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Relevant bibliographies by topics / Symmetry of solution

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Academic literature on the topic 'Symmetry of solution'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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Journal articles on the topic "Symmetry of solution"

1

Heule, Marijn, and Toby Walsh. "Symmetry in Solutions." Proceedings of the AAAI Conference on Artificial Intelligence 24, no. 1 (July 3, 2010): 77–82. http://dx.doi.org/10.1609/aaai.v24i1.7549.

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We define the concept of an internal symmetry. This is a symmety within a solution of a constraint satisfaction problem. We compare this to solution symmetry, which is a mapping between different solutions of the same problem. We argue that we may be able to exploit both types of symmetry when finding solutions. We illustrate the potential of exploiting internal symmetries on two benchmark domains: Van der Waerden numbers and graceful graphs. By identifying internal symmetries we are able to extend the state of the art in both cases.

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Okino, Shinya, and Masato Nagata. "Asymmetric travelling waves in a square duct." Journal of Fluid Mechanics 693 (January 6, 2012): 57–68. http://dx.doi.org/10.1017/jfm.2011.455.

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AbstractTwo types of asymmetric solutions are found numerically in square-duct flow. They emerge through a symmetry-breaking bifurcation from the mirror-symmetric solutions discovered by Okino et al. (J. Fluid Mech., vol. 657, 2010, pp. 413–429). One of them is characterized by a pair of streamwise vortices and a low-speed streak localized near one of the sidewalls and retains the shift-and-reflect symmetry. The bifurcation nature as well as the flow structure of the solution show striking resemblance to those of the asymmetric solution in pipe flow found by Pringle & Kerswell (Phys. Rev. Lett., vol. 99, 2007, A074502), despite the geometrical difference between their cross-sections. The solution seems to be embedded in the edge state of square-duct flow identified by Biau & Bottaro (Phil. Trans. R. Soc. Lond. A, vol. 367, 2009, pp. 529–544). The other solution deviates slightly from the mirror-symmetric solution from which it bifurcates: the shift-and-rotate symmetry is retained but the mirror symmetry is broken.

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AMDJADI, FARIDON. "THE CALCULATION OF THE HOPF/HOPF MODE INTERACTION POINT IN PROBLEMS WITH Z2-SYMMETRY." International Journal of Bifurcation and Chaos 12, no. 08 (August 2002): 1925–35. http://dx.doi.org/10.1142/s0218127402005595.

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A direct method for finding the mode interaction point of a symmetry breaking Hopf bifurcation and a symmetry preserving Hopf bifurcation in problems with ℤ2-symmetry is developed. It has been shown that the mode interaction point corresponds to an isolated solution of an extended system. The existence of this solution relies on the occurrence of the mode interaction point and this is interpreted in the context of the mode interaction, using centre manifold reduction. A numerical example with the symmetry group O(2), which has a branch of ℤ2-symmetric nontrivial steady state solutions, is considered to provide clarification of the method.

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Perrin, Charles L. "Symmetry of hydrogen bonds in solution." Pure and Applied Chemistry 81, no. 4 (January 1, 2009): 571–83. http://dx.doi.org/10.1351/pac-con-08-08-14.

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A classic question regarding hydrogen bonds (H-bonds) concerns their symmetry. Is the hydrogen centered or is it closer to one donor and jumping between them? These possibilities correspond to single- and double-well potentials, respectively. The NMR method of isotopic perturbation can answer this question. It is illustrated with 3-hydroxy-2-phenylpropenal and then applied to dicarboxylate monoanions. The 18O-induced 13C NMR splittings signify that their intramolecular H-bonds are asymmetric and that each species is a pair of tautomers, not a single symmetric structure, even though maleate and phthalate are symmetric in crystals. The asymmetry is seen across a wide range of solvents and a wide variety of monoanions, including 2,3-di-tert-butylsuccinate and zwitterionic phthalates. Asymmetry is also seen in monoprotonated 1,8-bis(dimethylamino)naphthalenediamines, N,N'-diaryl-6-aminofulvene-2-aldimines, and 6-hydroxy-2-formylfulvene. The asymmetry is attributed to the disorder of the local environment, establishing an equilibrium between solvatomers. The broader implications of these results regarding the role of solvation in breaking symmetry are discussed. It was prudent to confirm a secondary deuterium isotope effect (IE) on amine basicity by NMR titration of a mixture of PhCH2NH2 and PhCHDNH2. The IE is of stereoelectronic origin. It is proposed that symmetric H-bonds can be observed in crystals but not in solution because a disordered environment induces asymmetry, whereas a crystal can guarantee a symmetric environment. The implications for the controversial role of low-barrier H-bonds in enzyme-catalyzed reactions are discussed.

