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We recently proposed a class of type IIB vacua that yield, at low energies, four–dimensional Minkowski spaces with broken supersymmetry and a constant string coupling. They are compactifications with an internal five-torus bearing a five–form flux Φ and warp factors depending on a single coordinate. The breaking of supersymmetry occurs when the internal space includes a finite interval. A probe-brane analysis revealed a gravitational repulsion and a charge attraction of equal magnitude from the left end of the interval, together with a singularity at the other end. Here we complete the analysis revealing the presence, at one end, of an effective O 3 of negative tension and positive five–form charge. We also determine the values of these quantities, showing that T = − Q = Φ , and characterize the singularity present at the other end of the interval, which hosts an opposite charge. Finally, we discuss various forms of the gravity action in the presence of a boundary and identify a self–adjoint form for its fluctuations. Invited contribution to the special issue of Journal of Physics A: Mathematical and Theoretical on 'Fields, Gravity, Strings and Beyond: In Memory of Stanley Deser' [ABSTRACT FROM AUTHOR]

In this manuscript, we introduce (symmetric) Tetranacci polynomials ξ j as a twofold generalization of ordinary Tetranacci numbers, considering both non unity coefficients and generic initial values. We derive a complete closed form expression for any ξ j with the key feature of a decomposition in terms of generalized Fibonacci polynomials. For suitable conditions, ξ j can be understood as the superposition of standing waves. The issue of Tetranacci polynomials originated from their application in condensed matter physics. We explicitly demonstrate the approach for the spectrum, eigenvectors, Green's functions and transmission probability for an atomic tight binding chain exhibiting both nearest and next nearest neighbor processes. We demonstrate that in topological trivial models, complex wavevectors can form bulk states as a result of the open boundary conditions. We describe how effective next nearest neighbor bonding is engineered in state of the art theory/experiment exploiting onsite degrees of freedom and close range hopping. We argue about experimental tune ability and on-demand complex wavevectors. [ABSTRACT FROM AUTHOR]

This article covers fluid dynamics and principles of flight. This complex topic and the related theory are typically taught in the second and third years of aerospace engineering degrees, but the present work adapts it to three different levels of learning: primary school, secondary school and science, technology, engineering and mathematics (STEM) degrees. Here we divide the topic into three sections, each one representing a project that can be developed in class. Depending on the student's level, we propose to develop project 1 (primary school), project 2 (secondary school) or project 3 (STEM degree). The main goal of the article is twofold: (i) to increase students' motivation from primary to university levels in the topics of mathematics and physics, showing students that the theoretical concepts that they learn in class can be applied to solve real-life problems, and (ii) to introduce original ideas for teachers to develop extracurricular activities in class, also with the aim of motivating students. Projects 1 and 3 have been carried out in class and results show that after performing these activities, students have acquired new complex knowledge and at the same time their motivation in scientific subjects has increased. Project-based learning and learning by playing are the two main methodologies of the activities presented in this article. The present work follows the spirit of 'The Enigma of Aerodynamic Lift' (an article recently published in Scientific American 322, 2020), and can be considered as an original extension with new material suitable for the teacher to be used in class. [ABSTRACT FROM AUTHOR]

This document is a preface to a journal article titled "Claritons and the asymptotics of ideas: the physics of Michael Berry." The article discusses the work and contributions of Michael Berry, a physicist known for his discoveries in the borderland between different theories, such as quantum and classical mechanics, and wave and geometric optics. Berry's approach to mathematical physics emphasizes exploration and explication over rigorous proof, and his ideas have found applications in various fields, including condensed matter physics, quantum information, high-energy physics, optics, and mathematics. The preface is written by Mark Dennis, Christopher Howls, Jonathan Robbins, and Pragya Shukla, who express their regard and affection for Berry and edit this volume dedicated to his 80th birthday. [Extracted from the article]

For more than a century, the Painlevé I equation has played an important role in both physics and mathematics. Its two-parameter family of solutions was studied in many different ways, yet still leads to new surprises and discoveries. Two popular tools in these studies are the theory of isomonodromic deformation that uses the exact WKB method, and the asymptotic description of transcendents in terms of two-parameter transseries. Combining methods from both schools of thought, we follow work by Takei and collaborators to formulate complete, two-parameter connection formulae for solutions when they cross arbitrary Stokes lines in the complex plane. These formulae allow us to study Stokes phenomenon for the full two-parameter family of transseries solutions. In particular, we recover the exact expressions for the Stokes data that were recently found by Baldino, Schwick, Schiappa and Vega and compare our connection formulae to theirs. We also explain several ambiguities in relating transseries parameter choices to actual Painlevé transcendents, study the monodromy of formal solutions, and provide high-precision numerical tests of our results. [ABSTRACT FROM AUTHOR]

