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Akutsu, Yasuhiro, Atsuo Kuniba, and Miki Wadati. "Exactly Solvable IRF Models. III. A New Hierarchy of Solvable Models." Journal of the Physical Society of Japan 55, no. 6 (June 15, 1986): 1880–86. http://dx.doi.org/10.1143/jpsj.55.1880.
Pulé, Joe V., André F. Verbeure, and Valentin A. Zagrebnov. "On solvable boson models." Journal of Mathematical Physics 49, no. 4 (April 2008): 043302. http://dx.doi.org/10.1063/1.2898480.
Date, E., M. Jimbo, A. Kuniba, T. Miwa, and M. Okado. "Exactly solvable SOS models." Nuclear Physics B 290 (January 1987): 231–73. http://dx.doi.org/10.1016/0550-3213(87)90187-8.
Cugliandolo, L. F., J. Kurchan, G. Parisi, and F. Ritort. "Matrix Models as Solvable Glass Models." Physical Review Letters 74, no. 6 (February 6, 1995): 1012–15. http://dx.doi.org/10.1103/physrevlett.74.1012.
Popkov, V. "Multilayer Extension of Two-Dimensional Solvable Statistical Models to Three Dimensions." International Journal of Modern Physics B 11, no. 01n02 (January 20, 1997): 175–81. http://dx.doi.org/10.1142/s021797929700023x.
We review the method of constructing solvable models in three dimensions, by starting from two-dimensional solvable models. The solvable three-dimensional models thus constructed do possess positive Boltzmann weights. These are multilayer two-dimensional systems with interactions in the third direction which can be interpreted as nearest-neighbour interactions. The set of conditions corresponding to the general 3D multilayer extension of solvable 2D models is derived.
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Kulish, Petr P. "Models solvable by Bethe Ansatz." Journal of Generalized Lie Theory and Applications 2, no. 3 (2008): 190–200. http://dx.doi.org/10.4303/jglta/s080317.
Carlone, R., R. Figari, C. Negulescu, and L. Tentarelli. "Solvable models of quantum beating." Nanosystems: Physics, Chemistry, Mathematics 9, no. 2 (April 12, 2018): 162–70. http://dx.doi.org/10.17586/2220-8054-2018-9-2-162-170.
Ghosh, Ranjan Kumar, P. K. Mohanty, and Sumathi Rao. "Exactly solvable fermionicN-band models." Journal of Physics A: Mathematical and General 32, no. 24 (January 1, 1999): 4343–50. http://dx.doi.org/10.1088/0305-4470/32/24/302.
Mézard, M., J. P. Nadal, and G. Toulouse. "Solvable models of working memories." Journal de Physique 47, no. 9 (1986): 1457–62. http://dx.doi.org/10.1051/jphys:019860047090145700.
Dissertations / Theses on the topic "Solvable models":
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de, Woul Jonas. "Fermions in two dimensions and exactly solvable models." Doctoral thesis, KTH, Matematisk fysik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-50471.
This Ph.D. thesis in mathematical physics concerns systems of interacting fermions with strong correlations. For these systems the physical properties can only be described in terms of the collective behavior of the fermions. Moreover, they are often characterized by a close competition between fermion localization versus delocalization, which can result in complex and exotic physical phenomena. Strongly correlated fermion systems are usually modelled by many-body Hamiltonians for which the kinetic- and interaction energy have the same order of magnitude. This makes them challenging to study as the application of conventional computational methods, like mean field- or perturbation theory, often gives unreliable results. Of particular interest are Hubbard-type models, which provide minimal descriptions of strongly correlated fermions. The research of this thesis focuses on such models defined on two-dimensional square lattices. One motivation for this is the so-called high-Tc problem of the cuprate superconductors. A main hypothesis is that there exists an underlying Fermi surface with nearly flat parts, i.e. regions where the surface is straight. It is shown that a particular continuum limit of the lattice system leads to an effective model amenable to computations. This limit is partial in that it only involves fermion degrees of freedom near the flat parts. The result is an effective quantum field theory that is analyzed using constructive bosonization methods. Various exactly solvable models of interacting fermions in two spatial dimensions are also derived and studied. QC 20111207
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Shum, Christopher. "Solvable Particle Models Related to the Beta-Ensemble." Thesis, University of Oregon, 2013. http://hdl.handle.net/1794/13302.