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DZHUNUSHALIEV, V., H. J. SCHMIDT, and O. RURENKO. "SPHERICALLY SYMMETRIC SOLUTIONS IN MULTIDIMENSIONAL GRAVITY WITH THE SU(2) GAUGE GROUP AS THE EXTRA DIMENSIONS." International Journal of Modern Physics D 11, no. 05 (May 2002): 685–701. http://dx.doi.org/10.1142/s0218271802001925.

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The multidimensional gravity on the principal bundle with the SU(2) gauge group is considered. The numerical investigation of the spherically symmetric metrics with the center of symmetry is made. The solution of the gravitational equations depends on the boundary conditions of the "SU(2) gauge potential" (off-diagonal metric components) at the symmetry center and on the type of symmetry (symmetrical or antisymmetrical) of these potentials. In the chosen range of the boundary conditions it is shown that there are two types of solutions: wormhole-like and flux tube. The physical application of such kind of solutions as quantum handles in a spacetime foam is discussed.

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Fakhar, K., Zu-Chi Chen, and Xiaoda Ji. "Symmetry analysis of rotating fluid." ANZIAM Journal 47, no. 1 (July 2005): 65–74. http://dx.doi.org/10.1017/s1446181100009779.

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AbstractThe machinery of Lie theory (groups and algebras) is applied to the unsteady equations of motion of rotating fluid. A special-function type solution for the steady state is derived. It is then shown how the solution generates an infinite number of time-dependent solutions via three arbitrary functions of time. This algebraic structure also provides the mechanism to search for other solutions since its character is inferred from the basic equations.

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GAZZINI, MARITA, and ROBERTA MUSINA. "HARDY–SOBOLEV–MAZ'YA INEQUALITIES: SYMMETRY AND BREAKING SYMMETRY OF EXTREMAL FUNCTIONS." Communications in Contemporary Mathematics 11, no. 06 (December 2009): 993–1007. http://dx.doi.org/10.1142/s0219199709003636.

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Denote points in ℝk × ℝN - k as pairs ξ = (x,y), and assume 2 ≤ k < N. In this paper, we study the problem [Formula: see text] where [Formula: see text] and [Formula: see text], the Hardy constant. Our results are the following: (i) Let [Formula: see text]. Then there exists at least an entire cylindrically symmetric solution. (ii) Let [Formula: see text] and λ ≥ 0. Then any solution v ∈ Lp(ℝN;|x|-bdξ) is cylindrically symmetric. (iii) Let [Formula: see text] and [Formula: see text]. Then ground state solutions are not cylindrically symmetric, and therefore there exist at least two distinct entire solutions. We prove also similar results for the degenerate problem [Formula: see text] namely, for the Euler–Lagrange equations of the Maz'ya inequality with cylindrical weights.

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Kovalenko, M. D., I. V. Menshova, A. P. Kerzhaev, and T. D. Shulyakovskaya. "Exact and beam solutions for a narrow clamped rectangle." Journal of Physics: Conference Series 2231, no. 1 (April 1, 2022): 012027. http://dx.doi.org/10.1088/1742-6596/2231/1/012027.

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Abstract The paper presents formulas describing an exact solution to the boundary value problem of the theory of elasticity in a rectangle in which the horizontal sides are rigidly clamped, and normal and tangential stresses are given on the vertical ones. Only an odd-symmetric deformation of the rectangle with respect to the horizontal axis of symmetry and an even-symmetric deformation of the rectangle with respect to the vertical axis of symmetry are considered. The paper is based on the previously obtained solutions for a free half-strip and a free rectangle.

