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Showing 1 to 20 of 37 for “"evolution equation"”.
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The evolution equation for closed magnetic geodesics
… to a system of (nonlinear) ordinary differential equations of second order. But we are only interested in periodic solutions. To this end, we study the corresponding system of (nonlinear) parabolic equations for closed magnetic geodesics and, as a main result, eventually prove the existence of …
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Asymptotic analysis of the parametrically driven damped nonlinear evolution equation
… methods are used to obtain amplitude equations for the parametrically driven damped linear and nonlinear oscillator, the linear and nonlinear Klein-Gordon equations in the small-amplitude limit in various frequency regimes. In the case of the parametrically driven linear oscillator, we …
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Investigating the 4-point truncation of the JIMWLK evolution equation
… in deep inelastic scattering (DIS). The JIMWLK equation describes the rapidity evolution of Wilson line correlators in the CGC framework, which are crucial for computing cross-sections in DIS. However, JIMWLK generates an infinite hierarchy of coupled integro-differential equations (the Balitsky …
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Derivation of an Evolution Equation for Two-Dimensional Waves on Thin Films
… a non-convex flux function in our thin film equation. We extend previous studies by deriving the thin film equation governing two-dimensional waves on the liquid layer. We then derive a simplified evolution equation governing weakly nonlinear, quasi-planar, and weakly dissipative waves on the …
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Modeling Collective Behavior of Dislocations in Crystalline Materials
… deals with the kinematics of dislocation density evolution. An explicit Galerkin/least-squares formulation is introduced for the quasilinear evolution equation, which leads to a symmetric and well-conditioned system of equations with constant coefficients, making it attractive for large-scale …
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Evolution Equations for Weakly Nonlinear, Quasi-Planar Waves in Isotropic Dielectrics and Elastomers
… and therefore, a classical Zabolotskaya-Khokhlov equation cannot give an accurate description of the wave evolution. To determine the general evolution equation in such systems, a multi-timing technique developed by Kluwick and Cox (1998) and Cramer and Webb (1998) will be employed. The resultant …
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Theory of Instability and Nonlinear Evolution of Self -Sustained Detonation Waves
… as intrinsic properties of the reactive Euler equations in the embedded sonic surface, which is a characteristic surface. The conditions generalize previously known sonic conditions for self-sustained detonations. We investigate the nature of the sonic conditions numerically with a new …
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Existence and stability of solutions to the equations of fibre suspension flows
… unknown variables for the problem. The governing equations are balance of linear momentum, the incompressibility condition, an evolution equation for A, and a constitutive equation for the stress. The evolution equation contains a fourth-order orientation tensor A, and it is necessary to …
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Continuity in Rigid Viscoplastic Flow
… manner through (local) ordinary differential equations, such as in the update of the rotation field in crystal plasticity. This approach emanates from how the deformation has been described, e.g. the multiplicative decomposition of the deformation gradient. In the present work, a continuity …
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Mathematics of double-walled carbon nanotube model: Asymptotic spectral and stability analysis
… as a coupled system of four partial differential equations of the hyperbolic type equipped with a four-parameter family of dynamical boundary conditions. We rewrite the system of four equations with the set of eight boundary conditions as the first order in time evolution equation in the state …
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Analysis of a Partial Differential Equation Model of Surface Electromigration
<p>A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. …
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Aspects of modern cosmology
… waves in a covariant way is achieved. The evolution equations for the electric and magnetic parts of the Weyl tensor are shown to be of different order. In particular, the electric part appears to have a third order evolution equation, while the magnetic part has a second order evolution …
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Cosmological And Astrophysical Tests Of Modified Gravity
… gravity theory which shares the same background equation with the massless case except the evolution equation for the tensor perturbations. The signature of the graviton mass on the cmb polarization spectrum will be studied. A moderate graviton mass (comparable to the hubble rate during …
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First-order geometric evolutions and semilinear evolution equations : a common mutational approach
… of "solution" for completely different types of evolutions. Such a common approach is to lay the foundations for solving systems whose components have their origins in diverse applications. The analytical touchstone of the general character consists of (1.) a semilinear evolution equation in a …
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Some theoretical aspects of fibre suspension flows
This thesis is concerned with properties of equations governing fibre suspensions. Of particular interest is the extent to which solutions, and their properties, depend on the type of closure used. For this purpose two closure rules are investigated: the linear and the quadratic closures. We show …
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Mathematical and Experimental Analysis of Microbicide Vaginal Gels
… a non-linear, second-order, partial differential equation that governs the evolution of the free surface of a spreading fluid. 3. A derivation and numerical solution for the 3-D power-law evolution equation. 4. A derivation and numerical solution for the 3-D Ellis evolution equation. All …
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Ricci Yang-Mills Flow
… K-bundle with connection A. We define a natural evolution equation for the pair (g,A) combining the Ricci flow for g and the Yang-Mills flow for A which we dub Ricci Yang-Mills flow. We show that these equations are, up to di eomorphism equivalence, the gradient flow equations for a Riemannian …
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A finite strain theory of elastoplasticity and its application to wave propagation
… of convex analysis lead in a natural way to the evolution equation or flow law. Non-smooth yield surfaces are included in the theory; nevertheless, the form of this theory makes a study of propagation of singular surfaces awkward. With a view to carrying out such a study, an alternative means of …
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mKdV Loop Travelling Waves and Interactions of Loop Solitons
The modified Korteweg-de Vries (mKdV) equation is an integrable nonlinear evolution equation which has applications in modeling various physical phenomena. It also describes the curvature of curve which undergoes a certain non-stretching geometrical evolution in the Euclidean plane. This curve …
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Modelling of dislocation-mobility-controlled brittle-to-ductile transition
… including the form of the dislocation-density evolution equation. The evolving-dislocation-density model not only predicts the BDT temperature at different loading rates, but also captures the sharpness of the transition. The numerical results of each model are compared with experimental …
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