Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier-Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e(vertical bar k vertical bar/kd) at high wavenumbers vertical bar k vertical bar. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e-(C(k/kd) ln(vertical bar k vertical bar/kd)) for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C-* = 1/ ln 2. The same behavior with a universal constant C-* is conjectured for the Navier-Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier-Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.

The Consequences of Phenotypic Plasticity in Cyclically Varying Environments: A Genetic Algorithm Study

By “phenotypic plasticity” we refer to the capacity of a genotype to exhibit different phenotypes, whether in the same or in different environments. We have previously demonstrated that phenotypic plasticity can improve the degree of adaptation achieved via natural selection (Behera & Nanjundiah, 1995). That result was obtained from a genetic algorithm model of haploid genotypes (idealized as one-dimensional strings of genes) evolving in a fixed environment. Here, the dynamics of evolution is examined under conditions of a cyclically varying environment. We find that the rate of evolution, as well as the extent of adaptation (as measured by mean population fitness) is lowered because of environmental cycling. The decrease is adaptation caused by a varying environment can, however, be partly or wholly compensated by an increase in the degree of plasticity that a genotype is capable of. Also, the reduction of population fitness caused by a variable environment can be partially offset by decreasing the total number of genetic loci. We conjecture that an increase in genome size may have been among the factors responsible for the evolution of phenotypic plasticity.

1,2,3-Trifluorobenzene

In the title compound, C6H3F3, weak electrostatic and dispersive forces between C(delta+)-F(delta-) and H(delta+)-C(delta-) groups are at the borderline of the hydrogen-bond phenomenon and are poorly directional and further deformed in the presence of pi-pi stacking interactions. The molecule lies on a twofold rotation axis. In the crystal structure, one-dimensional tapes are formed via two antidromic C-H center dot center dot center dot F hydrogen bonds. These tapes are, in turn, connected into corrugated two-dimensional sheets by bifurcated C-H center dot center dot center dot F hydrogen bonds. Packing in the third dimension is furnished by pi-pi stacking interactions with a centroid-centroid distance of 3.6362 (14) angstrom.

Nonspecifically bound proteins spin while diffusing along DNA

It is known that DNA-binding proteins can slide along the DNA helix while searching for specific binding sites, but their path of motion remains obscure. Do these proteins undergo simple one-dimensional (1D) translational diffusion, or do they rotate to maintain a specific orientation with respect to the DNA helix? We measured 1D diffusion constants as a function of protein size while maintaining the DNA-protein interface. Using bootstrap analysis of single-molecule diffusion data, we compared the results to theoretical predictions for pure translational motion and rotation-coupled sliding along the DNA. The data indicate that DNA-binding proteins undergo rotation-coupled sliding along the DNA helix and can be described by a model of diffusion along the DNA helix on a rugged free-energy landscape. A similar analysis including the 1D diffusion constants of eight proteins of varying size shows that rotation-coupled sliding is a general phenomenon. The average free-energy barrier for sliding along the DNA was 1.1 +/- 0.2 k(B)T. Such small barriers facilitate rapid search for binding sites.

Quantum phase analysis of 1D superconducting quantum dot lattice using extended Bose-Hubbard model

We have obtained the quantum phase diagram of a one-dimensional superconducting quantum dot lattice using the extended Bose-Hubbard model for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from the Mott insulating phase to the superconducting phase for integer band fillings of Cooper pairs. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, besides the charge density wave and superconducting phases for half-integer band fillings. We also predict that extended range interactions are necessary to obtain the correct phase boundary of a one-dimensional interacting Cooper system. We have used the density matrix renormalization group method and Abelian bosonization to study our system.

Constitutive model for municipal solid waste incorporating mechanical creep and biodegradation-induced compression

A constitutive model is proposed to describe the stress-strain behavior of municipal solid waste (MSW) under loading using the critical state soil mechanics framework. The modified cam clay model is extended to incorporate the effects of mechanical creep and time dependent biodegradation to calculate total compression under loading. Model parameters are evaluated based on one-dimensional compression and triaxial consolidated undrained test series conducted on three types of MSW: (a) fresh MSW obtained from working phase of a landfill, (b) landfilled waste retrieved from a landfill after 1.5 years of degradation, and (c) synthetic MSW with controlled composition. The model captures the stress-strain and pore water pressure response of these three types of MSW adequately. The model is useful for assessing the deformation and stability of landfills and any post-closure development structures located on landfills.

Complex solitons in Bose-Einstein condensates with two- and three-body interactions

For the first time, we find the complex solitons for a quasi-one-dimensional Bose-Einstein condensate with two-and three-body interactions. These localized solutions are characterized by a power law behaviour. Both dark and right solitons can be excited in the experimentally allowed parameter domain, when two-and three-body interactions are,respectively, repulsive and attractive. The dark solitons travel with a constant speed, which is quite different from the Lieb mode, where profiles with different speeds, bounded above by sound velocity, can exist for specified interaction strengths. We also study the properties of these solitons in the presence of harmonic confinement with time-dependent nonlinearity and loss. The modulational instability and the Vakhitov-Kolokolov criterion of stability are also studied.