For beta > 0, the beta-ensemble corresponds to the joint probability density on the real line proportional to
prod_{n > m}^N abs{x_n - x_m}^beta prod_{n = 1}^N w(x_n)
where w is the weight of the system. It has the application of being the Boltzmann factor for the configuration of N charge-one particles interacting logarithmically on an infinite wire inside an external field Q = -log w at inverse temperature beta. Similarly, the circular beta-ensemble has joint probability density proportional to
prod_{n > m}^N abs{e^{itheta_n} - e^{itheta_m}}^beta prod_{n = 1}^N w(x_n) quad for theta_n in [- pi, pi)
and can be interpreted as N charge-one particles on the unit circle interacting logarithmically with no external field. When beta = 1, 2, and 4, both ensembles are said to be solvable in that their correlation functions can be expressed in a form which allows for asymptotic calculations. It is not known, however, whether the general beta-ensemble is solvable.
We present four families of particle models which are solvable point processes related to the beta-ensemble. Two of the examples interpolate between the circular beta-ensembles for beta = 1, 2, and 4. These give alternate ways of connecting the classical beta-ensembles besides simply changing the values of beta. The other two examples are "mirrored" particle models, where each particle has a paired particle reflected about some point or axis of symmetry.
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Brown, Jeffrey Michael. "Exactly Solvable Light-Matter Interaction Models for Studying Filamentation Dynamics." Diss., The University of Arizona, 2016. http://hdl.handle.net/10150/612844.
This dissertation demonstrates the usefulness of exactly solvable quantum models in the investigation of light-matter interaction phenomena associated with the propagation of ultrashort laser pulses through gaseous media. This work fits into the larger research effort towards remedying the weaker portions of the standard set of medium modeling equations commonly used in simulations. The ultimate goal is to provide a self-consistent quantum mechanical description that can integrate Maxwell and Schrödinger systems and provide a means to realistically simulate nonlinear optical experiments on relevant scales. The study of exactly solvable models begins with one of the simplest quantum systems available, one with a 1D Dirac-delta function potential plus interaction with the light field. This model contains, in the simplest form, the most important "ingredients" that control optical filamentation, i.e. discrete and continuum electronic states. The importance of both states is emphasized in the optical intensity regime in which filaments form, where both kinds of electronic states simultaneously play a role and may not even be distinguishable. For this model atom, an analytical solution for the time-dependent light-induced atomic response from an arbitrary excitation waveform is obtained. Although this system is well-known and has been studied for decades, this result is probably the most practically useful and general one obtained thus far. Numerical implementation details of the result are also given as the task is far from trivial. Given an efficient implementation, the model is used in light-matter interaction simulations and from these it is apparent that even this toy model can qualitatively reproduce many of the nonlinear phenomena seen in experiments. Not only does this model capture the basic physics of optical filamentation, but it is also well-suited for high harmonic generation simulations. Next, a theoretical framework for using Stark resonant states (or metastable states) to represent the medium's polarization response is presented. Researchers have recognized long ago the utility of Gamow resonant states as a description of various decay processes. Even though a bound electron experiences a similar decay-like process as it transitions into the continuum upon ionization, it was unclear whether field-induced Stark resonant states carry physically relevant information. It is found that they do, and in particular it is possible to use them to capture a medium's polarization response. To this end, two quantum systems with potentials represented by a 1D Dirac-delta function and a 1D square well are solved, and all the necessary quantities for their use as medium models are presented. From these results it is possible to conjecture some general properties that hold for all resonance systems, including systems that reside in higher than one dimensional space. Finally, as a practical application of this theory, the Metastable Electronic State Approach (MESA) is presented as a quantum-based replacement for the standard medium modeling equations.
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Dey, Sanjib. "Solvable models on noncommutative spaces with minimal length uncertainty relations." Thesis, City University London, 2014. http://openaccess.city.ac.uk/5917/.
