Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 08 Aug 2020 09:24:50 GMT2020-08-08T09:24:50Z50121A new multicomponent Poincaré–Beckner inequalityhttp://hdl.handle.net/10316/43804Title: A new multicomponent Poincaré–Beckner inequality
Authors: Kondratyev, Stanislav; Monsaingeon, Léonard; Vorotnikov, Dmitry
Abstract: We prove a new vectorial functional inequality of Poincaré–Beckner type. The inequality may be interpreted as an entropy–entropy production one for a gradient flow in the metric space of Radon measures. The proof uses subtle analysis of combinations of related super- and sub-level sets employing the coarea formula and the relative isoperimetric inequality.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/438042017-01-01T00:00:00ZOn the Bulk Velocity of Brownian Ratchetshttp://hdl.handle.net/10316/44427Title: On the Bulk Velocity of Brownian Ratchets
Authors: Kondratyev, Stanislav; Urbano, José Miguel; Vorotnikov, Dmitry
Abstract: In this paper we study the unidirectional transport effect for Brownian ratchets modeled by Fokker--Planck-type equations. In particular, we consider the adiabatic and semiadiabatic limits for tilting ratchets, generic ratchets with small diffusion, and the multistate chemical ratchets. Having established a linear relation between the bulk transport velocity and the biperiodic solution, and using relative entropy estimates and new functional inequalities, we obtain explicit asymptotic formulas for the transport velocity and qualitative results concerning the direction of transport. In particular, we prove the conjecture by Blanchet, Dolbeault, and Kowalczyk that the bulk velocity of the stochastic Stokes' drift is nonzero for every nonconstant potential.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10316/444272016-01-01T00:00:00ZAnalysis of adaptive forward-backward diffusion flows with applications in image processinghttp://hdl.handle.net/10316/44400Title: Analysis of adaptive forward-backward diffusion flows with applications in image processing
Authors: Prasath, V B Surya; Urbano, José Miguel; Vorotnikov, Dmitry
Abstract: The nonlinear diffusion model introduced by Perona and Malik (1990 IEEE Trans. Pattern Anal. Mach. Intell. 12 629–39) is well suited to preserve salient edges while restoring noisy images. This model overcomes well-known edge smearing effects of the heat equation by using a gradient dependent diffusion function. Despite providing better denoizing results, the analysis of the PM scheme is difficult due to the forward-backward nature of the diffusion flow. We study a related adaptive forward-backward diffusion equation which uses a mollified inverse gradient term engrafted in the diffusion term of a general nonlinear parabolic equation. We prove a series of existence, uniqueness and regularity results for viscosity, weak and dissipative solutions for such forward-backward diffusion flows. In particular, we introduce a novel functional framework for wellposedness of flows of total variation type. A set of synthetic and real image processing examples are used to illustrate the properties and advantages of the proposed adaptive forward-backward diffusion flows.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/444002015-01-01T00:00:00ZMultiscale Tikhonov-Total Variation Image Restoration Using Spatially Varying Edge Coherence Exponenthttp://hdl.handle.net/10316/44429Title: Multiscale Tikhonov-Total Variation Image Restoration Using Spatially Varying Edge Coherence Exponent
Authors: Prasath, V. B. Surya; Vorotnikov, Dmitry; Pelapur, Rengarajan; Jose, Shani; Seetharaman, Guna; Palaniappan, Kannappan
Abstract: Edge preserving regularization using partial differential equation (PDE)-based methods although extensively studied and widely used for image restoration, still have limitations in adapting to local structures. We propose a spatially adaptive multiscale variable exponent-based anisotropic variational PDE method that overcomes current shortcomings, such as over smoothing and staircasing artifacts, while still retaining and enhancing edge structures across scale. Our innovative model automatically balances between Tikhonov and total variation (TV) regularization effects using scene content information by incorporating a spatially varying edge coherence exponent map constructed using the eigenvalues of the filtered structure tensor. The multiscale exponent model we develop leads to a novel restoration method that preserves edges better and provides selective denoising without generating artifacts for both additive and multiplicative noise models. Mathematical analysis of our proposed method in variable exponent space establishes the existence of a minimizer and its properties. The discretization method we use satisfies the maximum-minimum principle which guarantees that artificial edge regions are not created. Extensive experimental results using synthetic, and natural images indicate that the proposed multiscale Tikhonov-TV (MTTV) and dynamical MTTV methods perform better than many contemporary denoising algorithms in terms of several metrics, including signal-to-noise ratio improvement and structure preservation. Promising extensions to handle multiplicative noise models and multichannel imagery are also discussed.