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Kovalenko, M. D., I. V. Menshova, A. P. Kerzhaev, and T. D. Shulyakovskaya. "Exact and beam solutions for a narrow clamped rectangle." Journal of Physics: Conference Series 2231, no. 1 (April 1, 2022): 012027. http://dx.doi.org/10.1088/1742-6596/2231/1/012027.

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Abstract The paper presents formulas describing an exact solution to the boundary value problem of the theory of elasticity in a rectangle in which the horizontal sides are rigidly clamped, and normal and tangential stresses are given on the vertical ones. Only an odd-symmetric deformation of the rectangle with respect to the horizontal axis of symmetry and an even-symmetric deformation of the rectangle with respect to the vertical axis of symmetry are considered. The paper is based on the previously obtained solutions for a free half-strip and a free rectangle.

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TEH, ROSY, and K. M. WONG. "MULTIMONOPOLE–ANTIMONOPOLE SOLUTIONS OF THE SU(2) YANG–MILLS–HIGGS FIELD THEORY." International Journal of Modern Physics A 19, no. 03 (January 30, 2004): 371–91. http://dx.doi.org/10.1142/s0217751x04017653.

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In this paper we constructed exact static multimonopole–antimonopole solutions of the YMH field theory. By labelling these solutions as A1, A2, B1, and B2, we notice that the exact axially symmetric 1-monopole — two antimonopoles solution is actually a special case of the A1 solution when the topological index parameter m=1. Also the B1 solution will reduce to a spherically symmetric Wu–Yang type monopole of unit charge when m=0. All these exact solutions satisfy the first order Bogomol'nyi equations and possess infinite energy. Hence they are a different type of the BPS solution. Except for the A1 solution when m=1 and the B1 solution when m=0, these solutions in general do not possess axial symmetry. They represent different combinations of monopoles, multimonopole, and antimonopoles, symmetrically arranged about the z-axis.

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Dissertations / Theses on the topic "Symmetry of solution"

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Otto, Simon [Verfasser], and Klaus [Akademischer Betreuer] Solbach. "Solution to the Broadside Problem and Symmetry Properties of Periodic Leaky-Wave Antennas / Simon Otto. Betreuer: Klaus Solbach." Duisburg, 2016. http://d-nb.info/1109745710/34.

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ABATANGELO, LAURA. "Multiplicity of solutions to elliptic equations the case of singular potentials in second order problems and morse theory in a fourth order problem." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2011. http://hdl.handle.net/10281/20336.

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Symmetry properties of solutions to some nonlinear Schroedinger equations are investigated. In particular, here the Laplace operator is perturbed by singular potentials which do not belong to the Kato class. A result of symmetry breaking of solutions is obtained provided a preliminary theorem about biradial solutions is stated. Further, a problem involving the biharmonic operator and exponential nonlinearity in dimension 4 is studied, connecting degree counting formulas with direct methods of calculus of variations via Morse theory and deformation lemmas.

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Wang, Qun. "Solutions Périodiques Symétriques dans le Problème de N-Vortex." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLED069/document.

