Immersed Boundary Smooth Extension: A high-order method for solving PDE on arbitrary smooth domains using Fourier spectral methods

The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations (e.g. Fourier spectral methods). The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta-functions to communicate information between the computational grid and the boundary. We present a fast algorithm for solving elliptic equations, which forms the basis for simple, high-order implicit-time methods for parabolic PDE and implicit-explicit methods for related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat, Burgers', and Fitzhugh-Nagumo equations, and demonstrate fourth-order pointwise convergence for Dirichlet problems and third-order pointwise convergence for Neumann problems

Geometric relationships for homogenization in single-phase binary alloy systems

A semiempirical relationship is presented which describes the extent of interaction between constituents in single-phase binary alloy systems having planar, cylindrical, or spherical interfaces. This relationship makes possible a quick estimate of the extent of interaction without lengthy numerical calculations. It includes two parameters which are functions of mean concentration and interface geometry. Experimental data for the copper-nickel system are included to demonstrate the usefulness of this relationship

Magnetic correlations of the quasi-one-dimensional half-integer spin-chain antiferromagnets SrM2M_2V2_2O8_8 (MM = Co, Mn)

Magnetic correlations of two iso-structural quasi-one-dimensional (1D) antiferromagnetic spin-chain compounds Sr$M_2$V$_2$O$_8$ ($M$ = Co, Mn) have been investigated by magnetization and powder neutron diffraction. Two different collinear antiferromagnetic (AFM) structures, characterized by the propagation vectors, $k$ = (0 0 1) and $k$ = (0 0 0), have been found below $\sim$ 5.2 K and $\sim$ 42.2 K for the Co- and Mn-compounds, respectively. For the Mn-compound, AFM chains (along the $c$ axis) order ferromagnetically within the $ab$ plane, whereas, for the Co-compound, AFM chains order ferro-/antiferromagnetically along the $a/b$ direction. The critical exponent study confirms that the Co- and Mn-compounds belong to the Ising and Heisenberg universality classes, respectively. For both compounds, short-range spin-spin correlations are present over a wide temperature range above $T_N$. The reduced ordered moments at base temperature (1.5 K) indicate the presence of quantum fluctuations in both compounds due to the quasi-1D magnetic interactions.Comment: 14 pages, 10 figures, 9 table

The role of surface generated radicals in catalytic combustion

Experiments were conducted to better understand the role of catalytic surface reactions in determining the ignition characteristics of practical catalytic combustors. Hydrocarbon concentrations, carbon monoxide and carbon dioxide concentrations, hydroxyl radical concentrations, and gas temperature were measured at the exit of a platinum coated, stacked plate, catalytic combustor during the ignition of lean propane-air mixtures. The substrate temperature profile was also measured during the ignition transient. Ignition was initiated by suddenly turning on the fuel and the time to reach steady state was of the order of 10 minutes. The gas phase reaction, showed no pronounced effect due to the catalytic surface reactions, except the absence of a hydroxyl radical overshoot. It is found that the transient ignition measurements are valuable in understanding the steady state performance characteristics

Routine repeat head CT may not be necessary for patients with mild TBI.

Background:Routine repeat cranial CT (RHCT) is standard of care for CT-verified traumatic brain injury (TBI). Despite mixed evidence, those with mild TBI are subject to radiation and expense from serial CT scans. Thus, we investigated the necessity and utility of RHCT for patients with mild TBI. We hypothesized that repeat head CT in these patients would not alter patient care or outcomes. Methods:We retrospectively studied patients suffering from mild TBI (Glasgow Coma Scale (GCS) score 13-15) and treated at the R Adams Cowley Shock Trauma Center from November 2014 through January 2015. The primary outcome was the need for surgical intervention. Outcomes were compared using paired Student's t-test, and stratified by injury on initial CT, GCS change, demographics, and presenting vital signs (mean ± SD). Results:Eighty-five patients met inclusion criteria with an average initial GCS score=14.6±0.57. Our center sees about 2800 patients with TBI per year, or about 230 per month. This includes patients with concussions. This sample represents about 30% of patients with TBI seen during the study period. Ten patients required operation (four based on initial CT and others for worsening GCS, headaches, large unresolving injury). There was progression of injury on repeat CT scan in only two patients that required operation, and this accompanied clinical deterioration. The mean brain Abbreviated Injury Scale (AIS) score was 4.8±0.3 for surgical patients on initial CT scan compared with 3.4±0.6 (P<0.001) for non-surgical patients. Initial CT subdural hematoma size was 1.1±0.6 cm for surgical patients compared with 0.49±0.3 cm (P=0.05) for non-surgical patients. There was no significant difference between intervention groups in terms of other intracranial injuries, demographics, vital signs, or change in GCS. Overall, 75 patients that did not require surgical intervention received RHCT. At $340 per CT,$51 000 was spent on unnecessary imaging ($367 000/year, extrapolated). Discussion:In an environment of increased scrutiny on healthcare expenditures, it is necessary to question dogma and eliminate unnecessary cost. Our data questions the use of routine repeat head CT scans in every patient with anatomic TBI and suggests that clinically stable patients with small injury can simply be followed clinically. Level of evidence:Level III

Coupling of Transport and Chemical Processes in Catalytic Combustion

Catalytic combustors have demonstrated the ability to operate efficiently over a much wider range of fuel air ratios than are imposed by the flammability limits of conventional combustors. Extensive commercial use however needs the following: (1) the design of a catalyst with low ignition temperature and high temperature stability, (2) reducing fatigue due to thermal stresses during transient operation, and (3) the development of mathematical models that can be used as design optimization tools to isolate promising operating ranges for the numerous operating parameters. The current program of research involves the development of a two dimensional transient catalytic combustion model and the development of a new catalyst with low temperature light-off and high temperature stablity characteristics

Polarization and Charge Transfer in the Hydration of Chloride Ions

A theoretical study of the structural and electronic properties of the chloride ion and water molecules in the first hydration shell is presented. The calculations are performed on an ensemble of configurations obtained from molecular dynamics simulations of a single chloride ion in bulk water. The simulations utilize the polarizable AMOEBA force field for trajectory generation, and MP2-level calculations are performed to examine the electronic structure properties of the ions and surrounding waters in the external field of more distant waters. The ChelpG method is employed to explore the effective charges and dipoles on the chloride ions and first-shell waters. The Quantum Theory of Atoms in Molecules (QTAIM) is further utilized to examine charge transfer from the anion to surrounding water molecules. From the QTAIM analysis, 0.2 elementary charges are transferred from the ion to the first-shell water molecules. The default AMOEBA model overestimates the average dipole moment magnitude of the ion compared with the estimated quantum mechanical value. The average magnitude of the dipole moment of the water molecules in the first shell treated at the MP2 level, with the more distant waters handled with an AMOEBA effective charge model, is 2.67 D. This value is close to the AMOEBA result for first-shell waters (2.72 D) and is slightly reduced from the bulk AMOEBA value (2.78 D). The magnitude of the dipole moment of the water molecules in the first solvation shell is most strongly affected by the local water-water interactions and hydrogen bonds with the second solvation shell, rather than by interactions with the ion.Comment: Slight revision, in press at J. Chem. Phy