This article reviews some results of the SAGEX programme that have developed in the understanding of the interplay of supersymmetry and modular covariance of scattering amplitudes in type IIB superstring theory and its holographic image in N = 4 supersymmetric Yang–Mills theory (SYM). The first section includes the determination of exact expressions for BPS interactions in the low-energy expansion of type IIB superstring amplitudes. The second section concerns properties of a certain class of integrated correlators in N = 4 SYM with arbitrary classical gauge group that are exactly determined by supersymmetric localisation. Not only do these reproduce known features of perturbative and non-perturbative N = 4 SYM for any classical gauge group, but they have large- N expansions that are in accord with expectations based on the holographic correspondence with superstring theory. The final section focusses on modular graph functions. These are modular functions that are closely associated with coefficients in the low-energy expansion of superstring perturbation theory and have recently received quite a lot of interest in both the physics and mathematics literature. [ABSTRACT FROM AUTHOR]

Over the past two decades quantum engineering has made significant advances in our ability to create genuine quantum many-body systems using ultracold atoms. In particular, some prototypical exactly solvable Yang–Baxter systems have been successfully realized allowing us to confront elegant and sophisticated exact solutions of these systems with their experimental counterparts. The new experimental developments show a variety of fundamental one-dimensional (1D) phenomena, ranging from the generalized hydrodynamics to dynamical fermionization, Tomonaga–Luttinger liquids, collective excitations, fractional exclusion statistics, quantum holonomy, spin-charge separation, competing orders with high spin symmetry and quantum impurity problems. This article briefly reviews these developments and provides rigorous understanding of those observed phenomena based on the exact solutions while highlighting the uniqueness of 1D quantum physics. The precision of atomic physics realizations of integrable many-body problems continues to inspire significant developments in mathematics and physics while at the same time offering the prospect to contribute to future quantum technology. [ABSTRACT FROM AUTHOR]

This paper deals with the wavelet regularization for ill-posed problems involving linear constant-coefficient pseudo-differential operators. We concentrate on solving ill-posed equations involving these operators, which are behaving badly in theory and practice. Since a wide range of ill-posed and inverse problems in mathematical physics can be described and rewritten by the language of these operators, it has gathered significant attention in the literature. Based on a general framework, we classify ill-posed problems in terms of their degree of ill-posedness into mildly, moderately, and severely ill-posed problems in a certain Sobolev scale. Using wavelet multi-resolution approximations, it is shown that wavelet regularizers can achieve order-optimal rates of convergence for pseudo-differential operators in special Sobolev space both for the a priori and the a posteriori choice rules. Our strategy, however, turns out that both schemes yield comparable convergence rates. In this setting, ultimately, we provided some prototype examples for which our theoretical results correctly predict improved rates of convergence. [ABSTRACT FROM AUTHOR]

We connect two a priori unrelated topics, the theory of geodesically equivalent metrics in differential geometry, and the theory of compatible infinite-dimensional Poisson brackets of hydrodynamic type in mathematical physics. Namely, we prove that a pair of geodesically equivalent metrics such that one is flat produces a pair of such brackets. We construct Casimirs for these brackets and the corresponding commuting flows. There are two ways to produce a large family of compatible Poisson structures from a pair of geodesically equivalent metrics one of which is flat. One of these families is (n + 1)(n + 2)/2 dimensional; we describe it completely and show that it is maximal. Another has dimension ⩽n + 2 and is, in a certain sense, polynomial. We show that a nontrivial polynomial family of compatible Poisson structures of dimension n + 2 is unique and comes from a pair of geodesically equivalent metrics. In addition, we generalize a result of Sinjukov (1961) from constant curvature metrics to arbitrary Einstein metrics. [ABSTRACT FROM AUTHOR]

This study examined the effect of transfer of learning on undergraduate students of physics education. Because mathematical methods are valuable for presenting and solving physics problems, students of physics must learn to use their knowledge of mathematics in a physical context rather than struggling with complicated mathematical problems. This study sought to determine whether or not practice with physics problems by a physics instructor for the course could help the undergraduate students transfer their mathematics knowledge to a physics context. To do this, the experimental and control groups of physics education students were provided with an exam sheet and interviewed about difficulties after passing the course taught by either a physics or mathematics instructor. After completion of the course, the student responses to the exam and interviews were analyzed qualitatively. It was concluded that simply learning mathematics by the control group suppressed their initiative and caused them to resist completing the physics problems. The experimental group felt capable of attempting this kind of problem, but lacked additional factors that prevented them from producing complete solutions. [ABSTRACT FROM AUTHOR]