Intuitive arguments involving standard quantum mechanical uncertainty relations suggest that at length scales close to the Planck length, strong gravity effects limit the spatial as well as temporal resolution smaller than fundamental length scale, leading to space-space as well as spacetime uncertainties. Space-time cannot be probed with a resolution beyond this scale i.e. space-time becomes "fuzzy" below this scale, resulting into noncommutative spacetime. Hence it becomes important and interesting to study in detail the structure of such noncommutative spacetimes and their properties, because it not only helps us to improve our understanding of the Planck scale physics but also helps in bridging standard particle physics with physics at Planck scale. Our main focus in this thesis is to explore different methods of constructing models in these kind of spaces in higher dimensions. In particular, we provide a systematic procedure to relate a three dimensional q-deformed oscillator algebra to the corresponding algebra satisfied by canonical variables describing non-commutative spaces. The representations for the corresponding operators obey algebras whose uncertainty relations lead to minimal length, areas and volumes in phase space, which are in principle natural candidates of many different approaches of quantum gravity. We study some explicit models on these types of non-commutative spaces, in particular, we provide solutions of three dimensional harmonic oscillator as well as its decomposed versions into lower dimensions. Because the solutions are computed in these cases by utilising the standard Rayleigh-Schrodinger perturbation theory, we investigate a method afterwards to construct models in an exact manner. We demonstrate three characteristically different solvable models on these spaces, the harmonic oscillator, the manifestly non-Hermitian Swanson model and an intrinsically non-commutative model with Poschl-Teller type potential. In many cases the operators are not Hermitian with regard to the standard inner products and that is the reason why we use PT -symmetry and pseudo-Hermiticity property, wherever applicable, to make them self-consistent well designed physical observables. We construct an exact form of the metric operator, which is rare in the literature, and provide Hermitian versions of the non-Hermitian Euclidean Lie algebraic type Hamiltonian systems. We also indicate the region of broken and unbroken PT -symmetry and provide a theoretical treatment of the gain loss behaviour of these types of systems in the unbroken PT -regime, which draws more attention to the experimental physicists in recent days. Apart from building mathematical models, we focus on the physical implications of noncommutative theories too. We construct Klauder coherent states for the perturbative and nonperturbative noncommutative harmonic oscillator associated with uncertainty relations implying minimal lengths. In both cases, the uncertainty relations for the constructed states are shown to be saturated and thus imply to the squeezed coherent states. They are also shown to satisfy the Ehrenfest theorem dictating the classical like nature of the coherent wavepacket. The quality of those states are further underpinned by the fractional revival structure which compares the quality of the coherent states with that of the classical particle directly. More investigations into the comparison are carried out by a qualitative comparison between the dynamics of the classical particle and that of the coherent states based on numerical techniques. We find the qualitative behaviour to be governed by the Mandel parameter determining the regime in which the wavefunctions evolve as soliton like structures. We demonstrate these features explicitly for the harmonic oscillator, the Poschl-Teller potential and a Calogero type potential having singularity at the origin, we argue on the fact that the effects are less visible from the mathematical analysis and stress that the method is quite useful for the precession measurement required for the experimental purpose. In the context of complex classical mechanics we also find the claim that "the trajectories of classical particles in complex potential are always closed and periodic when its energy is real, and open when the energy is complex", which is demanded in the literature, is not in general true and we show that particles with complex energies can possess a closed and periodic orbit and particles with real energies can produce open trajectories.
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Wagner, Fabian. "Exactly solvable models, Yang-Baxter algebras and the algebraic Bethe Ansatz." Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621030.
Sinitsyn, Nikolai. "Generalizations of the Landau-Zener theory in the physics of nanoscale systems." Diss., Texas A&M University, 2003. http://hdl.handle.net/1969.1/216.