[B4O9H2] Cyclic Borate Units as the Building Unit in a Family of Zinc Borate Structures

A solvothermal reaction of ZnO, boric acid (B(OH)(3)), and aliphatic airlines in a water-pyridine mixture gave four zinc borate phases of different dimensionalities: [Zn(B4O8H2)(C3H10N2)], I (one-dimensional); [Zn(B4O8H2)(C3H10N2)] H2O, II (two-dimensional); [Zn(B5O10H3)(C10H24N4)]center dot H2O, III (two-dimensional): and [Zn-2(B8O15H2)(C3H10N2)(2)], IV (three-dimensional). The structures are formed by the connectivity involving polyborate chains and layers with Zn2+ species. In all the compounds, the amine molecules act its file ligand binding either the same or different zn centers. The formation of two different structures, II and IV, from the same amine by varying the reaction time is noteworthy. Transformation studies on II indicate that the formation of IV. from II, is facile and has been investigated for the first time. Two of file compounds, I and III, exhibit activity for second-order nonlinear optical behavior. The UV exposure of the sample indicates the absorption of all the UV radiation suggesting that the zinc borate compounds could be exploited for UV-blocking applications. The compounds have been characterized by powder X-ray diffraction, infrared spectroscopy, thermogravimetric analysis, UV-vis, photoluminescence, and NMR studies.

1,3-Difluorobenzene

The weak electrostatic and dispersive forces between C([delta]+)-F([delta]-) and H([delta]+)-C([delta]-) are at the borderline of the hydrogen-bond phenomenon and are poorly directional and further deformed in the presence of other dominant interactions, e.g. C-H...[pi]. The title compound, C6H4F2, Z' = 2, forms one-dimensional tapes along two homodromic C-H...F hydrogen bonds. The one-dimensional tapes are connected into corrugated two-dimensional sheets by further bi- or trifrucated C-H...F hydrogen bonds. Packing in the third dimension is controlled by C-H...[pi] interactions.

Magnetic behaviour in metal-organic frameworks-Some recent examples

The article describes the synthesis, structure and magnetic investigations of a series of metal-organic framework compounds formed with Mn+2 and Ni+2 ions. The structures, determined using the single crystal X-ray diffraction, indicated that the structures possess two- and three-dimensional structures with magnetically active dimers, tetramers, chains, two-dimensional layers connected by polycarboxylic acids. These compounds provide good examples for the investigations of magnetic behaviour. Magnetic studies have been carried out using SQUID magnetometer in the range of 2-300 K and the behaviour indicates a predominant anti-ferromagnetic interactions, which appears to differ based on the M-O-C-O-M and/or the M-O-M (M = metal ions) linkages. Thus, compounds with carboxylate (Mn-O-C-O-Mn) connected ones, [C3N2H [Mn(H2O)''C6H3(COO)(3)''], I, [''Mn(H2O (3)''aEuroeC(12)H(8)O(COO)(2)'']center dot H2O, II, [''Mn(H2O)''aEuroeC(12)H(8)O(COO)(2)''], III, show simple anti-ferromagnetic behaviour. The compounds with Mn-O/OH-Mn connected dimer and tetramer units in [NaMn''C6H3(COO)(3)''], IV, [Mn-2(A mu(3)-OH) (H2O)(2)''C6H3(COO)(3)'']center dot 2H(2)O, V, show canted-antiferromagnetic and anti-ferromagnetic behaviour, respectively. The presence of infinite one-dimensional -Ni-OH-Ni- chains in the compound, [Ni-2(H2O)(A mu(3)-OH)(2)(C8H5NO4], VI, gives rise to ferromagnet-like behaviour at low temperatures. The compounds, [Mn-3''C6H3(COO)(3)''(2)], VII and [''Mn(OH)''(2)''C12H8O(COO)(2)''], VIII, have two-dimensional infinite -Mn-O/OH-Mn- layers with triangular magnetic lattices, which resemble the Kagome and brucite-like layer. The magnetic studies indicated canted-antiferromagnetic behaviour in both the cases. Variable temperature EPR and theoretical magnetic modelling studies have been carried out on selected compounds to probe the nature of the magnetic species and their interactions with them.

A new open-framework zinc arsenate [C4N3H16](2)[Zn-5(AsO4)(4)(HAsO4)(2)]

A three-dimensional zinc arsenate with an interrupted zeolitic framework (-IIO), [C4N3H16](2)[Zn-5(AsO4)(4)(HAsO4)(2)], I has been synthesized solvothermally. The structure is built up from ZnO4, AsO4 and HAsO4 tetrahedral units connected alternatively through their vertices forming the 3-D structure possessing one-dimensional channels bound by 10 T-atoms (T = Zn, As), The framework density of the structure is 10.4 T-atoms which indicates considerable openness in its structure. (C) 2009 Elsevier B.V. All rights reserved.