The result of the only known good quality observations of September 18, 2017 Venus occultation by the Moon is presented in this article. This kind of observation can be done by students using a common camera, and the analysis can be designed as a mathematics and physics exercise. Several observations were carried out in Malang and Jakarta, but high quality data were obtained only in Jakarta. An analysis of the occultation geometry then showed that the shortest distance between Venus and the center of the Moon disk was 249 arcsec. We were also able to fit the occultation light curve with a simple geometric model using an additional correction factor (1 + sin2 ϕ) to compensate for the hill-shaped intensity variation in the Venus disk. [ABSTRACT FROM AUTHOR]

Rev.Lett.86 2913 Strunz W T, Haake F and Braun D 2003 Universality of decoherence for macroscopic quantum superpositionsPhys. Rev.Lett.93 014103 Müller S, Heusler S, Braun P, Haake F and Altland A 2005 Periodic-Orbit theory of universality in quantum chaosPhys. Petr, who was a full professor in St Petersburg, became a frequent guest of Fritz since the 1990s, and later indeed joined the University of Essen. Rev.Lett.41 1685 HaakeF1979TheoryofSuperfluorescence (SpringerSeriesinOpticalSciences,LaserSpectroscopy IV)vol 21 (Berlin: Springer) [4] BraunD,BraunPAandHaake F1999 Semiclassicsforadissipativequantum mapPhys.D131265 Braun D, Braun P A and Haake F 2000 Long-lived quantum coherence between macroscopically distinct states in superradianceOpt. [Extracted from the article]

This article is firstly a historic review of the theory of Riemann–Hilbert problems with particular emphasis placed on their original appearance in the context of Hilbert's 21st problem and Plemelj's work associated with it. The secondary purpose of this note is to invite a new generation of mathematicians to the fascinating world of Riemann–Hilbert techniques and their modern appearances in nonlinear mathematical physics. We set out to achieve this goal with six examples, including a new proof of the integro-differential Painlevé-II formula of Amir et al (2011 Commun. Pure Appl. Math. 64 466–537) that enters in the description of the Kardar–Parisi–Zhang crossover distribution. Parts of this text are based on the author's Szegő prize lecture at the 15th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA) in Hagenberg, Austria. [ABSTRACT FROM AUTHOR]

Derived in this article is a mathematical model of a cyclist riding over uneven terrain. The model is very general; it is expressed in terms of arbitrary functions that describe how the elevation changes with horizontal distance and how the cyclist's power output varies, and also accounts for road friction and air resistance. The model was validated by considering special cases such as horizontal and inclined surfaces. Although the governing equation is too complicated to solve exactly for the general case, a numerical solution procedure is proposed and tested. In addition, an approximate analytical solution procedure is outlined. As an illustration some numerical results are presented for the case of a cyclist riding over rolling hills. The adopted approach is well suited for undergraduate students in mathematical physics. The formulation equally applies to a vehicle driving over a variable landscape. This work also unites concepts from physics with mathematical modelling and coding. Lastly, a video abstract is also provided. [ABSTRACT FROM AUTHOR]

We study the traveling wave and other solutions of the perturbed Kaup–Newell Schrödinger dynamical equation that signifies long waves parallel to the magnetic field. The wave solutions such as bright-dark (solitons), solitary waves, periodic and other wave solutions of the perturbed Kaup–Newell Schrödinger equation in mathematical physics are achieved by utilizing two mathematical techniques, namely, the extended F-expansion technique and the proposed exp(–ϕ(ζ))-expansion technique. This dynamical model describes propagation of pluses in optical fibers and can be observed as a special case of the generalized higher order nonlinear Schrödinger equation. In engineering and applied physics, these wave results have key applications. Graphically, the structures of some solutions are presented by giving specific values to parameters. By using modulation instability analysis, the stability of the model is tested, which shows that the model is stable and the solutions are exact. These techniques can be fruitfully employed to further sculpt models that arise in mathematical physics. [ABSTRACT FROM AUTHOR]