Nanoscale systems have sizes intermediate between atomic and macroscopic ones. Therefore their treatment often requires a combination of methods from atomic and condensed matter physics. The conventional Landau-Zener theory, being a powerful tool in atomic physics, often fails to predict correctly nonadiabatic transition probabilities in various nanostructures because it does not include many-body effects typical for mesoscopics. In this research project the generalizations of the Landau-Zener theory that solve this problem were studied. The multistate, multiparticle and nonunitary extensions of the theory have been proposed and investigated. New classes of exactly solvable models have been derived. I discuss their applications in problems of the molecular condensate dissociation and of the driven charge transport. In application to the physics of nanomagnets new approaches in modeling the influence of the environment on the Landau-Zener evolution are proposed and simple universal formulas are derived for the extensions of the theory that include the coupling to noise and the nuclear spin bath.
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Downing, Charles Andrew. "Quantum confinement in low-dimensional Dirac materials." Thesis, University of Exeter, 2015. http://hdl.handle.net/10871/17215.
This thesis is devoted to quantum confinement effects in low-dimensional Dirac materials. We propose a variety of schemes in which massless Dirac fermions, which are notoriously diffcult to manipulate, can be trapped in a bound state. Primarily we appeal for the use of external electromagnetic fields. As a consequence of this endeavor, we find several interesting condensed matter analogues to effects from relativistic quantum mechanics, as well as entirely new effects and a possible novel state of matter. For example, in our study of the effective Coulomb interaction in one dimension, we demonstrate how atomic collapse may arise in carbon nanotubes or graphene nanoribbons, and describe the critical importance of the size of the band gap. Meanwhile, inspired by groundbreaking experiments investigating the effects of strain, we propose how to confine the elusive charge carriers in so-called velocity barriers, which arise due to a spatially inhomogeneous Fermi velocity triggered by a strained lattice. We also present a new and beautiful quasi-exactly solvable model of quantum mechanics, showing the possibilities for confinement in magnetic quantum dots are not as stringent as previously thought. We also reveal that Klein tunnelling is not as pernicious as widely believed, as we show bound states can arise from purely electrostatic means at the Dirac point energy. Finally, we show from an analytical solution to the quasi-relativistic two-body problem, how an exotic same-particle paring can occur and speculate on its implications if found in the laboratory.
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Himberg, Benjamin Evert. "Accelerating Quantum Monte Carlo via Graphics Processing Units." ScholarWorks @ UVM, 2017. http://scholarworks.uvm.edu/graddis/728.
An exact quantum Monte Carlo algorithm for interacting particles in the spatial continuum is extended to exploit the massive parallelism offered by graphics processing units. Its efficacy is tested on the Calogero-Sutherland model describing a system of bosons interacting in one spatial dimension via an inverse square law. Due to the long range nature of the interactions, this model has proved difficult to simulate via conventional path integral Monte Carlo methods running on conventional processors. Using Graphics Processing Units, optimal speedup factors of up to 640 times are obtained for N = 126 particles. The known results for the ground state energy are confirmed and, for the first time, the effects of thermal fluctuations at finite temperature are explored.
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Aldarak, Helal. "Spin chain with A and D-type algebra and Coderivative." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2023. http://www.theses.fr/2023UBFCK100.