Amino Acid Based MOFs: Synthesis, Structure, Single Crystal to Single Crystal Transformation, Magnetic and Related Studies in a Family of Cobalt and Nickel Aminoisophthales

Four new 5-aminoisophthalates of cobalt and nickel have been prepared employing hydro/solvothermal methods: [Co2(C8H5NO4)2(C4H4N2)(H2O)2]·3H2O (I), [Ni2(C8H5NO4)2(C4H4N2)(H2O)2]·3H2O (II), [Co2(H2O)(μ3-OH)2(C8H5NO4)] (III), and [Ni2(H2O)(μ3-OH)2(C8H5NO4)] (IV). Compounds I and II are isostructural, having anion-deficient CdCl2 related layers bridged by a pyrazine ligand, giving rise to a bilayer arrangement. Compounds III and IV have one-dimensional M−O(H)−M chains connected by the 5-aminoisophthalate units forming a three-dimensional structure. The coordinated as well as the lattice water molecules of I and II could be removed and inserted by simple heating−cooling cycles under the atmospheric conditions. The removal of the coordinated water molecule is accompanied by changes in the coordination environment around the M2+ (M = Co, Ni) and color of the samples (purple to blue, Co; green to dark yellow, Ni). This change has been examined by a variety of techniques that include in situ single crystal to single crystal transformation studies and in situ IR and UV−vis spectroscopic studies. Magnetic studies indicate antiferromagnetic behavior in I and II, a field-induced magnetism in III, and a canted antiferromagnetic behavior in IV.

A Model of Anomalous Chain Translocation Dynamics

A model of polymer translocation based on the stochastic dynamics of the number of monomers on one side of a pore-containing surface is formulated in terms of a one-dimensional generalized Langevin equation, in which the random force is assumed to be characterized by long-ranged temporal correlations. The model is introduced to rationalize anomalies in measured and simulated values of the average time of passage through the pore, which in general cannot be satisfactorily accounted for by simple Brownian diffusion mechanisms. Calculations are presented of the mean first passage time for barrier crossing and of the mean square displacement of a monomeric segment, in the limits of strong and weak diffusive bias. The calculations produce estimates of the exponents in various scaling relations that are in satisfactory agreement with available data.

An asymptotic analysis for the coupled dispersion characteristics of a structural acoustic waveguide

Analytical expressions are derived, using asymptotics, for the fluid-structure coupled wavenumbers in a one-dimensional (1-D) structural acoustic waveguide. The coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation with an added term due to the fluid-structure coupling. As a result of this coupling, the prior uncoupled structural and acoustic wavenumbers, now become coupled structural and acoustic wavenumbers. A fluid-loading parameter e, defined as the ratio of mass of fluid to mass of the structure per unit area, is introduced which when set to zero yields the uncoupled dispersion equation. The coupled wavenumber is then expressed in terms of an asymptotic series in e. Analytical expressions are found as e is varied from small to large values. Different asymptotic expansions are used for different frequency ranges with continuous transitions occurring between them. This systematic derivation helps to continuously track the wavenumber solutions as the fluid-loading parameter is varied from small to large values. Though the asymptotic expansion used is limited to the first-order correction factor, the results are close to the numerical results. A general trend is that a given wavenumber branch transits from a rigid-walled solution to a pressure-release solution with increasing E. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an-intersection in the coupled case, but a gap is created at that frequency. (c) 2007 Elsevier Ltd. All rights reserved.

Coordination polymers and hybrid networks of different dimensionalities formed by metal sulfites

In our effort to explore the use of the sulfite ion to design hybrid and open-framework materials, we have been able to prepare, under hydrothermal conditions, zero-dimensional [Zn(C12H8N2)(SO3)]center dot 2H(2)O, I (a = 7.5737(5) angstrom, b = 10.3969(6) angstrom, c = 10.3986(6) angstrom, alpha = 64.172(1)degrees, beta = 69.395(1)degrees, gamma = 79.333(1)degrees, Z = 2, and space group P (1) over bar), one-dimensional [Zn-2(C12H8N2)(SO3)(2)(H2O)], II (a = 8.0247(3) angstrom, b = 9.4962(3) angstrom, c = 10.2740(2) A, alpha = 81.070(1)degrees, beta = 80.438(1)degrees, gamma = 75.66(5)degrees, Z = 2, and space group P (1) over bar), two-dimensional [Zn-2(C10H8N2)(SO3)(2)]center dot H2O, III (a = 16.6062(1) angstrom, b = 4.7935(1) angstrom, c = 19.2721(5) angstrom, beta = 100.674(2)degrees, Z = 4, and space group C2/c), and three-dimensional [Zn-4(C6H12N2)(SO3)(4)(H2O)(4)], IV (a = 11.0793(3) angstrom, c = 8.8246(3) angstrom, Z = 2, and space group P42nm), of which the last three are coordination polymers. A hybrid open-framework sulfite-sulfate of the composition [C2H10N2][Nd(SO3)(SO4)(H2O)](2), V (a = 9.0880(3) angstrom, b = 6.9429(2) angstrom, c = 13.0805(5) A, beta = 91.551(2)degrees, Z = 2, and space group P2(1)/c), with a layered structure containing metal-oxygen-metal bonds has also been described.