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/444292015-01-01T00:00:00ZOn a System of Adaptive Coupled PDEs for Image Restorationhttp://hdl.handle.net/10316/43903Title: On a System of Adaptive Coupled PDEs for Image Restoration
Authors: Prasath, V. B. Surya; Vorotnikov, Dmitry
Abstract: In this paper, we consider a coupled system of partial differential equations (PDEs) based model for image restoration. Both the image and the edge variables are incorporated by coupling them into two different PDEs. It is shown that the initial-boundary value problem has global in time dissipative solutions (in a sense going back to P.-L. Lions), and several properties of these solutions are established. Some numerical examples are given to highlight the denoising nature of the proposed model along with some comparison results.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10316/439032012-01-01T00:00:00ZAnalytical aspects of the Brownian motor effect in randomly flashing ratchetshttp://hdl.handle.net/10316/43907Title: Analytical aspects of the Brownian motor effect in randomly flashing ratchets
Authors: Vorotnikov, Dmitry
Abstract: The muscle contraction, operation of ATP synthase, maintaining the shape of a cell are believed to be secured by motor proteins, which can be modelled using the Brownian ratchet mechanism. We consider the randomly flashing ratchet model of a Brownian motor, where the particles can be in two states, only one of which is sensitive the applied spatially periodic potential (the mathematical setting is a pair of weakly coupled reaction-diffusion and Fokker-Planck equations). We prove that this mechanism indeed generates unidirectional transport by showing that the amount of mass in the wells of the potential decreases/increases from left to right. The direction of transport is unambiguously determined by the location of each minimum of the potential with respect to the so-called diffusive mean of its adjacent maxima. The transport can be generated not only by an asymmetric potential, but also by a symmetric potential and asymmetric transition rates, and as a consequence of the general result we derive explicit conditions when the latter happens. When the transitions are localized on narrow active sites in the protein conformation space, we find a more explicit characterization of the bulk transport direction, and infer that some common preconditions of the motor effect are redundant.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/439072013-01-01T00:00:00ZAnalysis of adaptive forward-backward diffusion flows with applications in image processinghttp://hdl.handle.net/10316/43904Title: Analysis of adaptive forward-backward diffusion flows with applications in image processing
Authors: Prasath, V B Surya; Urbano, José Miguel; Vorotnikov, Dmitry
Abstract: The nonlinear diffusion model introduced by Perona and Malik (1990 IEEE Trans. Pattern Anal. Mach. Intell. 12 629–39) is well suited to preserve salient edges while restoring noisy images. This model overcomes well-known edge smearing effects of the heat equation by using a gradient dependent diffusion function. Despite providing better denoizing results, the analysis of the PM scheme is difficult due to the forward-backward nature of the diffusion flow. We study a related adaptive forward-backward diffusion equation which uses a mollified inverse gradient term engrafted in the diffusion term of a general nonlinear parabolic equation. We prove a series of existence, uniqueness and regularity results for viscosity, weak and dissipative solutions for such forward-backward diffusion flows. In particular, we introduce a novel functional framework for wellposedness of flows of total variation type. A set of synthetic and real image processing examples are used to illustrate the properties and advantages of the proposed adaptive forward-backward diffusion flows.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/439042015-01-01T00:00:00ZGeneralized solutions for inextensible string equationshttp://hdl.handle.net/10316/43808Title: Generalized solutions for inextensible string equations