Cette thèse porte sur l'étude de système quantique intégrable spécifique ``chaînes de spin'' présentant différentes symétries. Ces chaînes de spin sont considérées comme des modèles jouets de certaines théories bidimensionnelles des champs lorsque la taille de ces modèles est finie. En particulier, certaines relations fonctionnelles dans ces chaînes de spin ont été généralisées aux théories des champs en utilisant un nombre fini d'équations pour trouver leur spectre.Nous commençons cette thèse en décrivant la chaîne de spins rationnelle bien étudiée avec symétrie GL(n) en utilisant l'opérateur de ``codérivée'' pour construire un « opérateur Q » polynomial qui nous permet de diagonaliser l'hamiltonien. Nous montrons l'équivalence avec une autre construction s'appuyant sur des représentations explicites en termes d’oscillateurs harmoniques.Nous étudions ensuite une chaîne de spins moins connue présentant une symétrie SO(2r). Nous construisons le ``Q-opérateur'' pour les représentations connues. Nous essayons ensuite plusieurs méthodes pour construire lesdits opérateurs pour des représentations générales. Ces tentatives montrent clairement que, d’une part, elles suggèrent fortement que la codérivative n’est pas suffisante pour décrire des représentations générales dans l’espace auxiliaire. Nous espérons en revanche qu’ils aideront à trouver quels outils supplémentaires pourraient nous permettre de les décrire This thesis is concerned with the study of specific integrable quantum system ``spin chains'' with different symmetries. These spin chains are considered toy models of some two-dimensional field theories when the size of these models is finite. In particular, some functional relations in these spin chains were generalized to field theories using a finite number of equations to find their spectrum.We start this thesis by describing the well-studied rational spin chain with GL(n) symmetry using the Coderivative operator to build a polynomial ``Q-operator'' that allows us to diagonalize the Hamiltonian. We show the equivalence with another construction relying on representations that are explicit in terms of harmonic oscillators.We then study a lesser-known spin chain with SO(2r) symmetry. We build the ``Q-operator'' for the known representations. Then we attempt several methods to build said operators for general representations. These attempts clearly show that, on the one hand, the attempts strongly suggest the Coderivative is not sufficient to describe general representations in auxiliary space. On the other hand, we hope they will help to find what additional tools may allow us to describe them
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Thiery, Thimothée. "Analytical methods and field theory for disordered systems." Thesis, Paris Sciences et Lettres (ComUE), 2016. http://www.theses.fr/2016PSLEE017/document.
Cette thèse présente plusieurs aspects de la physique des systèmes élastiques désordonnés et des méthodes analytiques utilisées pour les étudier. On s’intéressera d’une part aux propriétés universelles des processus d’avalanches statiques et dynamiques (à la transition de dépiégeage) d’interfaces élastiques de dimension arbitraire en milieu aléatoire à température nulle. Pour étudier ces questions nous utiliserons le groupe de renormalisation fonctionnel. Après une revue de ces aspects,nous présenterons plus particulièrement les résultats obtenus pendant la thèse sur (i) la structure spatiale des avalanches et (ii) les corrélations entre avalanches.On s’intéressera d’autre part aux propriétés statiques à température finie de polymères dirigés en dimension 1+1, et en particulier aux observables liées à la classe d’universalité KPZ. Dans ce contexte l’étude de modèles exactement solubles a récemment permis de grands progrès. Après une revue de ces aspects, nous nous intéresserons plus particulièrement aux modèles exactement solubles de polymère dirigé sur le réseau carré, et présenterons les résultats obtenus pendantla thèse dans cette voie: (i) classification des modèles à température finie sur le réseau carré exactement solubles par ansatz de Bethe; (ii) universalité KPZ pour les modèles Log-Gamma et Inverse-Beta; (iii) universalité et nonuniversalitéKPZ pour le modèle Beta; (iv) mesures stationnaires du modèle Inverse-Beta et des modèles à température nulle associés This thesis presents several aspects of the physics of disordered elastic systems and of the analytical methods used for their study.On one hand we will be interested in universal properties of avalanche processes in the statics and dynamics (at the depinning transition) of elastic interfaces of arbitrary dimension in disordered media at zero temperature. To study these questions we will use the functional renormalization group. After a review of these aspects we will more particularly present the results obtained during the thesis on (i) the spatial structure of avalanches and (ii) the correlations between avalanches.On the other hand we will be interested in static properties of directed polymers in 1+1 dimension, and in particular in observables related to the KPZ universality class. In this context the study of exactly solvable models has recently led to important progress. After a review of these aspects we will be more particularly interested in exactly solvable models of directed polymer on the square lattice and present the results obtained during the thesis in this direction: (i) classification ofBethe ansatz exactly solvable models of directed polymer at finite temperature on the square lattice; (ii) KPZ universality for the Log-Gamma and Inverse-Beta models; (iii) KPZ universality and non-universality for the Beta model; (iv) stationary measures of the Inverse- Beta model and of related zero temperature models
Jimbo, M. Algebraic analysis of solvable lattice models. Providence: Published for the Conference Board of the Mathematical Sciences by the American Mathematcal Society, 1995.
Henkel, Malte, and Michel Pleimling. "Exactly Solvable Models." In Theoretical and Mathematical Physics, 95–140. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-90-481-2869-3_2.