This review is a primer on recently established geometric methods for observables in quantum field theories. The main emphasis is on amplituhedra, i.e. geometries encoding scattering amplitudes for a variety of theories. These pertain to a broader family of geometries called positive geometries, whose basics we review. We also describe other members of this family that are associated with different physical quantities and briefly consider the most recent developments related to positive geometries. Finally, we discuss the main open problems in the field. This is a Topical Review invited by Journal of Physics A: Mathematical and Theoretical. [ABSTRACT FROM AUTHOR]

In this paper, approximate bright-soliton solutions of the higher-order nonlinear Schrödinger equation are constructed by treating the higher-order terms as small perturbations. The first-, second-, and third-order asymptotic solutions are obtained. The errors between the asymptotic solutions and the numerical/analytical solutions are discussed, which gives a high accuracy of the approximate solutions. It is pointed that the asymptotic solutions can be used as the initial value to improve the accuracy of the numerical solutions. This paper may be helpful for undergraduate and graduate students in mathematics and physics to understand the approximate soliton solutions of the higher-order nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]

A recurrence relation is said to have the Laurent property if all of its iterates are Laurent polynomials in the initial values with integer coefficients. Recurrences with this property appear in diverse areas of mathematics and physics, ranging from Lie theory and supersymmetric gauge theories to Teichmüller theory and dimer models. In many cases where such recurrences appear, there is a common structural thread running between these different areas, in the form of Fomin and Zelevinsky's theory of cluster algebras. Laurent phenomenon algebras, as defined by Lam and Pylyavskyy, are an extension of cluster algebras, and share with them the feature that all the generators of the algebra are Laurent polynomials in any initial set of generators (seed). Here we consider a family of nonlinear recurrences with the Laurent property, referred to as 'Little Pi', which was derived by Alman et al via a construction of periodic seeds in Laurent phenomenon algebras, and generalizes the Heideman–Hogan family of recurrences. Each member of the family is shown to be linearizable, in the sense that the iterates satisfy linear recurrence relations with constant coefficients. We derive the latter from linear relations with periodic coefficients, which were found recently by Kamiya et al from travelling wave reductions of a linearizable lattice equation on a six-point stencil. By making use of the periodic coefficients, we further show that the birational maps corresponding to the Little Pi family are maximally superintegrable. We also introduce another linearizable lattice equation on the same six-point stencil, and present the corresponding linearization for its travelling wave reductions. Finally, for both of the six-point lattice equations considered, we use the formalism of van der Kamp to construct a broad class of initial value problems with the Laurent property. [ABSTRACT FROM AUTHOR]

Analysis of institutional data for physics majors showing predictive relationships between required mathematics and physics courses in various years is important for contemplating how the courses build on each other and whether there is need to make changes to the curriculum for the majors to strengthen these relationships. We used 15 years of institutional data at a US-based large research university to investigate how introductory physics and mathematics courses predict male and female physics majors' performance on required advanced physics and mathematics courses. We used structure equation modeling (SEM) to investigate these predictive relationships and find that among introductory and advanced physics and mathematics courses, there are gender differences in performance in favor of male students only in the introductory physics courses after controlling for high school GPA. We found that a measurement invariance fully holds in a multi-group SEM by gender, so it was possible to carry out analysis with gender mediated by introductory physics and high school GPA. Moreover, we find that these introductory physics courses that have gender differences do not predict performance in advanced physics courses. In other words, students could be using invalid data about their introductory physics performance to make their decision about whether physics is the right field for them to pursue, and those invalid data in introductory physics favor male students. Also, introductory mathematics courses predict performance in advanced mathematics courses which in turn predict performance in advanced physics courses. Furthermore, apart from the introductory physics courses that do not predict performance in future physics courses, there is a strong predictive relationship between the sophomore, junior and senior level physics courses. [ABSTRACT FROM AUTHOR]

This topical review introduces the theoretical and experimental advances in continuous-variable (CV)—i.e. qumode-based in lieu of qubit-based—large-scale, fault-tolerant quantum computing and quantum simulation. An introduction to the physics and mathematics of multipartite entangled CV cluster states is given, and their connection to experimental concepts is delineated. Paths toward fault tolerance are also presented. It is the hope of the author that this review attract more contributors to the field and promote its extension to the promising technology of integrated quantum photonics. [ABSTRACT FROM AUTHOR]

