Search

This present study is concerned with the group-invariant solutions of the (3 + 1)-dimensional Martinez Alonso–Shabat equation by using the Lie symmetry method. The Lie transformation technique is used to deduce the infinitesimals, Lie symmetry operators, commutation relations, and symmetry reductions. The optimal system for the obtained Lie symmetry algebra is obtained by using the concept of the adjoint map. As for now, the considered model equation is converted into nonlinear ordinary differential equations (ODEs) in two cases in the symmetry reductions. The exact closed-form solutions are obtained by applying constraint conditions on the symmetry generators. Due to the presence of arbitrary functional parameters, these group-invariant solutions are displayed based on suitable numerical simulations. The conservation laws are obtained by using the multiplier method. The conclusion is accounted for toward the end. [ABSTRACT FROM AUTHOR]

The “field tensor” is the tensor product of the electric fields of the interacting waves during a sum‐ or difference‐frequency generation nonlinear optical interaction. It is therefore a tensor describing light interacting with matter, the latter being characterized by the “electric susceptibility tensor.” The contracted product of these two tensors of equal rank gives the light‐matter interaction energy, whether or not propagation occurs. This notion having been explicitly or implicitly present from the early pioneering studies in nonlinear optics, its practical use has led to original developments in many highly topical theoretical or experimental situations, at the microscopic as well macroscopic level throughout a variety of coherent or non‐coherent processes. The aim of this review article is to rigorously explain the field tensor formalism in the context of tensor algebra and nonlinear optics in terms of a general time‐space multi‐convolutional development, using spherical tensors, with components expressed in the frame of a common basis set of irreducible tensors, or Cartesian tensors. A wide variety of media are considered, including biological tissues and their imaging, artificially engineered by various combinations of optical and static electric fields, with the two extremes of all‐optical and purely electric poling, and also bulk single crystals. [ABSTRACT FROM AUTHOR]

It is well known that k -contact geometry is a suitable framework to deal with non-conservative field theories. In this paper, we study some relations between solutions of the k -contact Euler–Lagrange equations, symmetries, dissipation laws and Newtonoid vector fields. We review the k -contact Euler–Lagrange equations written in terms of k -vector fields and sections and provide new results relating the solutions in both approaches. We also study different kinds of symmetries depending on the structures they preserve: natural (preserving the Lagrangian function), dynamical (preserving the solutions), and k -contact (preserving the underlying geometric structures) symmetries. For some of these symmetries, we provide Noether-like theorems relating symmetries and dissipation laws. We also analyze the relation between k -contact symmetries and Newtonoid vector fields. Throughout the paper, we will use the damped vibrating string as our main illustrative example. [ABSTRACT FROM AUTHOR]

Mathematical models and numerical simulations are necessary to understand the dynamical behaviors of complex systems. The aim of this work is to investigate closed-form solutions for the ball–plate problem considering a system derived from an optimal control problem for ball–plate dynamics. The nonlinear properties of ball and plate control system are presented in this work. To semi-analytically solve this system, we explored a second-order nonlinear differential equation. Consequently, we obtained the approximate closed-form solutions by the Optimal Parametric Iteration Method (OPIM) using only one iteration. A comparison between the analytical and corresponding numerical procedures reflects the advantages of the first one. The accordance between the obtained results and the numerical ones highlights that the procedure used is accurate, effective, and good to implement in applications such as sliding mode control to the ball-and-plate problem. [ABSTRACT FROM AUTHOR]

We investigate the two-component BKP hierarchy equation for its Lie point symmetries. To obtain a complete classification of the group-invariant solution, we derive the one-dimensional optimal system of subalgebras of A3,3(D⨂sT2). By employing those subalgebras, we construct the invariant solutions which are represented through Weierstrass elliptic functions, Jacobi elliptic functions, and soliton solutions. Also, we analyse the existence of a bounded travelling-wave solution for the equation. Moreover, through the utilization of scale-invariant symmetry, we derive a self-similar solution. Additionally, by conducting singularity analysis, the solution can be expressed in the form of a right Painlevè series.