Petrina, D. Ya. "Exactly Solvable Models." In Mathematical Foundations of Quantum Statistical Mechanics, 307–400. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0185-1_6.
Kapoor, A. K., Prasanta K. Panigrahi, and S. Sree Ranjani. "Exactly Solvable Models." In SpringerBriefs in Physics, 29–46. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-10624-8_3.
Deguchi, Tetsuo. "Link Polynomials and Solvable Models." In NATO ASI Series, 583–603. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4615-3802-8_18.
Ivanchenko, Yuli M., and Alexander A. Lisyansky. "Exactly Solvable Models and RG." In Graduate Texts in Contemporary Physics, 287–322. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-4204-8_8.
Rakityansky, Sergei A. "Some Exactly Solvable Potential Models." In Jost Functions in Quantum Mechanics, 539–70. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-07761-6_18.
DRAAYER, J. P., V. G. GUEORGUIEV, K. D. SVIRATCHEVA, C. BAHRI, FENG PAN, and A. I. GEORGIEVA. "EXACTLY SOLVABLE PAIRING MODELS." In Proceedings of the 8th International Spring Seminar on Nuclear Physics. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702265_0053.
Malev, A. V. "Solvable Models of Optical Resonators." In Nonlinear Dynamics in Optical Systems. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nldos.1992.tuc23.
Transverse effects in optical systems have been intensively studied in last years/1,2/. But it is rather difficult to analyze resonator diffraction effects and especially to take into account the influence of space inhomogeneities on laser generation in the framework of standard approach. However one can solve this problems in a mathematically sound way using the self-adjoint extension theory. The extension theory technique provides almost analytically describing of different physical processes (see /3,4/ for details and examples). This technique was used in /5/ for chaotic behavior studies of quantum systems.
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Yépez-Martínez, Tochtli, P. O. Hess, A. Szczepaniak, O. Civitarese, S. Lerma H., Kurt B. Wolf, Luis Benet, Juan Mauricio Torres, and Peter O. Hess. "Solvable models and hidden symmetries in QCD." In SYMMETRIES IN NATURE: SYMPOSIUM IN MEMORIAM MARCOS MOSHINSKY. AIP, 2010. http://dx.doi.org/10.1063/1.3537841.
Dukelsky, J. "Exactly Solvable Models Based on the Pairing Interaction." In MAPPING THE TRIANGLE: International Conference on Nuclear Structure. AIP, 2002. http://dx.doi.org/10.1063/1.1517947.
Makhaldiani, Nugzar. "Hadronization and solvable models of renormdynamics of QCD." In XXII International Baldin Seminar on High Energy Physics Problems. Trieste, Italy: Sissa Medialab, 2015. http://dx.doi.org/10.22323/1.225.0040.
DUKELSKY, J., C. ESEBBAG, and S. PITTEL. "NEW EXACTLY SOLVABLE MODELS OF INTERACTING BOSONS AND FERMIONS." In Proceedings of the Symposium in Honor of Jerry P Draayer's 60th Birthday. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812703026_0010.
Ganikhodjaev, Nasir, Siti Fatimah Zakaria, and Wan Nur Fairuz Alwani Wan Rozali. "On exactly solvable phases of models with competing interactions." In PROCEEDINGS OF THE 14TH ASIA-PACIFIC PHYSICS CONFERENCE. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0039353.
NAGHIEV, S. M., and R. M. IMANOV. "EXACTLY SOLVABLE FINITE DIFFERENCE MODELS OF LINEAR HARMONIC OSCILLATOR." In Proceedings of the XI Regional Conference. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701862_0037.
Ramos, Juan, Vladimir Belavin, and Doron Gepner. "A large family of IRF solvable lattice models based on WZW models." In 41st International Conference on High Energy physics. Trieste, Italy: Sissa Medialab, 2022. http://dx.doi.org/10.22323/1.414.0432.
Burdik, Cestmir, and Ondrej Navratil. On Matrix Solvable Calogero Models of B2 Type. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-6-2006-11-15.
