94 research outputs found
Scalar auxiliary variable finite element scheme for the parabolic-parabolic Keller-Segel model
No full textWe describe and analyze a finite element numerical scheme for the parabolic-parabolic Keller-Segel model. The scalar auxiliary variable method is used to retrieve the monotonic decay of the energy associated with the system at the discrete level. This method relies on the interpretation of the Keller-Segel model as a gradient flow. The resulting numerical scheme is efficient and easy to implement. We show the existence of a unique non-negative solution and that a modified discrete energy is obtained due to the use of the SAV method. We also prove the convergence of the discrete solutions to the ones of the weak form of the continuous Keller-Segel model
A new study on the Newell-Whitehead-Segel equation with Caputo-Fabrizio fractional derivative
No full textIn this research, we propose a new numerical method that combines with the Caputo-Fabrizio Elzaki transform and the q-homotopy analysis transform method. This work aims to analyze the Caputo-Fabrizio fractional Newell-Whitehead-Segel (NWS) equation utilizing the Caputo-Fabrizio q-Elzaki homotopy analysis transform method. The Newell-Whitehead-Segel equation is a partial differential equation employed for modeling the dynamics of reaction-diffusion systems, specifically in the realm of pattern generation in biological and chemical systems. A convergence analysis of the proposed method was performed. Two-dimensional and three-dimensional graphs of the solutions have been drawn with the Maple software. It is seen that the resulting proposed method is more powerful and effective than the Aboodh transform homotopy perturbation method and conformable Laplace decomposition method in the results. © 2024 the Author(s), licensee AIMS Press
Reduced Differential Transform Approach Using Fixed Grid Size for Solving Newell–Whitehead–Segel (NWS) Equation
No full textIn this study, the Equation of Newell-Whitehead Segel (NWS) is solved with a new method named as Reduced Differential Transform by using Fixed Grid Size (RDTM with FGS) [1–3, 12]. The method is quite useful for linear and nonlinear differential equation solutions. The simplicity efficiency, success and trustworthiness of the mentioned method, two equations were solved in the implementation part and results were compared through the Method of Variational Iteration (VIM) [5–18]. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG
A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation
No full textThis paper solves fractional differential equations using the Shehu transform in combination with the q-homotopy analysis transform method (q-HATM). As the Shehu transform is only applicable to linear equations, q-HATM is an efficient technique for approximating solutions to nonlinear differential equations. In nonlinear systems that explain the emergence of stripes in 2D systems, the Newell–Whitehead–Segel equation plays a significant role. The findings indicate that the outcomes derived from the tables yield superior results compared to the existing LTDM in the literature. Maple is utilized to depict three-dimensional surfaces and find numerical values that are displayed in a table. © The Author(s) 2024
The Keller-Segel model in R d : global existence in the case of linear and non-linear diffusion
No full textDas Ziel dieser Diplomarbeit war es die Arbeit von Martin Burger, Marco di Francesco und Yasim Dolak-Struss in dem wissenschaftlichen Artikel "Keller-Segel Model for Chemotaxis with Prevention of Overcrowding: Linear vs. Nonlinear Diffusion" auszuformulieren und zu erweitern. Unter gewissen Voraussetzungen an die Parameter haben die oben genannten Autoren globale Existenz für einen Spezialfall des Modells, das die Bewegung von Zellen und einer Chemikalie in einer Flüssigkeit beschreibt, bewiesen.Diese Diplomarbeit beschäftigt sich mit einer größeren Klasse an partiellen Differentialgleichungen und zeigt, dass unter nahezu natürlichen Bedingungen an Diffusions- und Sensibilitätsfunktionen, Eigenschaften wie globale Existenz und charakteristisches Langzeitverhalten trotzdem erhalten bleiben.The goal of this diploma thesis was to write out and extend the paper "Keller-Segel Model for Chemotaxis with Prevention of Overcrowding: Linear vs. Nonlinear Diffusion" by Martin Burger, Marco di Francesco and Yasim Dolak-Struss, dealing with two different versions of the so called Keller-Segel model, describing diffusion and movement of certain cells and a chemoattractant in a liquid. They achieved global-in-time existence under certain restrictions to the parameters and analysed the long time behaviour of the densities for linear and non-linear diffusion in the special case where overcrowding does not occur.In this thesis the author has been proven that similar results can be obtained for a wider class of differential equations both in the case of linear and non-linear diffusion, either for subcritical mass or for models where overcrowding is prevented. The author has shown that under almost natural restrictions to the sensitivity and diffusivity functions, global-in-time solutions exist