Historically and to date, the continuity equation (C.E.) has served as a consistency criterion for the development of physical theories. In this paper, we study the C.E. employing the mathematical framework of space–time algebra (STA), showing how common equations in mathematical physics can be identified and derived from the C.E.'s structure. We show that, in STA, the nabla equation given by the geometric product between the vector derivative operator and a generalized multivector can be identified as a system of scalar and vectorial C.E.—and, thus, another form of the C.E. itself. Associated with this continuity system, decoupling conditions are determined, and a system of wave equations and the generalized analogous quantities to the energy–momentum vectors and the Lorentz force density (and their corresponding C.E.) are constructed. From the symmetry transformations that make the C.E. system's structure invariant, a system with the structure of Maxwell's field equations is derived. This indicates that a Maxwellian system can be derived not only from the nabla equation and the generalized continuity system as special cases, but also from the symmetries of the C.E. structure. Upon reduction to well-known simpler quantities, the results found are consistent with the usual STA treatment of electrodynamics and hydrodynamics. The diffusion equation is explored from the continuity system, where it is found that, for decoupled systems with constant or explicitly dependent diffusion coefficients, the absence of external vector sources implies a loss in the diffusion equation structure, transforming it into Helmholtz-like and wave equations. [ABSTRACT FROM AUTHOR]

This work offers a (semi-analytical) solution for a second-order nonlinear differential equation associated to the dynamical Kermack–McKendrick system. The approximate closed-form solutions are obtained by means of the Optimal Homotopy Asymptotic Method (OHAM) using only one iteration. These solutions represent the ε -approximate OHAM solutions. The advantages of this analytical procedure are reflected by comparison between the analytical solutions, numerical results, and corresponding iterative solutions (via a known iterative method). The obtained results are in a good agreement with the exact parametric solutions and corresponding numerical results, and they highlight that our procedure is effective, accurate, and useful for implementation in applications. [ABSTRACT FROM AUTHOR]

We present the experimental finding of multiple simultaneous two-fold degeneracies in the spectrum of a Kerr oscillator subjected to a squeezing drive. This squeezing drive resulting from a three-wave mixing process, in combination with the Kerr interaction, creates an effective static two-well potential in the phase space rotating at half the frequency of the sinusoidal drive generating the squeezing. Remarkably, these degeneracies can be turned on-and-off on demand, as well as their number by simply adjusting the frequency of the squeezing drive. We find that when the detuning Δ between the frequency of the oscillator and the second subharmonic of the drive equals an even multiple of the Kerr coefficient K, Δ/K = 2m, the oscillator displays m+1 exact, parity-protected, spectral degeneracies, insensitive to the drive amplitude. These degeneracies can be explained by the unusual destructive interference of tunnel paths in the classically forbidden region of the double well static effective potential that models our experiment. Exploiting this interference, we measure a peaked enhancement of the incoherent well-switching lifetime, thus creating a protected cat qubit in the ground state manifold of our oscillator. Our results illustrate the relationship between degeneracies and noise protection in a driven quantum system. [ABSTRACT FROM AUTHOR]

Atomistic simulation is performed to study the defect properties and spectroscopy in the MgGa2O4 structure. The calculations indicate that the most favorable type of intrinsic defect is generated by the cation antisite defect, in which there is an exchange of positions between Mg2+ and Ga3+ ions. The calculation also indicates that the incorporation of Eu3+ dopant at the Ga3+(2) site is the most energetically favorable. According to a spectroscopic study using the crystal field approach, Eu3+ replaces the Ga3+ site occupying a combination of C4 and C4h symmetries while maintaining the same amount of the non‐null crystal field parameters. This result is important for the reproduction of experimental energy sublevels and ΔE (7F1) manifold splitting. [ABSTRACT FROM AUTHOR]

In the paper, we describe a method for deriving generalized symmetries for a generic discrete quadrilateral equation that allows a Lax pair. Its symmetry can be interpreted as a flow along the tangent direction of its solution evolving with a Lie group parameter t. Starting from the spectral problem of the quadrilateral equation and assuming the eigenfunction evolves with the parameter t, one can obtain a differential-difference equation hierarchy, of which the flows are proved to be commuting symmetries of the quadrilateral equation. We prove this result by using the zero-curvature representations of these flows. As an example, we apply this method to derive symmetries for the lattice potential Korteweg–de Vries equation. [ABSTRACT FROM AUTHOR]