Bihun, Oksana, and Francesco Calogero. Solvable and/or Integrable Many-Body Models on a Circle. Journal of Geometry and Symmetry in Physics, 2013. http://dx.doi.org/10.7546/jgsp-30-2013-1-18.
Tanaka, K. Solvable two-dimensional supersymmetric models and the supersymmetric Virasoro algebra. Office of Scientific and Technical Information (OSTI), January 1990. http://dx.doi.org/10.2172/6902042.
Yao, Hong. Algebraic spin liquid in an exactly solvable spin model. Office of Scientific and Technical Information (OSTI), March 2010. http://dx.doi.org/10.2172/974187.
Jury, William A., and David Russo. Characterization of Field-Scale Solute Transport in Spatially Variable Unsaturated Field Soils. United States Department of Agriculture, January 1994. http://dx.doi.org/10.32747/1994.7568772.bard.
This report describes activity conducted in several lines of research associated with field-scale water and solute processes. A major effort was put forth developing a stochastic continuum analysis for an important class of problems involving flow of reactive and non reactive chemicals under steady unsaturated flow. The field-scale velocity covariance tensor has been derived from local soil properties and their variability, producing a large-scale description of the medium that embodies all of the local variability in a statistical sense. Special cases of anisotropic medium properties not aligned along the flow direction of spatially variable solute sorption were analysed in detail, revealing a dependence of solute spreading on subtle features of the variability of the medium, such as cross-correlations between sorption and conductivity. A novel method was developed and tested for measuring hydraulic conductivity at the scale of observation through the interpretation of a solute transport outflow curve as a stochastic-convective process. This undertaking provided a host of new K(q) relationships for existing solute experiments and also laid the foundation for future work developing a self-consistent description of flow and transport under these conditions. Numerical codes were developed for calculating K(q) functions for a variety of solute pulse outflow shapes, including lognormal, Fickian, Mobile-Immobile water, and bimodal. Testing of this new approach against conventional methodology was mixed, and agreed most closely when the assumptions of the new method were met. We conclude that this procedure offers a valuable alternative to conventional methods of measuring K(q), particularly when the application of the method is at a scale (e.g. and agricultural field) that is large compared to the common scale at which conventional K(q) devices operate. The same problem was approached from a numerical perspective, by studying the feasibility of inverting a solute outflow signal to yield the hydraulic parameters of the medium that housed the experiment. We found that the inverse problem was solvable under certain conditions, depending on the amount of noise in the signal and the degree of heterogeneity in the medium. A realistic three dimensional model of transient water and solute movement in a heterogeneous medium that contains plant roots was developed and tested. The approach taken was to generate a single realization of this complex flow event, and examine the results to see whether features were present that might be overlooked in less sophisticated model efforts. One such feature revealed is transverse dispersion, which is a critically important component in the development of macrodispersion in the longitudinal direction. The lateral mixing that was observed greatly exceeded that predicted from simpler approaches, suggesting that at least part of the important physics of the mixing process is embedded in the complexity of three dimensional flow. Another important finding was the observation that variability can produce a pseudo-kinetic behavior for solute adsorption, even when the local models used are equilibrium.
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Baader, Franz, Stefan Borgwardt, and Barbara Morawska. Computing Minimal EL-Unifiers is Hard. Technische Universität Dresden, 2012. http://dx.doi.org/10.25368/2022.187.
Unification has been investigated both in modal logics and in description logics, albeit with different motivations. In description logics, unification can be used to detect redundancies in ontologies. In this context, it is not sufficient to decide unifiability, one must also compute appropriate unifiers and present them to the user. For the description logic EL, which is used to define several large biomedical ontologies, deciding unifiability is an NP-complete problem. It is known that every solvable EL-unification problem has a minimal unifier, and that every minimal unifier is a local unifier. Existing unification algorithms for EL compute all minimal unifiers, but additionally (all or some) non-minimal local unifiers. Computing only the minimal unifiers would be better since there are considerably less minimal unifiers than local ones, and their size is usually also quite small. In this paper we investigate the question whether the known algorithms for EL-unification can be modified such that they compute exactly the minimal unifiers without changing the complexity and the basic nature of the algorithms. Basically, the answer we give to this question is negative.