Two-dimensional quantum gravity, defined either via scaling limits of random discrete surfaces or via Liouville quantum gravity, is known to possess a geometry that is genuinely fractal with a Hausdorff dimension equal to 4. Coupling gravity to a statistical system at criticality changes the fractal properties of the geometry in a way that depends on the central charge of the critical system. Establishing the dependence of the Hausdorff dimension on this central charge c has been an important open problem in physics and mathematics in the past decades. All simulation data produced thus far has supported a formula put forward by Watabiki in the nineties. However, recent rigorous bounds on the Hausdorff dimension in Liouville quantum gravity show that Watabiki's formula cannot be correct when c approaches. Based on simulations of discrete surfaces encoded by random planar maps and a numerical implementation of Liouville quantum gravity, we obtain new finite-size scaling estimates of the Hausdorff dimension that are in clear contradiction with Watabiki's formula for all simulated values of. Instead, the most reliable data in the range is in very good agreement with an alternative formula that was recently suggested by Ding and Gwynne. The estimates for display a negative deviation from the latter formula, but the scaling is seen to be less accurate in this regime. [ABSTRACT FROM AUTHOR]

An intriguing correspondence between four-qubit systems and simple singularity of type D4 is established. We first consider the algebraic variety X of separable states within the projective Hilbert space . Then, cutting X with a specific hyperplane H, we prove that the X-hypersurface, defined from the section X∩H⊂X, has an isolated singularity of type D4; it is also shown that this is the ‘worst-possible’ isolated singularity that one can obtain by this construction. Moreover, it is demonstrated that this correspondence admits a dual version, by proving that the equation of the dual variety of X, which is nothing but the Cayley hyperdeterminant of type 2 × 2 × 2 × 2, can be expressed in terms of the stochastic local operation and classical communication-invariant polynomials as the discriminant of the miniversal deformation of the D4-singularity. As a consequence of this correspondence one obtains a finer-grained classification of entanglement classes of four-qubit systems. [ABSTRACT FROM AUTHOR]

The Ablowitz–Ladik equation is a very important model in nonlinear mathematical physics. In this paper, the hyperbolic function solitary wave solutions, the trigonometric function periodic wave solutions, and the rational wave solutions with more arbitrary parameters of two-dimensional Ablowitz–Ladik equation are derived by using the (G′/G)-expansion method, and the effects of the parameters (including the coupling constant and other parameters) on the linear stability of the exact solutions are analysed and numerically simulated. [ABSTRACT FROM AUTHOR]

Thermal noise in a cellular automaton (CA) refers to a random perturbation in its function which eventually leads the automaton to an equilibrium state controlled by a temperature parameter. We study the one-dimensional majority-3 CA under this model of noise. Without noise, each cell in the automaton decides its next state by majority voting among itself and its left and right neighbour cells. Transfer matrix analysis shows that the automaton always reaches a state in which every cell is in one of its two states with probability 1/2 and thus cannot remember even one bit of information. Numerical experiments, however, support the possibility of reliable computation for a long but finite time. [ABSTRACT FROM AUTHOR]

The lattice Boltzmann modeling of immiscible multiphase flows needs to be further validated, especially when density variation occurs between the different flow phases. From this perspective, the goal of this research is to introduce the multiple-relaxation-time operator into a lattice Boltzmann model in order to improve its numerical stability in the presence of large density and viscosity ratios. Essentially, this research shows that the introduction of this operator greatly improves the numerical stability of the approach compared to the original single-relaxation-time collision operator. In many lattice Boltzmann research studies, multiphase lattice Boltzmann methods are validated using a reduced number of test cases, and unsteady flow test cases are frequently omitted before much more complex flow configurations are simulated. In this context, several test cases are proposed to evaluate the behavior of a lattice Boltzmann method for simulating immiscible multiphase flows with high density and viscosity ratios. These are: (1) two-phase Couette flow; (2) three-phase Laplace law; (3) three-phase Zalesak disk; (4) two-phase flow between oscillating plates; (5) two-phase capillary wave; and (6) the two-phase oscillating cylindrical bubble. The first two involve a steady regime, and the remaining four an unsteady regime. [ABSTRACT FROM AUTHOR]

We present several classes of solitons in (1 + 1)-dimensional models where the standard canonical kinetic term is replaced by a Dirac–Born–Infeld (DBI) one. These are static solutions with finite energy and different properties, namely, they can have compact support, or be kink or lump-like, according to the type of potential chosen, which depend on the DBI parameter β. Through a combination of numerical and analytical arguments, by which the equation of motion is seen as that corresponding to another canonical model with a new β-dependent potential and a β-deformed energy density, we construct models in which increasing smoothly the DBI parameter both the compacton radius, the thickness of the kink and the width of the lump get modified until each soliton reaches its standard canonical shape as β → ∞. In addition we present compacton solutions whose canonical counterparts are not compact. [ABSTRACT FROM AUTHOR]