Atomistic simulation is performed to study the defect properties and spectroscopy in the MgGa2O4 structure. The calculations indicate that the most favorable type of intrinsic defect is generated by the cation antisite defect, in which there is an exchange of positions between Mg2+ and Ga3+ ions. The calculation also indicates that the incorporation of Eu3+ dopant at the Ga3+(2) site is the most energetically favorable. According to a spectroscopic study using the crystal field approach, Eu3+ replaces the Ga3+ site occupying a combination of C4 and C4h symmetries while maintaining the same amount of the non‐null crystal field parameters. This result is important for the reproduction of experimental energy sublevels and ΔE (7F1) manifold splitting. [ABSTRACT FROM AUTHOR]

This article analyzes the analytic and solitary wave solutions of the one-dimensional Zabolotskaya-Khokholov (ZK) dynamical model which provides information about the propagation of sound beam or confined wave beam in nonlinear media and studies of beam deformation. By the Lie symmetry analysis method, we acquire the vector fields, commutation relations, optimal system, reduction, and analytic solutions to the specified equation by exerting the Lie group method. Moreover, the solitary wave solutions of the ZK model are procured by exerting the new auxiliary equation method (NAEM). The behavior of the acquired outcomes for several cases is exhibited graphically through two and three-dimensional dynamical wave profiles. Furthermore, the conservation laws of the ZK model are acquired by Ibragimov’s new conservation theorem.

By considering the basis-covariant constituents of N-Higgs-doublet potentials, we derive necessary and sufficient conditions for canonical SO(4)C Custodial Symmetry (CS) of potentials with N>2 doublets, based on representation-theoretical and geometrical relations. In essence, our characterization relates the presence of canonical CS to basis-covariant vectors corresponding to particular bases of the defining representation of the orthogonal Lie algebras. For N=3,4 and 5, the conditions demand little computational effort to be evaluated, and we provide practical algorithms that may be efficiently implemented in a computer program, for deciding whether or not a potential is custodial-symmetric.

We study various classes of the nonlinear dynamics of some high order parabolic equations like the Oskolkov–Benjamin–Bona–Mahony–Burgers and Benjamin–Bona–Mahony–Peregrine–Burger equations that arise in the study of some wave phenomena. Also, a broader class of partial differential equations are used in modelling ocean waves that originate from the Ostrovsky equation. We study the invariance properties via the Lie invariance method for the nonlinear systems and further establish classes of conservation laws for models arises in this study. We show how the relationship leads to double reductions of the systems. This relationship is determined by a recent result involving multipliers that lead to a total divergence or closed form of the differential equation under investigation.

The symmetry approach to the classification of evolution integrable partial differential equations (see, for example (Mikhailov et al.,1991)) produces an infinite series of functions, defined in terms of the right hand side, that are conserved densities of any equation having infinitely many infinitesimal symmetries. For instance, the function ∂f∂ux has to be a conserved density of any integrable equation of the KdV type ut=uxxx+f(u,ux). This fact imposes very strong conditions on the form of the function f. In this paper we construct similar canonical densities for equations of the Boussinesq type. In order to do that, we write the equations as evolution systems and generalise the formal diagonalisation procedure proposed in Mikhailov et al. (1987) to these systems.

