types of the Kozai–Lidov oscillations of a non-negligible subset of individual orbits in the disk, showing a remarkable robustness of this classical mechanism. Among others, we demonstrate that under certain circumstances, the presence of an additional spherical cluster (which is generally known to damp Kozai–Lidov oscillations) may trigger such oscillations as a result of affecting the internal flow of the angular momentum through the disk. We conclude that the Kozai–Lidov oscillations are capable of substantially modifying the initial structure of the disk (its thickness and distribution of eccentricities, in particular). [ABSTRACT FROM AUTHOR]

We show how the derivation of the Derrida–Lebowitz–Speer–Spohn equation can be prolonged to obtain a new equation, generalizing the models obtained in the paper by these authors. We then investigate its properties from both an analytical and numerical perspective. Specifically, a numerical method is presented to approximate solutions of the prolonged equation. Using this method, we investigate the relationship between the solutions of the prolonged equation and the Tracy–Widom GOE distribution. [ABSTRACT FROM AUTHOR]

State sum constructions, such as Kuperberg’s algorithm, give partition functions of physical systems, like lattice gauge theories, in various dimensions by associating local tensors or weights with different parts of a closed triangulated manifold. Here we extend this construction by including matter fields to build partition functions in both two and three space–time dimensions. The matter fields introduce new weights to the vertices and they correspond to Potts spin configurations described by an -module with an inner product. Performing this construction on a triangulated manifold with a boundary we obtain transfer matrices which are decomposed into a product of local operators acting on vertices, links and plaquettes. The vertex and plaquette operators are similar to the ones appearing in the quantum double models (QDMs) of Kitaev. The link operator couples the gauge and the matter fields, and it reduces to the usual interaction terms in known models such as gauge theory with matter fields. The transfer matrices lead to Hamiltonians that are frustration-free and are exactly solvable. According to the choice of the initial input, that of the gauge group and a matter module, we obtain interesting models which have a new kind of ground state degeneracy that depends on the number of equivalence classes in the matter module under gauge action. Some of the models have confined flux excitations in the bulk which become deconfined at the surface. These edge modes are protected by an energy gap provided by the link operator. These properties also appear in ‘confined Walker–Wang’ models which are 3D models having interesting surface states. Apart from the gauge excitations there are also excitations in the matter sector which are immobile and can be thought of as defects like in the Ising model. We only consider bosonic matter fields in this paper. [ABSTRACT FROM AUTHOR]

In this paper we prove that given a weakly almost periodic measure μ supported inside some model set with closed window W, then the strongly almost periodic component and the null weakly almost periodic component μ0 are both supported inside . As a consequence we prove that given any translation bounded measure ω, supported inside some model set, then each of the pure point diffraction spectrum and the continuous diffraction spectrum is either trivial or has a relatively dense support. [ABSTRACT FROM AUTHOR]