The field of computer-aided diagnosis (CAD) of brain tumors has been transformed by developments in medical imaging and artificial intelligence. The accuracy and interpretability of brain tumor classification are impr...
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In order to improve learning outcomes and reduce dropouts, educational institutions must anticipate students' academic performance. This study focuses on identifying effective prediction models and employing a wra...
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This article concerns numerical approximation of a parabolic interface problem with general L 2 initial *** problem is discretized by a finite element method with a quasi-uniform triangulation of the domain fitting th...
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This article concerns numerical approximation of a parabolic interface problem with general L 2 initial *** problem is discretized by a finite element method with a quasi-uniform triangulation of the domain fitting the interface,with piecewise linear approximation to the *** semi-discrete finite element problem is furthermore discretized in time by the k-step backward difference formula with k=1,...,*** maintain high-order convergence in time for possibly nonsmooth L 2 initial value,we modify the standard backward difference formula at the first k−1 time levels by using a method recently developed for fractional evolution *** error bound of O(t−k nτk+t−1 n h 2|log h|)is established for the fully discrete finite element method for general L 2 initial data.
Regularity criteria in terms of bounds for the pressure are derived for the 3D MHD equations in a bounded domain with slip boundary conditions.A list of three regularity criteria is shown.
Regularity criteria in terms of bounds for the pressure are derived for the 3D MHD equations in a bounded domain with slip boundary conditions.A list of three regularity criteria is shown.
Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier *** methods have been used in partial differential equation(PDE)-solvers and have d...
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Fourier continuation(FC)is an approach used to create periodic extensions of non-periodic functions to obtain highly-accurate Fourier *** methods have been used in partial differential equation(PDE)-solvers and have demonstrated high-order convergence and spectrally accurate dispersion relations in numerical *** Galerkin(DG)methods are increasingly used for solving PDEs and,as all Galerkin formulations,come with a strong framework for proving the stability and the *** we propose the use of FC in forming a new basis for the DG framework.
We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational *** higher-order derivative of un...
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We employ the Galerkin method to prove the global existence of weak solutions to a phase-field model which is suitable to describe a sort of interface motion driven by configurational *** higher-order derivative of unknown S exists in the sense of local weak derivatives since it may be not summable over the original open *** existence proof is valid in the one-dimensional case.
Unsupervised methods for dimensionality reduction of neural activity and behavior have provided unprecedented insights into the underpinnings of neural information processing. One popular approach involves the recurre...
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Nonequilibrium dynamics governed by electron–phonon(e-ph)interactions plays a key role in electronic devices and spectroscopies and is central to understanding electronic excitations in *** real-time Boltzmann transp...
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Nonequilibrium dynamics governed by electron–phonon(e-ph)interactions plays a key role in electronic devices and spectroscopies and is central to understanding electronic excitations in *** real-time Boltzmann transport equation(rt-BTE)with collision processes computed from first principles can describe the coupled dynamics of electrons and atomic vibrations(phonons).Yet,a bottleneck of these simulations is the calculation of e–ph scattering integrals on dense momentum grids at each time *** we show a data-driven approach based on dynamic mode decomposition(DMD)that can accelerate the time propagation of the rt-BTE and identify dominant electronic *** apply this approach to two case studies,high-field charge transport and ultrafast excited electron *** both cases,simulating only a short time window of~10%of the dynamics suffices to predict the dynamics from initial excitation to steady state using DMD *** of the momentum-space modes extracted from DMD sheds light on the microscopic mechanisms governing electron relaxation to a steady state or *** combination of accuracy and efficiency makes our DMD-based method a valuable tool for investigating ultrafast dynamics in a wide range of materials.
We analyze the low-Reynolds-number translation of a sphere towards or away from a rigid plane in an Oldroyd-B fluid under two scenarios: prescribing the sphere's translational velocity, and prescribing the force o...
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We analyze the low-Reynolds-number translation of a sphere towards or away from a rigid plane in an Oldroyd-B fluid under two scenarios: prescribing the sphere's translational velocity, and prescribing the force on the sphere. Leveraging the lubrication approximation and a perturbation expansion in powers of the Deborah number, we develop a comprehensive theoretical analysis that yields analytical approximations for velocity fields, pressures, and forces acting on the sphere. Our framework aids in understanding temporal microstructural changes as the particle-wall gap evolves over time. In particular, we show that alterations in the polymer conformation tensor in response to geometric changes induce additional forces on the sphere. For cases with prescribed velocity, we present a theoretical approach for calculating resistive forces at any order in the Deborah number and utilize a reciprocal theorem to obtain higher-order corrections based on velocity fields in the previous orders. When the sphere translates with a constant velocity, the fluid viscoelasticity decreases the resistive force at the first order. However, at the second-order correction, the direction of the sphere's movement determines whether viscoelasticity increases or decreases the resistive force. For cases with prescribed force, we show that understanding the influence of viscoelasticity on the sphere's translational velocity necessitates a more intricate analysis even at low Deborah numbers. Specifically, we introduce an ansatz for constant force scenarios, and we derive solution forms for general prescribed forces using the method of multiple scales. We find that when a sphere undergoes sedimentation due to its own weight, the fluid viscoelasticity results in a slower settling process, reducing the leading-order sedimentation rate.
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