In this lecture note, we give a basic introduction to the rapidly developing concepts of generalized symmetries, from the perspectives of both high energy physics and condensed matter physics. In particular, we emphasize on the (invertible) higher-form and higher group symmetries. For the physical applications, we discuss the geometric engineering of QFTs in string theory and the symmetry-protected topological (SPT) phases in condensed matter physics. The lecture note is based on a short course on generalized symmetries, jointly given by Yi-Nan Wang and Qing-Rui Wang in Feb. 2023, which took place at School of Physics, Peking University (https://indico.ihep.ac.cn/event/18796/). [ABSTRACT FROM AUTHOR]

Mathematical models and numerical simulations are necessary to understand the functions of biological rhythms, to comprehend the transition from simple to complex behavior and to delineate the conditions under which they arise. The aim of this work is to investigate the R o ¨ ssler-type system. This system could be proposed as a theoretical model for biological rhythms, generalizing this formula for chaotic behavior. It is assumed that the R o ¨ ssler-type system has a Hamilton–Poisson realization. To semi-analytically solve this system, a Bratu-type equation was explored. The approximate closed-form solutions are obtained using the Optimal Parametric Iteration Method (OPIM) using only one iteration. The advantages of this analytical procedure are reflected through a comparison between the analytical and corresponding numerical results. The obtained results are in a good agreement with the numerical results, and they highlight that our procedure is effective, accurate and usefully for implementation in applicationssuch as an oscillator with cubic and harmonic restoring forces, the Thomas–Fermi equation and the Lotka–Voltera model with three species. [ABSTRACT FROM AUTHOR]

We describe all metrics geodesically compatible with a gl -regular Nijenhuis operator L. The set of such metrics is large enough so that a generic local curve γ is a geodesic for a suitable metric g from this set. Next, we show that a certain evolutionary PDE system of hydrodynamic type constructed from L preserves the property of γ to be a g-geodesic. This implies that every metric g geodesically compatible with L gives us a finite-dimensional reduction of this PDE system. We show that its restriction onto the set of g-geodesics is naturally equivalent to the Poisson action of R n on the cotangent bundle generated by the integrals coming from geodesic compatibility. [ABSTRACT FROM AUTHOR]

We presented a new and complete algorithm for detecting isometries and symmetries of implicit algebraic surfaces. First, our method reduced the problem to the case of isometries fixing the origin. Second, using tools from elimination theory and polynomial factoring, we determined the desired isometries between the surfaces. We have implemented the algorithm in Maple to provide evidences of the efficiency of the method.

These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form symmetries and their properties including 't Hooft anomalies, gauging and spontaneous symmetry breaking. We also introduce the useful notion of symmetry topological field theories (SymTFTs). Furthermore, an introduction to higher-group symmetries describing mixings of higher-form symmetries is provided. Some advanced topics covered include the encoding of higher-form symmetries in holography and geometric engineering constructions in string theory. Throughout the text, all concepts are consistently illustrated using gauge theories as examples. [ABSTRACT FROM AUTHOR]

We study the role of symmetries in control systems through the geometric algebra approach. We discuss two specific control problems on Carnot groups of step 2 invariant with respect to the action of SO(3)$$ SO(3) $$. We understand the geodesics as the curves in suitable geometric algebras which allows us to assess a new algorithm for the local control. [ABSTRACT FROM AUTHOR]

In this paper we present the theorem on Lie integrability by quadratures for time-independent Hamiltonian systems on symplectic and contact manifolds, and for time-dependent Hamiltonian systems on cosymplectic and cocontact manifolds. We show that having a solvable Lie algebra of constants of motion for a Hamiltonian system is equivalent to having a solvable Lie algebra of symmetries of the vector field defining the dynamics of the system, which allows us to find solutions of the equations of motion by quadratures. [ABSTRACT FROM AUTHOR]

We presented a new and complete algorithm for detecting isometries and symmetries of implicit algebraic surfaces. First, our method reduced the problem to the case of isometries fixing the origin. Second, using tools from elimination theory and polynomial factoring, we determined the desired isometries between the surfaces. We have implemented the algorithm in Maple to provide evidences of the efficiency of the method. [ABSTRACT FROM AUTHOR]

