Asymptotic Research of Nonlinear Wave Processes in Saturated Porous Media

The problem of nonlinear wave dynamics of a fluid-saturated porous medium is investigated. The mathematical model proposed is based on the classical Frenkel--Biot--Nikolaevskiy theory concerning elastic wave propagation and includes mass, momentum, energy conservation laws, as well as rheological and thermodynamic relations. The model describes nonlinear, dispersive, and dissipative medium. To solve the system of differential equations, an asymptotic modified two-scales method is developed and a Cauchy problem for initial equations system is transformed to a Cauchy problem for nonlinear generalized Korteweg--de Vries--Burgers equation for modulated quick wave amplitudes and an inhomogeneous set of equations for slow background motion. Stationary solutions of the derived evolutionary equation that have been constructed numerically reflect different regimes of elastic wave attenuation: diffusive, oscillating, and soliton-like.     

Magnetic circular dichroism and optical absorption in TmAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The polarized spectra of absorption and magnetic circular dichroism in a TmAl₃(BO₃)₄ single crystal are studied in the region of ³ H ₆ → ³ F ₄, ³ H ₆ → ³ F ₃, and ³ H ₆ → ³ F ₂ electronic transitions in the Tm³⁺ ion. The structure of the spectra is interpreted qualitatively. It is shown that the magnetic circular dichroism of the ³ H ₆ → ³ F ₄ transition is determined by the contribution from the splitting of the ground state, whereas the magnetic circular dichroism of the ³ H ₆ → ³ F ₃ transition is governed by the contribution from the splitting of an excited state in a trigonal crystal field.     

Unilamellar Vesicles from Amphiphilic Graphene Quantum Dots

Graphene quantum dots (GQDs) have attracted considerable interest due to their unique physicochemical properties and various applications. For the first time it is shown that GQDs surface‐functionalized with hydrocarbon chains (i.e., amphiphilic GQDs) self‐assemble into unilamellar spherical vesicles in aqueous solution. The amphiphilic GQD vesicles exhibit multicolor luminescence that can be readily exploited for membrane studies by fluorescence spectroscopy and microscopy. The GQD vesicles were used for microscopic analysis of membrane interactions and disruption by the peptide beta‐amyloid.     

On conjugate gradient-like methods for eigen-like problems

Numerical analysts, physicists, and signal processing engineers have proposed algorithms that might be called conjugate gradient for problems associated with the computation of eigenvalues. There are many variations, mostly one eigenvalue at a time though sometimes block algorithms are proposed. Is there a correct “conjugate gradient” algorithm for the eigenvalue problem? How are the algorithms related amongst themselves and with other related algorithms such as Lanczos, the Newton method, and the Rayleigh quotient?     

On the Financial Value of Information

Results of Kelly [5] and Breiman [2] relating optimal growth rates for gambling and investing to information distances are generalised to include return distributions for virtually any type of game or asset. These results are achieved by first introducing the notion of the optimal financial derivative instrument for a given gamble or investment and then solving the related optimisation problem. For assets varying continuously over time, a formula for optimal dynamic portfolio adjustment follows for commonly occurring models, assuming no transaction costs. The latter results are applied to assets with normal and lognormal returns. The results for these are demonstrated using simulation.     

Amplified Degradation of Photosystem II D1 and D2 Proteins under a Mixture of Photosynthetically Active Radiation and UVB Radiation: Dependence on Redox Status of Photosystem II

Abstract— Plants exposed to a mixture of photosynthetically active radiation (PAR) and UVB radiation exhibit a marked boost in degradation of the D1 and D2 photosysteni II (PS II) reaction center proteins beyond that predicted by the sum of rates in PAR and UVB alone (amplified degradation). Becausee degradation driven by visible or UVB radiation alone is uncoupled from PS II redox status, it was therefore assumed that the mixed-light-amplified component of degradation would behave similarly. Surprisingly, amplified degradation proved to be coupled tightly to the redox status of PS II. We show that inactivation of the PS II water oxidation by heat shock or oxidation of the plastosemiquinone (Q_A-) by silicomolybdate nullifies only the amplified component of degradation but not the basic rates of degradation under PAR or UVB alone. The data are interpreted to indicate that formation of plastosemiquinone or an active water-oxidizing Mn₄ cluster, is the UVB chromophore involved in amplified degradation of the D1 and D2 proteins. Furthermore, accumulation of Q_A-by 3-(3,4-dichlorophenyl)-1,1-dimethylurea or 2-bromo-3-methyl-6-isopropyl-4-nitrophenol stimulated the mixed-light-amplified degradation component. Thus, amplified degradation of the D1 and D2 proteins in mixed radiance of PAR plus UVB (which simulates naturally occurring radiance) proceeds by a mechanism clearly distinct from that involved in degradation under PAR or UVB alone.     

The lattice of convex sets of an oriented matroid

Using the theory of the anti-exchange closure the structure of the lattice of convex sets of an acyclic oriented matroid is described. A new expression for the characteristic polynomial of the underlying matroid is proven using this analysis.     

The Probability that a Random Real Gaussian Matrix haskReal Eigenvalues, Related Distributions, and the Circular Law

LetAbe annbynmatrix whose elements are independent random variables with standard normal distributions. Girko's (more general) circular law states that the distribution of appropriately normalized eigenvalues is asymptotically uniform in the unit disk in the complex plane. We derive the exact expected empirical spectral distribution of the complex eigenvalues for finiten, from which convergence in the expected distribution to the circular law for normally distributed matrices may be derived. Similar methodology allows us to derive a joint distribution formula for the real Schur decomposition ofA. Integration of this distribution yields the probability thatAhas exactlykreal eigenvalues. For example, we show that the probability thatAhas all real eigenvalues is exactly 2^{−n(n−1)/4}.     

Stanislaw Ulam: The warmth and brilliance of an eclectic mind

We discuss several of Stanislaw Ulam's contributions to theoretical biology, in particular, his ideas on morphogenesis and on higher functions of the nervous system.     

Hydration‐mediated effects of saccharide stereochemistry on poly(N‐isopropylacrylamide) gel swelling

To shed new light on the mechanisms of saccharide stereochemistry effect on macromolecules in aqueous solutions, we studied the effect of three monosaccharide stereoisomers, glucose, galactose, and mannose, on the swelling of Poly(N‐isopropylacrylamide) (PNIPA) hydrogels. We equilibrated PNIPA hydrogels in sugar solutions of different concentrations at 25 °C, and determined gel volume and mass swelling ratios, and sugar concentration imbalance. The volume‐phase‐transition occurred at molal concentrations of 0.587 ± 0.004 (galactose), 0.724 ± 0.003 (glucose), and 0.846 ± 0.004 (mannose). The same order of sugars emerged for the gel‐swelling and the magnitude of the sugar concentration‐imbalance, which correlated with sugar isentropic molar compressibility and hydration number. The more hydrated the sugar, the worse a cosolvent it is for the polymer, hence the larger the deswelling and the more negative the sugar concentration imbalance. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011