A bounded upwinding scheme for computing convection-dominated transport problems

A practical high resolution upwind differencing scheme for the numerical solution of convection-dominated transport problems is presented. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite difference methodology. The performance of the scheme is investigated by solving the 1D/2D scalar advection equations, 1D inviscid Burgers’ equation, 1D scalar convection–diffusion equation, 1D/2D compressible Euler’s equations, and 2D incompressible Navier–Stokes equations. The numerical results displayed good agreement with other existing numerical and experimental data

Allgrove syndrome and motor neuron disease

Allgrove or triple A syndrome (AS or AAA) is a rare autosomal recessive syndrome with variable phenotype due to mutations in AAAS gene which encodes a protein called ALADIN. Generally, it’s characterized by of adrenal insufficiency in consequence of adrenocorticotropic hormone (ACTH) resistance, besides of achalasia, and alacrimia. Neurologic features are varied and have been the subject of several case reports and reviews. A few cases of Allgrove syndrome with motor neuron disease have been already described. A 25-year-old white man, at the age of four, presented slowly progressive distal amyotrophy and weakness, autonomic dysfunction, dysphagia and lack of tears. He suffered later of orthostatic hypotension and erectile dysfunction. He presented distal amytrophy in four limbs, tongue myofasiculations, alacrimia, hoarseness and dysphagia due to achalasia. The ENMG showed generalized denervation with normal conduction velocities. Genetic testing revealed 2 known pathogenic variants in the AAAS gene (c.938T>C and c.1144_1147delTCTG). Our case presented a distal spinal amyotrophy with slow evolution and symptoms and signs of AS with a mutation in AAAS gen. Some cases of motor neuron disease, as ours, may be due to AAS. Early diagnosis is extremely important for symptomatic treatment

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio