DSpace Collection: 2016 Volume 26
http://hdl.handle.net/10525/3549
Proceedings of the Third International conference on New Trends of the Applications of Differential Equations in Sciences (NTADES 2016) with the Cooperation of the Society of Industrial and Applied Mathematics (SIAM). Guest Editor: A. Slavova, Sofia, 2016.The Collection's search engineSearch the Channelsearch
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On Soliton Equations in Classical Differential Geometry
http://hdl.handle.net/10525/3570
Title: On Soliton Equations in Classical Differential Geometry<br/><br/>Authors: Valchev, Tihomir<br/><br/>Abstract: In this survey report we shall briefly sketch certain problems from the classical differential geometry of curves and surfaces that lead to nonlinear partial differential equations known from soliton theory. Thus an alternative viewpoint on these completely integrable equations will be presented. 2010 Mathematics Subject Classification: 37K25, 53A04, 53A05.<br/><br/>Description: [Valchev Tihomir; Вълчев Тихомир]Scattering for Systems of N Weakly Coupled NLS Equations on R^D x M^2 in the Energy Space
http://hdl.handle.net/10525/3569
Title: Scattering for Systems of N Weakly Coupled NLS Equations on R^D x M^2 in the Energy Space<br/><br/>Authors: Tarulli, Mirko; Venkov, George<br/><br/>Abstract: 2010 Mathematics Subject Classification: 35J10, 35Q55, 35G50, 35P25.<br/><br/>Description: [Venkov George; Венков Георги]Discrete Dirac−Kähler Equation and its Formulation in Algebraic Form
http://hdl.handle.net/10525/3568
Title: Discrete Dirac−Kähler Equation and its Formulation in Algebraic Form<br/><br/>Authors: Sushch, Volodymyr<br/><br/>Abstract: A relationship between the discrete Dirac−Kähler equation and discrete analogues of some Dirac type equations in the geometric spacetime algebra is discussed. We show that a solution of the discrete Dirac−Kähler equation can be represented as the sum and difference of solutions of discrete Dirac type equations with the corresponding sign of the mass term. 2010 Mathematics Subject Classification: 39A12, 39A70, 81Q05.A New Approach to Improve the Numerical Procedure for 2D Anti-Plane Crack Problems in Functionally Graded Magneto-Electro-Elastic Materials
http://hdl.handle.net/10525/3567
Title: A New Approach to Improve the Numerical Procedure for 2D Anti-Plane Crack Problems in Functionally Graded Magneto-Electro-Elastic Materials<br/><br/>Authors: Stoynov, Yonko<br/><br/>Abstract: Magneto-electro-elastic composite materials have extensive applications in modern smart structures, because they possess good coupling between mechanical, electrical and magnetic fields. This new effect was reported for the first time by Van Suchtelen [1] in 1972. Due to their ceramic structure cracks inevitably exist in these materials. If these cracks extend the material may lose its structural integrity and/or functional properties. In this study we consider functionally graded magneto-electro-elastic materials (MEEM) subjected to anti-plane time-harmonic load. Our purpose is to evaluate the dependence of the stress concentration near the crack tips on the frequency of the applied external load. We use boundary integral equation method (BIEM) for the numerical solution. For materials with complex geometry of cracks the numerical procedure becomes too cumbersome. To increase the speed of the computations we derive new fundamental solutions by the Fourier transform. The more simple form of these fundamental solutions leads to decreasing of the number of the numerical computations. Asymptotic for small arguments of the new solutions will be presented. The results can be used to improve the numerical procedure based on the BIEM for complex crack configurations in MEEM. 2010 Mathematics Subject Classification: 65M38, 65N80, 65Z05.<br/><br/>Description: [Stoynov Yonko; Стойнов Йонко]Dynamics of Hysteresis CNN with Memristor Synapses
http://hdl.handle.net/10525/3566
Title: Dynamics of Hysteresis CNN with Memristor Synapses<br/><br/>Authors: Slavova, Angela; Tetzlaff, Ronald<br/><br/>Abstract: In this paper a new hysteresis Cellular Nonlinear Networks (CNN) model will be studied in which we shall introduce memristor in the synapses. Dynamics of such model will be investigated. Local activity theory will be applied in order to determine the edge of chaos domain of the parameter set in which the model under consideration can exhibit complexity. Simulations and applications will be provided. 2010 Mathematics Subject Classification: 92B20, 34C55, 34C28.<br/><br/>Description: [Slavova Angela; Славова Анжела]A Generalized Mountain Pass Theorem
http://hdl.handle.net/10525/3565
Title: A Generalized Mountain Pass Theorem<br/><br/>Authors: Ruppen, Hans-Jörg<br/><br/>Abstract: 2010 Mathematics Subject Classification: 58E05, 58E30.Dynamic Behaviour of a Crack at Macro- and Nano- Scale in Anisotropic Plane by BIEM
http://hdl.handle.net/10525/3564
Title: Dynamic Behaviour of a Crack at Macro- and Nano- Scale in Anisotropic Plane by BIEM<br/><br/>Authors: Rangelov, Tsviatko; Dineva, Petia<br/><br/>Abstract: The two-dimensional in-plane time-harmonic elastodynamic problem for anisotropic infinite plane with a crack at macro and nano scale subjected to incident plane longitudinal P or shear SV wave is studied. The continuum mechanics model of surface elasticity proposed by Gurtin and Murdoch [1] is applied to account for the effects of surface elasticity for a crack at nano-level. The non-hypersingular traction boundary integral equation method (BIEM) is used in conjunction with closed form frequency dependent fundamental solution, obtained by Radon transform. In addition a parametric study for the dynamic stress intensity factor (SIF) and stress concentration field (SCF) sensitivity to the frequency, crack-size, surface effects and material anisotropy is presented. 2010 Mathematics Subject Classification: 35Q74, 74S15, 74H35.<br/><br/>Description: [Rangelov Tsviatko; Рангелов Цвятко]; [Dineva Petia; Динева Петя]Solvability in Classical Sense of Quasi-Linear Non-Cooperative Elliptic Systems and Application
http://hdl.handle.net/10525/3563
Title: Solvability in Classical Sense of Quasi-Linear Non-Cooperative Elliptic Systems and Application<br/><br/>Authors: Popivanov, P.; Boyadzhiev, G.; Markov, Y.<br/><br/>Abstract: 2010 Mathematics Subject Classification: 35J47, 35J57.<br/><br/>Description: [Popivanov P.; Popivanov Petar; Попиванов Петър]; [Boyadzhiev G.; Бояджиев Г.]; [Markov Y.; Марков Й.]Aerodynamic Characteristics of Joukowsky Like Wings
http://hdl.handle.net/10525/3562
Title: Aerodynamic Characteristics of Joukowsky Like Wings<br/><br/>Authors: Mochimaru, Yoshihiro<br/><br/>Abstract: Aerodynamic characteristics of Joukowsky like airfoils are analyzed, under the assumption that the flow near the airfoil is governed by two-dimensional incompressible isothermal Newtonian fluid flow, beyond the viscous boundarylayer of which is approximated by a potential flow with a new parameter. Vorticity transport equation is solved numerically, using a spectral finitedifference scheme to give steady-state various characteristics. 2010 Mathematics Subject Classification: 31A35, 33E05, 65N06, 76D05.Control of Chaotic Behavior of Integro-Differential CNN Model Arising in Piezoelectric Material with Nano-Heterogeneities
http://hdl.handle.net/10525/3561
Title: Control of Chaotic Behavior of Integro-Differential CNN Model Arising in Piezoelectric Material with Nano-Heterogeneities<br/><br/>Authors: Litsyn, Elena; Slavova, Angela<br/><br/>Abstract: Piezoelectrical material with heterogeneities of nano-holes or nano-inclusions is considered in the case when it is subjected to time harmonic electromechanical load. The model is reduced to a system of integro-differential equations (IDE). We construct Cellular Nonlinear/Nanoscale Network (CNN) architecture for the boundary value IDE problem under consideration. For such IDE CNN model we shall determine “edge of chaos” region of the parameter set.Validation will be provided as well. Feedback control will be applied in order to stabilize the model. The computer simulations will illustrate the obtained theoretical results. 2010 Mathematics Subject Classification: 92B20,74F15, 35K57, 35Q68.<br/><br/>Description: [Slavova Angela; Славова Анжела]On The Numerical Solution of the General “Ligand–Gated Neuroreceptors Model” via CAS MATHEMATICA
http://hdl.handle.net/10525/3560
Title: On The Numerical Solution of the General “Ligand–Gated Neuroreceptors Model” via CAS MATHEMATICA<br/><br/>Authors: Kyurkchiev, Nikolay<br/><br/>Abstract: We present a software module for analysis of the general “ligand–gated neuroreceptors model” (GLGNM) within the programming environment of CAS Mathematica. Numerical examples which demonstrate scientific applications and visualization properties of the module are presented. 2010 Mathematics Subject Classification: 92B05, 92E10, 92C40, 92C45.<br/><br/>Description: [Kyurkchiev Nikolay; Кюркчиев Николай]Global Solvability to Double Dispersion Equation with Bernoulli Type Nonlinearity via One Parametric Family of Potential Wells
http://hdl.handle.net/10525/3559
Title: Global Solvability to Double Dispersion Equation with Bernoulli Type Nonlinearity via One Parametric Family of Potential Wells<br/><br/>Authors: Kutev, N.; Dimova, M.; Kolkovska, N.<br/><br/>Abstract: One parametric family of potential wells for double dispersion equation with Bernoulli type nonlinearity is introduced. Sign preserving properties of the Nehari functionals are obtained. Global existence of the weak solution to the Cauchy problem is proved for wider class of initial data than the corresponding ones in the classical potential well method. 2010 Mathematics Subject Classification: 35L30, 35L75.<br/><br/>Description: [Kutev N.; Kutev Nikolai; Кутев Николай]; [Dimova M.; Димова М.]; [Kolkovska N.; Кольковска Н.]Numerical Simulation of the Flow Around Two Bluff Bodies Separated by a Gap
http://hdl.handle.net/10525/3558
Title: Numerical Simulation of the Flow Around Two Bluff Bodies Separated by a Gap<br/><br/>Authors: Filipov, Kostadin; Tabakova, Sonia<br/><br/>Abstract: 2010 Mathematics Subject Classification: 76D05, 76M12.<br/><br/>Description: [Filipov Kostadin; Филипов Костадин]; [Tabakova Sonia; Табакова Соня]Models of Internal Waves in the Presence of Currents
http://hdl.handle.net/10525/3557
Title: Models of Internal Waves in the Presence of Currents<br/><br/>Authors: Compelli, Alan; Ivanov, Rossen<br/><br/>Abstract: A fluid system consisting of two domains is examined. The system is considered as being bounded at the bottom and top by a flatbed and wave-free surface respectively. An internal wave propagating in one direction, driven by gravity, acts as a free common interface between the fluids. Various current profiles are considered. The Hamiltonian of the system is determinedand expressed in terms of canonical wave-related variables. Limiting behaviour is examined and compared to that of other known models. The linearised equations as well as long-wave approximations are formulated.The presented models provide potential applications to modelling of internal geophysical waves. 2010 Mathematics Subject Classification: 35Q35, 37K05, 74J30.<br/><br/>Description: [Ivanov Rossen; Иванов Росен]Boundary-Value Problems for PDEs Arising in the Valuation of Structured Financial Products
http://hdl.handle.net/10525/3556
Title: Boundary-Value Problems for PDEs Arising in the Valuation of Structured Financial Products<br/><br/>Authors: Agliardi, Rossella<br/><br/>Abstract: We explicitly solve some mixed initial/boundary value problems for generalized Black-Scholes PDEs with financially relevant boundary conditions.As an illustration, new pricing formulas are obtained for convertible and reverse convertible bonds under credit risk. 2010 Mathematics Subject Classification: 35K20, 91G20, 91G80.Bifurcations of Periodic Solutions to Differential Equations and Multivalent Guiding Functions Method
http://hdl.handle.net/10525/3555
Title: Bifurcations of Periodic Solutions to Differential Equations and Multivalent Guiding Functions Method<br/><br/>Authors: Obukhovskii, Valeri; Zecca, Pietro; Van Loi, Nguyen; Kornev, Sergei<br/><br/>Abstract: In this paper, we define a new class of multivalent guiding functions calledlocal multivalent guiding functions and use it to study the global bifurcationproblem of periodic soluions to a parameterized differential equation. 2010 Mathematics Subject Classification: 34C23, 34C25.