We review some aspects of higher spin symmetry, in (Anti-)de Sitter and flat space–times, aiming at closing the gap between the constantly curved and flat cases. On (Anti-)de Sitter space, non-Abelian higher spin algebras are at the core of the construction of interacting theories of higher spin gravity. By considering a suitable contraction of these algebras, we show that similar considerations can apply to Minkowski space–time. We identify a unique candidate to the role of higher spin symmetry in flat space that can also be built as a quotient of the universal enveloping algebra of the isometries of the vacuum, as in the (Anti-)de Sitter case. We then show how to recover the free dynamics from the gauging of the resulting algebra at the linear level. Finally, we show how to realise this gauge algebra as a subset of the global symmetries of a Carrollian conformal scalar field theory living on the null infinity of Minkowski space–time. This theory emerges as the limit of vanishing speed of light of a free massless relativistic scalar. The identification of the same higher spin algebra that rules the dynamics in the bulk of space–time within the global symmetries of this boundary theory paves the way to a flat counterpart of higher spin holography. [ABSTRACT FROM AUTHOR]

Quasicrystals endowed with piezoelectric properties belong nowadays to novel piezoelectric materials. In this work, the basic framework of generalized piezoelectricity theory of quasicrystals is investigated by providing an improvement of the existing constitutive modelling. It is shown, for the first time, that the tensor of phason piezoelectric moduli is fully asymmetric without any major or minor symmetry, which has important consequences on the constitutive relations as well as on its classification with respect to the crystal systems and Laue classes. The exploration of the tensor of phason piezoelectric moduli has a significant impact on the understanding of the piezoelectric properties of quasicrystals. Using the group representation theory, the classification of the tensor of phason piezoelectric moduli with respect to the crystal systems and Laue classes is given for one-dimensional quasicrystals. The number of independent components of the phason piezoelectric moduli is determined for all 31 point groups of one-dimensional quasicrystals. It is proven that the 10 centrosymmetric crystallographic point groups have no piezoelectric effects and that the remaining 21 non-centrosymmetric crystallographic point groups exhibit piezoelectric effects due to both phonon and phason fields. Moreover, the constitutive relations for one-dimensional hexagonal piezoelectric quasicrystals of Laue class 9 with point group 6 and Laue class 10 with point group 6 m m are explicitly derived, showing that the constitutive relations for piezoelectric quasicrystals depend on the considered Laue class as well as on the point group. Comparisons with existing results in the literature and discussion are also given. [ABSTRACT FROM AUTHOR]

In this paper, in order to provides a powerful new tool for quantitative and qualitative analysis of dynamics properties in flexible mechanical multibody systems, the symmetry theory and numerical algorithms for preserving structure in modern analytical mechanics is introduced into flexible multibody dynamics. First, taking the hub-beam systems as an example, the original nonlinear partial differential-integral equations of the system dynamics model are discretized into the finite-dimensional Lagrange equations by using the assumed modal method. Second, the group analysis theory is introduced and the criterion equations and the corresponding conserved quantities of Noether symmetries are given according to the invariance principle, which provide an effective way for analytic integral theory of dynamic equations. Finally, a conserved quantity-preserving numerical algorithm is constructed by coordinates incremental discrete gradient, which makes full use of the invariance of conserved quantity to eliminate the error consumption for a long time. The simulation results show that the deeper mechanical laws and motion characteristics of flexible mechanical multibody systems dynamics can be obtained with the help of symmetries and conserved quantities, which can provide reference for more precise dynamic optimization design and advanced control of systems.

This work offers a (semi-analytical) solution for a second-order nonlinear differential equation associated to the dynamical Kermack–McKendrick system. The approximate closed-form solutions are obtained by means of the Optimal Homotopy Asymptotic Method (OHAM) using only one iteration. These solutions represent the ε-approximate OHAM solutions. The advantages of this analytical procedure are reflected by comparison between the analytical solutions, numerical results, and corresponding iterative solutions (via a known iterative method). The obtained results are in a good agreement with the exact parametric solutions and corresponding numerical results, and they highlight that our procedure is effective, accurate, and useful for implementation in applications.

In the paper, we describe a method for deriving generalized symmetries for a generic discrete quadrilateral equation that allows a Lax pair. Its symmetry can be interpreted as a flow along the tangent direction of its solution evolving with a Lie group parameter t. Starting from the spectral problem of the quadrilateral equation and assuming the eigenfunction evolves with the parameter t, one can obtain a differential-difference equation hierarchy, of which the flows are proved to be commuting symmetries of the quadrilateral equation. We prove this result by using the zero-curvature representations of these flows. As an example, we apply this method to derive symmetries for the lattice potential Korteweg–de Vries equation.