The Alday–Gaiotto–Tachikawa relations reduce S-duality to the modular transformations of conformal blocks. It was recently conjectured that, for the four-point conformal block, the modular transform up to the non-perturbative contributions can be written in the form of the ordinary Fourier transform when β ≡ −ϵ1/ϵ2 = 1. Here I extend this conjecture to general values of ϵ1, ϵ2. Namely, I argue that, for a properly normalized four-point conformal block the S-duality is perturbatively given by the Fourier transform for arbitrary values of the deformation parameters ϵ1, ϵ2. The conjecture is based on explicit perturbative computations in the first few orders of the string coupling constant g2 ≡ −ϵ1ϵ2 and hypermultiplet masses. [ABSTRACT FROM AUTHOR]

The quantum Hamiltonian generates in time a family of evolution operators. Continuity of this family holds within any choice of representation and, in particular, for the Weyl propagator, even though its simplest semiclassical approximation may develop caustic singularities. The phase jumps of the Weyl propagator across caustics have not been previously determined. The semiclassical approximation relies on individual classical trajectories together with their neighbouring tangent map. Based on the latter, one defines a continuous family of unitary tangent propagators, with an exact Weyl representation that is close to the full semiclassical approximation in an appropriate neighbourhood. The phase increment of the semiclassical Weyl propagator, as a caustic is crossed, is derived from the facts that the corresponding family of tangent operators belong to the metaplectic group and that the products of the tangent propagators are obtained from Gaussian integrals. The Weyl representation of the metaplectic group is presented here, with the correct phases determined within an intrinsic ambiguity for the overall sign. The elements that fully determine the phase increment across a particular caustic are then analysed. [ABSTRACT FROM AUTHOR]

We consider the reverse problem of the distinguishability of two quantum channels, which we call the disguising problem. Given two quantum channels, the goal here is to make the two channels identical by mixing with some other channels with minimal mixing probabilities. This quantifies how much one channel can disguise as the other. In addition, the possibility to trade-off between the two mixing probabilities allows one channel to be more preserved (less mixed) at the expense of the other. We derive lower- and upper-bounds of the trade-off curve and apply them to a few example channels. Optimal trade-off is obtained in one example. We relate the disguising problem and the distinguishability problem by showing that the former can lower and upper bound the diamond norm. We also show that the disguising problem gives an upper-bound on the key generation rate in quantum cryptography. [ABSTRACT FROM AUTHOR]

In this paper, we present an analytical solution of the interaction of the nanotube (NT) with a wedge disclination dipole in nanotube-based composites. The corresponding boundary value problem is solved exactly by using complex potential functions. The explicit expression of the force exerted on disclination dipole is given by using the generalized Peach—Koehler formula. As a numerical illustration, both the equilibrium position and the stability of the disclination dipole are evaluated for different material combinations, relative thickness of an NT, surface/interface effects, and the features of the disclination dipole. The results show that as the thickness of the NT layer increases, the NT has a relatively major role in the force acting on the disclination dipole in the NT-based composite. The cooperative effect of surface/interface stresses and the NT becomes considerable as the increase of NT layer thickness. The equilibrium position may occur, even more than one, due to the influences of the surface/interface stress and the NT thickening. The influences of the surface/interface stresses and the thickness of the NT layer on the force are greatly dependent on the disclination angle. [ABSTRACT FROM AUTHOR]

In this paper, the variable-coefficient diffusion—advection (DA) equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended (G′/G)-expansion method is applied to the DA equation to construct some new non-traveling wave solutions. [ABSTRACT FROM AUTHOR]

We obtain a new solution to the star–triangle relation for an Ising-type model with two kinds of spin variables at each lattice site, taking continuous real values and arbitrary integer values, respectively. The Boltzmann weights are manifestly real and positive. They are expressed through the Euler gamma function and depend on sums and differences of spins at the ends of an edge of the lattice. [ABSTRACT FROM AUTHOR]

We propose alternative definitions of classical states and quantumnesswitnesses by focusing on the algebra of observables of the system. A central role is assumed by the anticommutator of the observables, namely the Jordan product. This approach turns out to be suitable for generalizations to infinite dimensional systems. We then show that the whole algebra of observables can be generated by three elements by repeated application of the Jordan product. [ABSTRACT FROM AUTHOR]