Authors: Şengül, Yasemin; Vorotnikov, Dmitry
Abstract: We study the system of equations of motion for inextensible strings. This system can be recast into a discontinuous system of conservation laws as well as into the total variation wave equation. We prove existence of generalized Young measure solutions with non-negative tension after transforming the problem into a system of conservation laws and approximating it with a regularized system for which we obtain uniform estimates of the energy and the tension. We also discuss sufficient conditions for non-negativity of the tension for strong solutions.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/438082017-01-01T00:00:00ZA fitness-driven cross-diffusion system from population dynamics as a gradient flowhttp://hdl.handle.net/10316/43805Title: A fitness-driven cross-diffusion system from population dynamics as a gradient flow
Authors: Kondratyev, Stanislav; Monsaingeon, Léonard; Vorotnikov, Dmitry
Abstract: We consider a fitness-driven model of dispersal of N interacting populations, which was previously studied merely in the case N=1. Based on some optimal transport distance recently introduced, we identify the model as a gradient flow in the metric space of Radon measures. We prove existence of global non-negative weak solutions to the corresponding system of parabolic PDEs, which involves degenerate cross-diffusion. Under some additional hypotheses and using a new multicomponent Poincaré–Beckner functional inequality, we show that the solutions converge exponentially to an ideal free distribution in the long time regime.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10316/438052016-01-01T00:00:00ZOn the well-posedness of a two-phase minimization problemhttp://hdl.handle.net/10316/13715Title: On the well-posedness of a two-phase minimization problem
Authors: Urbano, José Miguel; Vorotnikov, Dmitry
Abstract: We prove a series of results concerning the emptiness and non-emptiness
of a certain set of Sobolev functions related to the well-posedness of a two-phase
minimization problem, involving both the p(x)-norm and the in nity norm. The
results, although interesting in their own right, hold the promise of a wider applicability
since they can be relevant in the context of other problems where minimization
of the p-energy in a part of the domain is coupled with the more local minimization
of the L1-norm on another region
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10316/137152010-01-01T00:00:00ZThe flashing ratchet and unidirectional transport of matterhttp://hdl.handle.net/10316/13701Title: The flashing ratchet and unidirectional transport of matter
Authors: Vorotnikov, Dmitry
Abstract: We study the
ashing ratchet model of a Brownian motor, which consists
in cyclical switching between the Fokker-Planck equation with an asymmetric
ratchet-like potential and the pure di usion equation. We show that the motor really
performs unidirectional transport of mass, for proper parameters of the model,
by analyzing the attractor of the problem and the stationary vector of a related
Markov chain
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10316/137012010-01-01T00:00:00ZWeak solutions for a bioconvection model related to Bacillus subtilishttp://hdl.handle.net/10316/45270Title: Weak solutions for a bioconvection model related to Bacillus subtilis
Authors: Vorotnikov, Dmitry
Abstract: We consider the initial-boundary value problem for the coupled Navier-Stokes-Keller-Segel-Fisher-Kolmogorov-Petrovskii-Piskunov system in two- and three-dimensional domains. The problem describes oxytaxis and growth of Bacillus subtilis in moving water. We prove existence of global weak solutions to the problem. We distinguish between two cases determined by the cell diffusion term and the space dimension, which are referred to as the supercritical and subcritical ones. In the first case, the choice of the kinetic function enjoys a wide range of possibilities: in particular, it can be zero. Our results are new even in the absence of the kinetic term. In the second case, the restrictions on the kinetic function are less relaxed: for instance, it cannot be zero but can be Fisher-like. In the case of linear cell diffusion, the solution is regular and unique provided the domain is the whole plane. In addition, we study the long-time behavior of the problem, find dissipative estimates, and construct attractors.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/452702014-01-01T00:00:00Z