In this current study, the potential-KdV equation has been altered by the addition of a new stochastic term. The transmission of nonlinear optical solitons and photons is described by the new stochastic potential-KdV (spKdV), which applies to electric circuits and multi-component plasmas. The Lie symmetry approach is presented to find out the symmetry generators. The matrices method is applied to develop the one-dimensional optimal system for the acquired Lie algebra. Based on each element of the one-dimensional optimal system, symmetry reductions are used to reduce the considered model into nonlinear ordinary differential equations (ODEs). One of these nonlinear ODEs is solved using a new novel generalized exponential rational function (GERF) approach. Graphical interpretation of a few of the acquired results is added by taking the suitable values of the constants. A novel general theorem which is known as Ibragimov’s theorem enables the computation of conservation laws for any differential equation, without requiring the presence of Lagrangians. The idea of the self-adjoint equations for nonlinear equations serves as the foundation for this theorem. We present that the spKdV equation is nonlinearly self-adjoint. The conserved quantities are computed in line with each symmetry generator using Ibragimov’s theorem.

This review paper gives an overview of the method of multipliers for partial differential equations (PDEs). This method has made possible a lot of solutions to PDEs that are of interest in many areas such as applied mathematics, mathematical physics, engineering, etc. Looking at the history of the method and synthesizing the newest developments, we hope to give it the attention that it deserves to help develop the vast amount of work still needed to understand it and make the best use of it. It is also an interesting and a relevant method in itself that could possibly give interesting results in areas of mathematics such as modern algebra, group theory, topology, etc. The paper will be structured in such a manner that the last review known for this method will be presented to understand the theoretical framework of the method and then later work done will be presented. The information of four recent papers further developing the method will be synthesized and presented in such a manner that anyone interested in learning this method will have the most relevant information available and have all details cited for checking. [ABSTRACT FROM AUTHOR]

Classical forbidden processes paved the way for the description of mechanical systems with the help of complex Hamiltonians. Fractional integrals of complex order appear as a natural generalization of those of real order. We propose the complex fractional Euler-Lagrange equation, obtained by finding the stationary values associated with the fractional integral of complex order. The complex Hamiltonian obtained from the Lagrangian is suitable for describing nonconservative systems. We conclude by presenting the conserved quantities attached to Noether symmetries corresponding to complex systems. We illustrate the theory with the aid of the damped oscillatory system. [ABSTRACT FROM AUTHOR]

The possibility for one to recover the parameters—weights and biases—of a neural network thanks to the knowledge of its function on a subset of the input space can be, depending on the situation, a curse or a blessing. On one hand, recovering the parameters allows for better adversarial attacks and could also disclose sensitive information from the dataset used to construct the network. On the other hand, if the parameters of a network can be recovered, it guarantees the user that the features in the latent spaces can be interpreted. It also provides foundations to obtain formal guarantees on the performances of the network. It is therefore important to characterize the networks whose parameters can be identified and those whose parameters cannot. In this article, we provide a set of conditions on a deep fully-connected feedforward ReLU neural network under which the parameters of the network are uniquely identified—modulo permutation and positive rescaling—from the function it implements on a subset of the input space. [ABSTRACT FROM AUTHOR]

Bayesian Confirmation Measures (BCMs) are used to assess the degree to which an evidence (or premise) E supports or contradicts an hypothesis (or conclusion) H, making use of prior probability P r (H) , posterior probability P r (H | E) and of probability of evidence P r (E) . In the literature many BCMs have been defined with the consequent need for their comparison. For this purpose, various criteria have been proposed and some of these refer to symmetry properties. We relate the set of possible symmetries of BCMs, via an isomorphism, to the dihedral group of symmetries of the square. In this way it is possible to identify 10 subsets of symmetries that can coexist, for each subset we suggest a representative BCM, defining at this aim two new BCMs. The structure of the subgroups of the dihedral group allows also to provide an algorithm that simplifies the verification of the symmetry properties. Addressing the debate on which symmetry properties should be considered as desirable and which should not, we define asymmetry measures for BCMs. In fact, different BCMs that do not satisfy a specific symmetry property may exhibit different levels of asymmetry, this way resulting more (less) desirable. The evidence for the practical use of the approach is given through the numerical evaluation of the asymmetry degrees of some BCMs, showing this way how it is possible to discover some of their characteristics, similarities and differences. [ABSTRACT FROM AUTHOR]

