114 research outputs found
Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy
Time-fractional partial differential equations are nonlocal in time and show
an innate memory effect. In this work, we propose an augmented energy
functional which includes the history of the solution. Further, we prove the
equivalence of a time-fractional gradient flow problem to an integer-order one
based on our new energy. This equivalence guarantees the dissipating character
of the augmented energy. The state function of the integer-order gradient flow
acts on an extended domain similar to the Caffarelli-Silvestre extension for
the fractional Laplacian. Additionally, we apply a numerical scheme for solving
time-fractional gradient flows, which is based on kernel compressing methods.
We illustrate the behavior of the original and augmented energy in the case of
the Ginzburg-Landau energy functional
Time-fractional Cahn-Hilliard equation: Well-posedness, degeneracy, and numerical solutions
In this paper, we derive the time-fractional Cahn-Hilliard equation from
continuum mixture theory with a modification of Fick's law of diffusion. This
model describes the process of phase separation with nonlocal memory effects.
We analyze the existence, uniqueness, and regularity of weak solutions of the
time-fractional Cahn-Hilliard equation. In this regard, we consider
degenerating mobility functions and free energies of Landau, Flory--Huggins and
double-obstacle type. We apply the Faedo-Galerkin method to the system, derive
energy estimates, and use compactness theorems to pass to the limit in the
discrete form. In order to compensate for the missing chain rule of fractional
derivatives, we prove a fractional chain inequality for semiconvex functions.
The work concludes with numerical simulations and a sensitivity analysis
showing the influence of the fractional power. Here, we consider a convolution
quadrature scheme for the time-fractional component, and use a mixed finite
element method for the space discretization
MobilitĂ€tsoffensive fĂŒr das Land
MOBILITĂTSOFFENSIVE FĂR DAS LAND
MobilitĂ€tsoffensive fĂŒr das Land / Reuter, Christian (Rights reserved) ( -
Tiny Medicine: Nanomaterial-Based Biosensors
Tiny medicine refers to the development of small easy to use devices that can help in the early diagnosis and treatment of disease. Early diagnosis is the key to successfully treating many diseases. Nanomaterial-based biosensors utilize the unique properties of biological and physical nanomaterials to recognize a target molecule and effect transduction of an electronic signal. In general, the advantages of nanomaterial-based biosensors are fast response, small size, high sensitivity, and portability compared to existing large electrodes and sensors. Systems integration is the core technology that enables tiny medicine. Integration of nanomaterials, microfluidics, automatic samplers, and transduction devices on a single chip provides many advantages for point of care devices such as biosensors. Biosensors are also being used as new analytical tools to study medicine. Thus this paper reviews how nanomaterials can be used to build biosensors and how these biosensors can help now and in the future to detect disease and monitor therapies
A História da Alimentação: balizas historiogråficas
Os M. pretenderam traçar um quadro da HistĂłria da Alimentação, nĂŁo como um novo ramo epistemolĂłgico da disciplina, mas como um campo em desenvolvimento de prĂĄticas e atividades especializadas, incluindo pesquisa, formação, publicaçÔes, associaçÔes, encontros acadĂȘmicos, etc. Um breve relato das condiçÔes em que tal campo se assentou faz-se preceder de um panorama dos estudos de alimentação e temas correia tos, em geral, segundo cinco abardagens Ia biolĂłgica, a econĂŽmica, a social, a cultural e a filosĂłfica!, assim como da identificação das contribuiçÔes mais relevantes da Antropologia, Arqueologia, Sociologia e Geografia. A fim de comentar a multiforme e volumosa bibliografia histĂłrica, foi ela organizada segundo critĂ©rios morfolĂłgicos. A seguir, alguns tĂłpicos importantes mereceram tratamento Ă parte: a fome, o alimento e o domĂnio religioso, as descobertas europĂ©ias e a difusĂŁo mundial de alimentos, gosto e gastronomia. O artigo se encerra com um rĂĄpido balanço crĂtico da historiografia brasileira sobre o tema
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