A note on the forced Burgers equation

We obtain the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution for the velocity fields at multiple spatial points is obtained. A connection with stretched vortices in hydrodynamic flows is discussed.Comment: 10 page

Re-entrant Nematic Phase Established for Several Homologous Biaromatic Liquid Crystals by Investigation of Binary Mixed Systems

Several homologous series of biaromatic liquid crystals with structure type CnH2n+1O • C6H4 • M•C6H4-CN are investigated. By studying the phase transition temperatures in binary mixed systems a "re-entrant" nematic phase N(re) is established for all compounds exhibiting smectic A phases. The virtual transition temperatures N(re) - SA are found to decrease with increasing chain length of the alkyloxy group. The influence of the middle group M on the re-entrant behaviour can be attributed mainly to its dipole moment. The temperature range of the smectic A phase decreases when the middle group dipole moment is additive to that of the nitrile group. To summarize it can be said that the "re-entrant" behaviour of biaromatic liquid crystals is found to be very similar to that of triaromatic systems reported recently

Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Benard convection

An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Benard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the "background field" variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Benard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents alpha and beta in the presumed Nu similar to (PrRa beta)-Ra-alpha scaling relation. The computations clearly show that for Ra <= 10(10) at fixed L = 2 root 2, Nu <= 0.106Pr(0)Ra(5/12), which indicates that molecular transport cannot generally be neglected in the "ultimate" high-Ra regime.NSF DMS-0928098 DMS-1515161 DMS-0927587 PHY-1205219Simons FoundationNSFONRInstitute for Computational Engineering and Sciences (ICES

Retreatment with interferon-alpha and ribavirin in primary interferon-alpha non-responders with chronic hepatitis C

Background/Aims: Combination therapy with interferon-alpha (IFN-alpha) plus ribavirin is more efficacious than IFN-alpha monotherapy in previously untreated patients with chronic hepatitis C and patients with IFN-alpha relapse. Only limited data are available in IFN-alpha non-responders. In a multicenter trial we therefore evaluated the efficacy of combination therapy in IFN-alpha-resistant chronic hepatitis C. Methods: Eighty-two patients (mean age 46.8 years, 54 males, 28 females) with chronic hepatitis C were treated with IFN-alpha-2a (3 x 6 MIU/week) and ribavirin (14 mg/kg daily) for 12 weeks. Thereafter, treatment was continued only in virological responders (undetectable serum HCV RNA at week 12) with an IFN-alpha dose of 3 x 3 MIU/week and without ribavirin for a further 9 months. The primary study endpoint was an undetectable HCV RNA by RT-PCR at the end of the 24-week follow-up period. Results: After 12 weeks of combination therapy, an initial virological response was observed in 29 of 82 (35.4%) patients. Due to a high breakthrough rate after IFN-a dose reduction and ribavirin discontinuation, an end-of-treatment response was only achieved in 12 of 82 (14.6%) patients. After the follow-up period, a sustained virological response was observed in 8 of 82 (9.8%) patients. Infection with HCV genotype 3 was the only pretreatment parameter, which could predict a sustained response (HCV-1, 5%; HCV-3, 57.1%; p < 0.001). Conclusions: Despite a high initial response rate of 35.4%, sustained viral clearance was achieved only in 9.8% of the retreated primary IFN-alpha non-responders. Higher IFN-alpha induction and maintenance dose, as well as prolonged ribavirin treatment may possibly increase the virological response rates in non-responders, particularly in those infected by HCV-1

Hematological variations in healthy participants exposed 2 h to propylene glycol ethers under controlled conditions.