This paper discusses complexity theory, that is, the many theories that have been proposed for emergence of complexity from the underlying physics. Our aim is to identify which aspects have turned out to be the more fundamental ones as regards the emergence of biology, engineering, and digital computing, as opposed to those that are in fact more peripheral in these contexts. In the cases we consider, complexity arises via adaptive modular hierarchical structures that are open systems involving broken symmetries. Each emergent level is causally effective because of the meshing together of upwards and downwards causation that takes place consistently with the underlying physics. Various physical constraints limit the outcomes that can be achieved. The underlying issue concerns the origin of consciousness and agency given the basis of life in physics, which is structured starting from symmetries and variational principles with no trace of agency. A possible solution is to admit that consciousness is an irreducible emergent property of matter. [ABSTRACT FROM AUTHOR]

It is often claimed that one can avoid the kind of underdetermination that is a typical consequence of symmetries in physics by stipulating that symmetry-related models represent the same state of affairs (Leibniz Equivalence). But recent commentators (Dasgupta in Philos Perspect 25:115–160, 2011; Pooley in: Knox and Wilson (eds) The Routledge companion to the philosophy of physics, Routledge, Milton Park, 2021; Pooley and Read in Br J Philos Sci, 2021, ; Teitel in J Philos 119:233–278, 2021) have responded that claims about the representational capacities of models are irrelevant to the issue of underdetermination, which concerns possible worlds themselves. In this paper I distinguish two versions of this objection: (1) that a theory’s formalism does not (fully) determine the space of physical possibilities, and (2) that the relevant notion of possibility is not physical possibility. I offer a refutation of each. [ABSTRACT FROM AUTHOR]

Given r ⩾ 1 , the discrete C r -centralizer of a vector field is formed by the set of its symmetries, that is, the set of C r -diffeomorphisms commuting with the flow generated by it. Here we prove that if M is a compact surface and 2 ⩽ r ⩽ ∞ then there exists a C r -open and dense subset of vector fields O ⊂ X r (M) whose C r -discrete centralizer is abelian. Moreover, we show that every symmetry of the flow (X t) t ∈ R generated by X ∈ O is isomorphic to the direct product of the time-t maps of the flow and an abelian subgroup formed by involutions. In particular, we deduce that there exist C 1 -open sets of C r -Morse-Smale vector fields on surfaces whose C r -discrete centralizer is trivial. [ABSTRACT FROM AUTHOR]

In this paper, we present algebraic tools to obtain normal forms of ω -Hamiltonian vector fields under a semisymplectic action of a Lie group, by taking into account the symmetries and reversing symmetries of the vector field. The normal forms resulting from the process preserve the Hamiltonian condition and the types of symmetries of the original vector field. Our techniques combine the classical method of normal forms of Hamiltonian vector fields with the invariant theory of groups. [ABSTRACT FROM AUTHOR]

We define symmetries in non-relativistic quantum electrodynamics, which have the physical interpretation of rotation, parity, and time reversal symmetry. We collect transformation properties related to these symmetries in Fock space representation as well as in the Schrödinger representation. As an application, we generalize and improve theorems about Kramers' degeneracy in non-relativistic quantum electrodynamics. [ABSTRACT FROM AUTHOR]

The one-dimensional hyperbolic mean curvature flow for Lagrangian graphs is discussed in this paper. In the beginning, infinitesimal generators, symmetry groups and an optimal system of symmetries for the proposed hyperbolic Lagrangian mean curvature flow are obtained based on the Lie symmetry approach. Additionally, several invariant solutions are discovered using reduced equations. More specifically, we use the power series method to attain explicit solutions. [ABSTRACT FROM AUTHOR]