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Cette thèse porte sur l’étude des solutions périodiques du problème des N-tourbillons à vorticité positive. Ce problème, formulé par Helmholtz il y a plus de 160 ans, possède une histoire très riche et reste un domaine de recherche très actif. Pour un nombre quelconque de tourbillons et sans contrainte sur les vorticités, ce système n’est pas intégrable au sens de Liouville : on ne peut trouver de solution périodique non triviale par des méthodes explicites. Dans cette thèse, à l’aide de méthodes variationnelles, nous prouvons l’existence d’une infinité de solutions périodiques non triviales pour un système de N tourbillons à vorticités positives. De plus, lorsque les vorticités sont des nombres rationnels positifs, nous montrons qu’il n’existe qu’un nombre fini de niveaux d’énergie sur lesquels un équilibre relatif pourrait exister. Enfin, pour un système de N-tourbillons identiques, nous montrons qu’il existe une infinité de chorégraphies simples
This thesis focuses on the study of the periodic solutions of the N-vortex problem of positive vorticity. This problem was formulated by Helmholtz more than 160 years ago and remains an active research field. For an undetermined number of vortices and general vorticities the system is not Liouville integrable and periodic solutions cannot be determined explicitly, except for relative equilibria. By using variational methods, we prove the existence of infinitely many non-trivial periodic solutions for arbitrary N and arbitrary positive vorticities. Moreover, when the vorticities are positive rational numbers, we show that there exists only finitely many energy levels on which there might exist a relative equilibrium. Finally, for the identical N-vortex problem, we show that there exists infinitely many simple choreographies

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Sang, W. M. "A search for the Standard Model Higgs boson using the OPAL detector at LEP." Thesis, Brunel University, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.340840.

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Eschke, Andy. "Analytical solution of a linear, elliptic, inhomogeneous partial differential equation in the context of a special rotationally symmetric problem of linear elasticity." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-149970.

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In addition to previous publications, the paper presents the analytical solution of a special boundary value problem which arises in the context of elasticity theory for an extended constitutive law and a non-conservative symmetric ansatz. Besides deriving the general analytical solution, a specific form for linear boundary conditions is given for user convenience.

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Carter-Fenk, Kevin D. "Design and Implementation of Quantum Chemistry Methods for the Condensed Phase: Noncovalent Interactions at the Nanoscale and Excited States in Bulk Solution." The Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu161617640330551.

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Eschke, Andy. "Analytical solution of a linear, elliptic, inhomogeneous partial differential equation with inhomogeneous mixed Dirichlet- and Neumann-type boundary conditions for a special rotationally symmetric problem of linear elasticity." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-149965.

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The analytical solution of a given inhomogeneous boundary value problem of a linear, elliptic, inhomogeneous partial differential equation and a set of inhomogeneous mixed Dirichlet- and Neumann-type boundary conditions is derived in the present paper. In the context of elasticity theory, the problem arises for a non-conservative symmetric ansatz and an extended constitutive law shown earlier. For convenient user application, the scalar function expressed in cylindrical coordinates is primarily obtained for the general case before being expatiated on a special case of linear boundary conditions.

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MIRAGLIO, PIETRO. "ESTIMATES AND RIGIDITY FOR STABLE SOLUTIONS TO SOME NONLINEAR ELLIPTIC PROBLEMS." Doctoral thesis, Università degli Studi di Milano, 2020. http://hdl.handle.net/2434/704717.

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Questa tesi è incentrata sullo studio di equazioni differenziali alle derivate parziali di tipo ellittico. La prima parte della tesi riguarda la regolarità delle soluzioni stabili per un'equazione nonlineare con il p-Laplaciano, in un dominio limitato dello spazio Euclideo. La tecnica è basata sull'uso di disuguaglianze di tipo Hardy-Sobolev su ipersuperfici, del quale viene approfondito lo studio. Nella seconda parte viene preso in esame un problema nonlocale di tipo Dirichlet-Neumann. Studiamo la simmetria unidimensionale di alcune sottoclassi di soluzioni stabili, ottenendo risultati in dimensione n=2, 3. Inoltre, studiamo il comportamento asintotico dell'operatore associato a questo problema nonlocale, usando tecniche di Γ-convergenza.
This thesis deals with the study of elliptic PDEs. The first part of the thesis is focused on the regularity of stable solutions to a nonlinear equation involving the p-Laplacian, in a bounded domain of the Euclidean space. The technique is based on Hardy-Sobolev inequalities in hypersurfaces involving the mean curvature, which are also investigated in the thesis. The second part concerns, instead, a nonlocal problem of Dirichlet-to-Neumann type. We study the one-dimensional symmetry of some subclasses of stable solutions, obtaining new results in dimensions n=2, 3. In addition, we carry out the study of the asymptotic behaviour of the operator associated with this nonlocal problem, using Γ-convergence techniques.

