168 research outputs found
A new ghost cell/level set method for moving boundary problems:application to tumor growth
In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth
Electronic structure and magnetic properties of the linear chain cuprates Sr_2CuO_3 and Ca_2CuO_3
Sr_2CuO_3 and Ca_2CuO_3 are considered to be model systems of strongly
anisotropic, spin-1/2 Heisenberg antiferromagnets. We report on the basis of a
band-structure analysis within the local density approximation and on the basis
of available experimental data a careful analysis of model parameters for
extended Hubbard and Heisenberg models. Both insulating compounds show
half-filled nearly one-dimensional antibonding bands within the LDA. That
indicates the importance of strong on-site correlation effects. The bonding
bands of Ca_2CuO_3 are shifted downwards by 0.7 eV compared with Sr_2CuO_3,
pointing to different Madelung fields and different on-site energies within the
standard pd-model. Both compounds differ also significantly in the magnitude of
the inter-chain dispersion along the crystallographical a-direction: \approx
100 meV and 250 meV, respectively. Using the band-structure and experimental
data we parameterize a one-band extended Hubbard model for both materials which
can be further mapped onto an anisotropic Heisenberg model. From the
inter-chain dispersion we estimate a corresponding inter-chain exchange
constant J_{\perp} \approx 0.8 and 3.6 meV for Sr_2CuO_3 and Ca_2CuO_3,
respectively. Comparing several approaches to anisotropic Heisenberg problems,
namely the random phase spin wave approximation and modern versions of coupled
quantum spin chains approaches, we observe the advantage of the latter in the
reproduction of reasonable values for the N\'eel temperature T_N and the
magnetization m_0 at zero temperature. Our estimate of gives the
right order of magnitude and the correct tendency going from Sr_2CuO_3 to
Ca_2CuO_3. In a comparative study we also include CuGeO_3.Comment: 23 pages, 5 figures, 1 tabl
Quantum walks: a comprehensive review
Quantum walks, the quantum mechanical counterpart of classical random walks,
is an advanced tool for building quantum algorithms that has been recently
shown to constitute a universal model of quantum computation. Quantum walks is
now a solid field of research of quantum computation full of exciting open
problems for physicists, computer scientists, mathematicians and engineers.
In this paper we review theoretical advances on the foundations of both
discrete- and continuous-time quantum walks, together with the role that
randomness plays in quantum walks, the connections between the mathematical
models of coined discrete quantum walks and continuous quantum walks, the
quantumness of quantum walks, a summary of papers published on discrete quantum
walks and entanglement as well as a succinct review of experimental proposals
and realizations of discrete-time quantum walks. Furthermore, we have reviewed
several algorithms based on both discrete- and continuous-time quantum walks as
well as a most important result: the computational universality of both
continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing
Journa
Early Life Child Micronutrient Status, Maternal Reasoning, and a Nurturing Household Environment have Persistent Influences on Child Cognitive Development at Age 5 years : Results from MAL-ED
Funding Information: The Etiology, Risk Factors and Interactions of Enteric Infections and Malnutrition and the Consequences for Child Health and Development Project (MAL-ED) is carried out as a collaborative project supported by the Bill & Melinda Gates Foundation, the Foundation for the NIH, and the National Institutes of Health/Fogarty International Center. This work was also supported by the Fogarty International Center, National Institutes of Health (D43-TW009359 to ETR). Author disclosures: BJJM, SAR, LEC, LLP, JCS, BK, RR, RS, ES, LB, ZR, AM, RS, BN, SH, MR, RO, ETR, and LEM-K, no conflicts of interest. Supplemental Tables 1–5 and Supplemental Figures 1–3 are available from the “Supplementary data” link in the online posting of the article and from the same link in the online table of contents at https://academic.oup.com/jn/. Address correspondence to LEM-K (e-mail: [email protected]). Abbreviations used: HOME, Home Observation for Measurement of the Environment inventory; MAL-ED, The Etiology, Risk Factors, and Interactions of Enteric Infections and Malnutrition and the Consequences for Child Health and Development Project; TfR, transferrin receptor; WPPSI, Wechsler Preschool Primary Scales of Intelligence.Peer reviewe
Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics
This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of magnetized fluids. In order to be self-contained we first motivate the physical properties of a magnetic fluid and how it should behave under the laws of thermodynamics. Next, we introduce a mathematical model built from hyperbolic partial differential equations (PDEs) that translate physical laws into mathematical equations. After an overview of the continuous analysis, we thoroughly describe the derivation of a numerical approximation of the ideal MHD system that remains consistent to the continuous thermodynamic principles. The derivation of the method and the theorems contained within serve as the bulk of the review article. We demonstrate that the derived numerical approximation retains the correct entropic properties of the continuous model and show its applicability to a variety of standard numerical test cases for MHD schemes. We close with our conclusions and a brief discussion on future work in the area of entropy consistent numerical methods and the modeling of plasmas
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