Hele-Shaw flow as a singular limit of a Keller-Segel system with nonlinear diffusion
No full textWe study a singular limit of the classical parabolic-elliptic
Patlak-Keller-Segel (PKS) model for chemotaxis with non linear diffusion. The
main result is the convergence of the corresponding energy functional
toward the perimeter functional. Following recent work on this topic, we then
prove that under an energy convergence assumption, the solution of the PKS
model converges to a solution of the Hele-Shaw free boundary problem with
surface tension, which describes the evolution of the interface separating
regions with high density from those with low density. This result complements
a recent work by the author with I. Kim and Y. Wu, in which the same free
boundary problem is derived from the incompressible PKS model (which includes a
density constraint and a pressure term): It shows that the
incompressibility constraint is not necessary to observe phase separation and
surface tension phenomena
A lie and a libel the history of the Protocols of the Elders of Zion
No full textA strange and repugnant mystery of the twentieth century is the durability of the Protocols of the Elders of Zion, a clumsy forgery purporting to be evidence of the supposed Jewish plot to rule the world. Though it has been exposed as a forgery, some apprentice brownshirt is always rediscovering it, the latest in a line of gullibility that includes, most famously, Henry Ford. Recently it has been translated into Japanese and circulates once again with renewed virulence in the former Soviet Union and Eastern Europe. In 1924 in Germany the Jewish author and journalist Binjamin Segel wrote a major historical expose of the fraud and later edited his work into a shorter form, published as Welt-Krieg, Welt-Revolution, Welt-Verschworung, Welt-Oberregierung (Berlin 1926). Translator Richard S. Levy, a specialist on the history of antisemitism, provides an extensive introduction on the circumstances of Segel's work and the story of the Protocols up to the 1990s, including an explanation of its continuing psychological appeal and political function
Computer prediction of the braking and steering performance of the AM General Transbus. A summary report
No full textAM General Corporation, Warren, Mich.http://deepblue.lib.umich.edu/bitstream/2027.42/605/2/28679.0001.001.pd
New semi-analytical solution of fractional Newell–Whitehead–Segel equation arising in nonlinear optics with non-singular and non-local kernel derivative
No full textIn this paper, a combined form of Laplace transform is applied with the Adomian Decomposition technique for the first time to obtain new semi-analytical solutions of the fractional Newell–Whitehead–Segel equation which is a model arising in nonlinear optics with Caputo–Fabrizio derivative which involves non-singular and non-local kernels in its definition. The obtained results by the suggested method are compared with exact solutions, as a result of remarkable concurrence between the acquired results and the exact proposed method and the exacted solutions. Plotted graphs and given tables illustrate the efficiency and accuracy of the proposed technique. All the calculations are made by the computer software called MAPLE and Mathematica. © 2024, The Author(s).Türkiye Bilimsel ve Teknolojik Araştırma Kurumu, TÜBİTA
Boundedness in a quasilinear parabolic–parabolic Keller–Segel system with subcritical sensitivity
No full textAbstractWe consider the quasilinear parabolic–parabolic Keller–Segel system{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v),x∈Ω,t>0,vt=Δv−v+u,x∈Ω,t>0, under homogeneous Neumann boundary conditions in a convex smooth bounded domain Ω⊂Rn with n⩾1.It is proved that if S(u)D(u)⩽cuα with α<2n and some constant c>0 for all u>1, then the classical solutions to the above system are uniformly-in-time bounded, provided that D(u) satisfies some technical conditions such as algebraic upper and lower growth (resp. decay) estimates as u→∞. This boundedness result is optimal according to a recent result by the second author (Winkler, 2010 [27]), which says that if S(u)D(u)⩾cuα for u>1 with c>0 and some α>2n, n⩾2, then for each mass M>0 there exist blow-up solutions with mass ∫Ωu0=M.In addition, this paper also proves a general boundedness result for quasilinear non-uniformly parabolic equations by modifying the iterative technique of Moser–Alikakos (Alikakos, 1979 [1])
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