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Mehraban, Arash. "Non-Classical Symmetry Solutions to the Fitzhugh Nagumo Equation." Digital Commons @ East Tennessee State University, 2010. https://dc.etsu.edu/etd/1736.

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In Reaction-Diffusion systems, some parameters can influence the behavior of other parameters in that system. Thus reaction diffusion equations are often used to model the behavior of biological phenomena. The Fitzhugh Nagumo partial differential equation is a reaction diffusion equation that arises both in population genetics and in modeling the transmission of action potentials in the nervous system. In this paper we are interested in finding solutions to this equation. Using Lie groups in particular, we would like to find symmetries of the Fitzhugh Nagumo equation that reduce this non-linear PDE to an Ordinary Differential Equation. In order to accomplish this task, the non-classical method is utilized to find the infinitesimal generator and the invariant surface condition for the subgroup where the solutions for the desired PDE exist. Using the infinitesimal generator and the invariant surface condition, we reduce the PDE to a mildly nonlinear ordinary differential equation that could be explored numerically or perhaps solved in closed form.

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Lau, Tracy. "Numerical solution of skew-symmetric linear systems." Thesis, University of British Columbia, 2009. http://hdl.handle.net/2429/17435.

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We are concerned with iterative solvers for large and sparse skew-symmetric linear systems. First we discuss algorithms for computing incomplete factorizations as a source of preconditioners. This leads to a new Crout variant of Gaussian elimination for skew-symmetric matrices. Details on how to implement the algorithms eﬃciently are provided. A few numerical results are presented for these preconditioners. We also examine a specialized preconditioned minimum residual solver. An explicit derivation is given, detailing the eﬀects of skew-symmetry on the algorithm.

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Books on the topic "Symmetry of solution"

1

Stephani, Hans. Differential equations: Their solution using symmetries. Cambridge [England]: Cambridge University Press, 1989.

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Gunzburger, Max D. On substructuring algorithms and solution techniques for the numerical approximation of partial differential equations. [Washington, D.C: National Aeronautics and Space Administration, 1986.

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1943-, Bluman George W., ed. Symmetry and integration methods for differential equations. New York: Springer, 2002.

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Fiedler, Bernold. Global Bifurcation of Periodic Solutions with Symmetry. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0082943.

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Fiedler, Bernold. Global bifurcation of periodic solutions with symmetry. Berlin: Springer-Verlag, 1988.

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Hydon, Peter E. Symmetry methods for differential equations: A beginner's guide. New York: Cambridge University Press, 2000.

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Gerd, Baumann. Symmetry analysis of differential equations with Mathematica. New York: Springer/Telos, 1998.

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Thurston, Gaylen A. A parallel solution for the symmetric eigenproblem. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1987.

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Polynomial based iteration methods for symmetric linear systems. Chichester: Wiley, 1996.

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Bernd, Fischer. Polynomial based iteration methods for symmetric linear systems. Philadelphia: Society for Industrial and Applied Mathematics, 2011.

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Book chapters on the topic "Symmetry of solution"

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Miller, James, and Connie J. Weeks. "Schwarzschild Solution for Spherical Symmetry." In General Relativity for Planetary Navigation, 31–46. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-77546-9_2.

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Ramm, Alexander G. "Solution to the Navier-Stokes Problem." In Symmetry Problems. The Navier-Stokes Problem., 39–57. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-031-02415-3_5.

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Scheut jens, J. M. H. M., F. A. M. Leermakers, N. A. M. Besseling, and J. Lyklema. "Lattice Theory for the Association of Amphipolar Molecules in Planar Symmetry." In Surfactants in Solution, 25–42. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4615-7984-7_2.

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Baumann, Gerd. "Solution of Coupled Linear Partial Differential Equations." In Symmetry Analysis of Differential Equations with Mathematica®, 457–82. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-2110-4_10.

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Zhen, Mei. "Solution Branches at Corank-2 Bifurcation Points with Symmetry." In Bifurcation and Chaos: Analysis, Algorithms, Applications, 277–81. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-7004-7_35.