Glycol ethers are solvents used in a plethora of occupational and household products exposing the users to potential toxic effects. Several glycol ethers derived from ethylene glycol induce hematological toxicity, such as anemia in workers. The exposure effects on blood cells of glycol ethers derived from propylene glycol are unknown in humans. The aim of our study was to evaluate blood parameters indicative of red blood cell (RBC) hemolysis and oxidative stress in participants exposed to propylene glycol (propylene glycol monobutyl ether (PGBE) and propylene glycol monomethyl ether (PGME)), two extensively used propylene glycol derivatives worldwide. Seventeen participants were exposed 2 h in a control inhalation exposure chamber to low PGME (35 ppm) and PGBE (15 ppm) air concentrations. Blood was regularly collected before, during (15, 30, 60, and 120 min), and 60 min after exposure for RBC and oxidative stress analyses. Urine was also collected for clinical effects related to hemolysis. Under the study conditions, our results showed that the blood parameters such as RBCs, hemoglobin concentration, and white blood cells tended to increase in response to PGME and PGBE exposures. These results raise questions about the possible effects in people regularly exposed to higher concentrations, such as workers

A Quantum Approach to Classical Statistical Mechanics

We present a new approach to study the thermodynamic properties of $d$-dimensional classical systems by reducing the problem to the computation of ground state properties of a $d$-dimensional quantum model. This classical-to-quantum mapping allows us to deal with standard optimization methods, such as simulated and quantum annealing, on an equal basis. Consequently, we extend the quantum annealing method to simulate classical systems at finite temperatures. Using the adiabatic theorem of quantum mechanics, we derive the rates to assure convergence to the optimal thermodynamic state. For simulated and quantum annealing, we obtain the asymptotic rates of $T(t) \approx (p N) /(k_B \log t)$ and $\gamma(t) \approx (Nt)^{-\bar{c}/N}$, for the temperature and magnetic field, respectively. Other annealing strategies, as well as their potential speed-up, are also discussed.Comment: 4 pages, no figure

Exact Equal Time Statistics of Orszag-McLaughlin Dynamics By The Hopf Characteristic Functional Approach

By employing Hopf's functional method, we find the exact characteristic functional for a simple nonlinear dynamical system introduced by Orszag. Steady-state equal-time statistics thus obtained are compared to direct numerical simulation. The solution is both non-trivial and strongly non-Gaussian.Comment: 6 pages and 2 figure

Amino acid coevolution reveals three-dimensional structure and functional domains of insect odorant receptors.

Insect odorant receptors (ORs) comprise an enormous protein family that translates environmental chemical signals into neuronal electrical activity. These heptahelical receptors are proposed to function as ligand-gated ion channels and/or to act metabotropically as G protein-coupled receptors (GPCRs). Resolving their signalling mechanism has been hampered by the lack of tertiary structural information and primary sequence similarity to other proteins. We use amino acid evolutionary covariation across these ORs to define restraints on structural proximity of residue pairs, which permit de novo generation of three-dimensional models. The validity of our analysis is supported by the location of functionally important residues in highly constrained regions of the protein. Importantly, insect OR models exhibit a distinct transmembrane domain packing arrangement to that of canonical GPCRs, establishing the structural unrelatedness of these receptor families. The evolutionary couplings and models predict odour binding and ion conduction domains, and provide a template for rationale structure-activity dissection

Quasi-Gaussian Statistics of Hydrodynamic Turbulence in 3/4+\epsilon dimensions

The statistics of 2-dimensional turbulence exhibit a riddle: the scaling exponents in the regime of inverse energy cascade agree with the K41 theory of turbulence far from equilibrium, but the probability distribution functions are close to Gaussian like in equilibrium. The skewness \C S \equiv S_3(R)/S^{3/2}_2(R) was measured as \C S_{\text{exp}}\approx 0.03. This contradiction is lifted by understanding that 2-dimensional turbulence is not far from a situation with equi-partition of enstrophy, which exist as true thermodynamic equilibrium with K41 exponents in space dimension of $d=4/3$. We evaluate theoretically the skewness \C S(d) in dimensions ${4/3}\le d\le 2$, show that \C S(d)=0 at $d=4/3$, and that it remains as small as \C S_{\text{exp}} in 2-dimensions.Comment: PRL, submitted, REVTeX 4, 4 page