Related papers: A perturbation basis for calculating NMR Diffusome…
The Bloch-Torrey equation governs the evolution of the transverse magnetization in diffusion magnetic resonance imaging, where two mechanisms are at play: diffusion of spins (Laplacian term) and their precession in a magnetic field gradient…
In this paper commutator expansions for solving the Bloch-Torrey's equation are derived. An exact solution for free diffusion in a constant magnetic field gradient is found. Furthermore the moments of the signal in the short gradient pulse…
The complex transverse water proton magnetization subject to diffusion-encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch-Torrey partial differential equation. The spatial…
The Bloch equation describes the evolution of classical particles tagged with a magnetisation vector in a strong magnetic field and is fundamental to many NMR and MRI contrast methods. The equation can be generalised to include the effects…
A perturbation method for computing quick estimates of the echo decay in pulsed spin echo gradient NMR diffusion experiments in the short gradient pulse limit is presented. The perturbation basis involves (relatively few) dipole…
Lattice diffusion and internal local magnetic field gradients in solids are investigated by numerical simulation of nuclear mangetic resonance(NMR) spin echo experiments. The Fourier-spectrum method is employed in order to solve the…
Recently, there has been an examination of the nonexponential relaxation profiles of the NMR signal. The exponential relaxation from Bloch-Torrey equations with constant diffusion coefficients are known to be an approximation, and research…
We discuss some challenges and recent advances in understanding the macroscopic signal formation at high non-narrow magnetic field gradients at which both the narrow pulse and the Gaussian phase approximations fail. The transverse…
A numerical method is developed to efficiently calculate the stress (and displacement) field in finite 2D rectangular media. The solution is expanded on a function basis with elements that satisfy the Navier-Cauchy equation. The obtained…
In this paper we provide some uniqueness results for the (multi-)coefficient identification problem of reconstructing the spatially varying spin density as well as the spin-lattice and spin-spin relaxation times and the local field…
We present an accurate and efficient method to calculate the effect of random fluctuations of the local field at the muon, for instance in the case muon diffusion, within the framework of the strong collision approximation. The method is…
We provide a numerical algorithm for the model characterizing anomalous diffusion in expanding media, which is derived in [F. Le Vot, E. Abad, and S. B. Yuste, Phys. Rev. E {\bf96} (2017) 032117]. The Sobolev regularity for the equation is…
Pulsed-gradient spin-echo (PGSE) MRI experiments probe molecular self-diffusion through spin phase accumulation under time-dependent magnetic field gradients. For diffusion confined to cylindrical surfaces, existing analytical signal models…
We adapt boundary deformation techniques to solve a Neumann problem for the Helmholtz equation with rough electric potentials in bounded domains. In particular, we study the dependance of Neumann eigenvalues of the perturbed Laplacian with…
This paper presents a mixed basis approach for Laplace eigenvalue problems, which treats the boundary as a perturbation of the free Laplace operator. The method separates the boundary from the volume via a generic function that can be…
In this paper we develop a multiscale method to solve problems in complicated porous microstructures with Neumann boundary conditions. By using a coarse-grid quasi-interpolation operator to define a fine detail space and local orthogonal…
Accurate and fast calculations of localized surface plasmon resonances (LSPR) in metallic nanoparticles is essential for applications in sensing, nano-optics, and energy harvesting. Although full-wave numerical techniques such as the…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications.…
Reduced Bloch mode expansion is presented for fast periodic media band structure calculations. The expansion employs a natural basis composed of a selected reduced set of Bloch eigenfunctions. The reduced basis is selected within the…