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Volchkov, V. V. "General Solution of Convolution Equation in Domains with Spherical Symmetry." In Integral Geometry and Convolution Equations, 169–90. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-010-0023-9_15.

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Aston, P. J. "Introduction to the Numerical Solution of Symmetry- Breaking Bifurcation Problems." In Continuation and Bifurcations: Numerical Techniques and Applications, 139–52. Dordrecht: Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-009-0659-4_9.

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Myers, A. B., and A. E. Johnson. "Electronic and Vibrational Dephasing in Solution by Dynamic Symmetry Breaking." In Springer Series in Chemical Physics, 288–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-80314-7_125.

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Urzhumtsev, Alexandre, Ludmila Urzhumtseva, and Ulrich Baumann. "Helical Symmetry of Nucleic Acids: Obstacle or Help in Structure Solution?" In Methods in Molecular Biology, 259–67. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4939-2763-0_16.

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Liu, Qiumei, Guanghui Wang, and Junling Zheng. "The Analytical Solution of Residual Stress in the Axial Symmetry Object." In Communications in Computer and Information Science, 30–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-27503-6_5.

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Conference papers on the topic "Symmetry of solution"

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Foster, J., and R. Lehnert. "Construction and Solution of Classical Finsler Systems." In Seventh Meeting on CPT and Lorentz Symmetry. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813148505_0068.

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Gatemann, K. "Symbolic solution polynomial equation systems with symmetry." In the international symposium. New York, New York, USA: ACM Press, 1990. http://dx.doi.org/10.1145/96877.96907.

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Myers, Anne B., Alan E. Johnson, Hirofumi Sato, and Fumio Hirata. "Symmetry-breaking effects on photoinduced processes in solution." In Optoelectronics and High-Power Lasers & Applications, edited by Norbert F. Scherer and Janice M. Hicks. SPIE, 1998. http://dx.doi.org/10.1117/12.306109.

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Tarzariol, Alice. "A Model-Oriented Approach for Lifting Symmetry-Breaking Constraints in Answer Set Programming." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/840.

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Writing correct models for combinatorial problems is relatively straightforward; however, they must be efficient to be usable with instances producing many solution candidates. In this work, we aim to automatically generalise the discarding of symmetric solutions of Answer Set Programming instances, improving the efficiency of the programs with first-order constraints derived from propositional symmetry-breaking constraints.

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Honda, Tomonori, Fabien Nicaise, and Erik K. Antonsson. "Synthesis of Structural Symmetry Driven by Cost Savings." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85111.

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An engineer presented with a design challenge often creates a symmetric solution. For instance, consider a table (front-back and left-right symmetry), a car (left and right symmetry), a bridge (front-back and left-right symmetry), or the space shuttle (left-right) symmetry. These examples may not be 100% symmetric, but their overriding features are remarkably similar. The reasons for the design of symmetric structures is not always clear. In some cases, like the table, symmetry may be a tradition. Similarly, the symmetry may be for aesthetic reasons. However in automated design algorithms, especially stochastic techniques, the output is often largely asymmetric, One reason for this is that fitness functions are not rewarded for symmetry. A possible resolution to this is to add a reward function for symmetry. Unfortunately, this approach is computationally intractable as well as arbitrary. In this paper a Genetic Algorithm based method is presented that rewards re-use of parts. The method is applied to a simple, idealized situation as well as to real design case. The results show that in some situations, symmetry naturally emerges from the synthesis, but that it does not provide clear performance advantages over asymmetric configurations.

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Panov, Aleksandr. "On reduction of one partially invariant solution in two-phase fluid." In MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (Symmetry 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5125081.

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Dimovski, Ivan, and Yulian Tsankov. "Explicit solution of a boundary value problem with axial symmetry." In PROCEEDINGS OF THE 45TH INTERNATIONAL CONFERENCE ON APPLICATION OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE’19). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5133528.

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Yenikaya, Bayram. "Full chip hierarchical inverse lithography: a solution with perfect symmetry." In SPIE Advanced Lithography, edited by Andreas Erdmann and Jongwook Kye. SPIE, 2017. http://dx.doi.org/10.1117/12.2257608.

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Long Li and Li-Jian Zhang. "Solution of the master equation for the PT-symmetry processes." In 2016 Progress in Electromagnetic Research Symposium (PIERS). IEEE, 2016. http://dx.doi.org/10.1109/piers.2016.7734584.

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Myers, Anne B., and Alan E. Johnson. "Electronic and Vibrational Dephasing in Solution by Dynamic Symmetry Breaking." In International Conference on Ultrafast Phenomena. Washington, D.C.: Optica Publishing Group, 1996. http://dx.doi.org/10.1364/up.1996.fe.25.

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Abstract:

All spectroscopies, whether explicitly time-resolved or steady-state, are sensitive to fluctuations in the spectroscopic environment of the chromophore on the time scale of the radiation-matter interaction(s). Simple "two-state jump" models that assume random hopping between just two spectroscopically distinct environments have been well studied. Such models can provide some qualitative insight into the influence of fluctuations on a particular spectroscopy even if the actual system accesses a continuous distribution of states, as is usually the case for chromophores in liquids. The usual two-state models assume that the states differ in their transition frequencies to one or more accessible excited states. In linear spectroscopies, such models predict the well-known coalescence from two discrete resonances to a single broad one which then motionally narrows as the fluctuation rate increases. For multiphoton spectroscopies the effects are more complicated; in particular, for monochromatically excited spontaneous emission, increasing the fluctuation rate causes evolution from a sharp, "resonance Raman-like" spectrum to one having increasing contributions from broad emission.1 The transition frequency fluctuations constitute a source of electronic pure dephasing at the level of the chromophore's density matrix, generating a "fluorescence" component to the emission.

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Reports on the topic "Symmetry of solution"

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Riley, M. E. Two-dimensional Green`s function Poisson solution appropriate for cylindrical-symmetry simulations. Office of Scientific and Technical Information (OSTI), April 1998. http://dx.doi.org/10.2172/674827.

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McHardy, James David. Application of symmetries to differential equations: symmetry reduction and solution transformation examples. Office of Scientific and Technical Information (OSTI), June 2019. http://dx.doi.org/10.2172/1529516.

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Golovin, Sergey V. Symmetry Approach and Exact Solutions in Hydrodynamics. GIQ, 2012. http://dx.doi.org/10.7546/giq-6-2005-191-202.

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Kuibin, Pavel Anatol'evich, and Valery Leonidovich Okulov. One-dimensional solutions for a flow with a helical symmetry. DOI СODE, 1996. http://dx.doi.org/10.18411/doicode-2022.072.

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Vassilev, Vassil. Geometric Symmetry Groups, Conservation Laws and Group-Invariant Solutions of the Willmore Equation. GIQ, 2012. http://dx.doi.org/10.7546/giq-5-2004-246-265.

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Vassilev, Vassil M., and Peter A. Djondjorov. Symmetry Groups, Conservation Laws and Group– Invariant Solutions of the Membrane Shape Equation. GIQ, 2012. http://dx.doi.org/10.7546/giq-7-2006-265-279.

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Grahovski, Georgi G., and Vladimir S. Gerdjikov. On the Multi-Component NLS Type Equations on Symmetric Spaces: Reductions and Soliton Solutions. GIQ, 2012. http://dx.doi.org/10.7546/giq-6-2005-203-217.

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Scandrett, Clyde. Comparison of Several Iterative Techniques in the Solution of Symmetric Banded Equations on a Two-Pipe Cyber 205. Fort Belvoir, VA: Defense Technical Information Center, November 1988. http://dx.doi.org/10.21236/ada204164.

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Passman, S. L., and D. E. Grady. Exact solutions for symmetric deformations of hollow bodies of ideal fluids with application to inertial stability. Office of Scientific and Technical Information (OSTI), May 1989. http://dx.doi.org/10.2172/6006247.

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