Analytical approach to viscous fingering in a cylindrical Hele-Shaw cell

We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it recovers the usual Darcy's law for flow in flat, rectangular cells, with corrections of higher order in b/a. We focus our interest on the influence of cell's radius of curvature on the instability characteristics. Linear and slightly nonlinear flow regimes are studied through a mode-coupling analysis. Our analytical results reveal that linear growth rates and finger competition are inhibited for increasingly larger radius of curvature. The absence of tip-splitting events in cylindrical cells is also discussed.Comment: 14 pages, 3 ps figures, Revte

Perturbation Theory in Two Dimensional Open String Field Theory

In this paper we develop the covariant string field theory approach to open 2d strings. Upon constructing the vertices, we apply the formalism to calculate the lowest order contributions to the 4- and 5- point tachyon--tachyon tree amplitudes. Our results are shown to match the `bulk' amplitude calculations of Bershadsky and Kutasov. In the present approach the pole structure of the amplitudes becomes manifest and their origin as coming from the higher string modes transparent.Comment: 26 page

SU(m) non-Abelian anyons in the Jain hierarchy of quantum Hall states

We show that different classes of topological order can be distinguished by the dynamical symmetry algebra of edge excitations. Fundamental topological order is realized when this algebra is the largest possible, the algebra of quantum area-preserving diffeomorphisms, called $W_{1+\infty}$. We argue that this order is realized in the Jain hierarchy of fractional quantum Hall states and show that it is more robust than the standard Abelian Chern-Simons order since it has a lower entanglement entropy due to the non-Abelian character of the quasi-particle anyon excitations. These behave as SU($m$) quarks, where $m$ is the number of components in the hierarchy. We propose the topological entanglement entropy as the experimental measure to detect the existence of these quantum Hall quarks. Non-Abelian anyons in the $\nu = 2/5$ fractional quantum Hall states could be the primary candidates to realize qbits for topological quantum computation.Comment: 5 pages, no figures, a few typos corrected, a reference adde

Entropy flow in near-critical quantum circuits

Near-critical quantum circuits are ideal physical systems for asymptotically large-scale quantum computers, because their low energy collective excitations evolve reversibly, effectively isolated from the environment. The design of reversible computers is constrained by the laws governing entropy flow within the computer. In near-critical quantum circuits, entropy flows as a locally conserved quantum current, obeying circuit laws analogous to the electric circuit laws. The quantum entropy current is just the energy current divided by the temperature. A quantum circuit made from a near-critical system (of conventional type) is described by a relativistic 1+1 dimensional relativistic quantum field theory on the circuit. The universal properties of the energy-momentum tensor constrain the entropy flow characteristics of the circuit components: the entropic conductivity of the quantum wires and the entropic admittance of the quantum circuit junctions. For example, near-critical quantum wires are always resistanceless inductors for entropy. A universal formula is derived for the entropic conductivity: \sigma_S(\omega)=iv^{2}S/\omega T, where \omega is the frequency, T the temperature, S the equilibrium entropy density and v the velocity of `light'. The thermal conductivity is Real(T\sigma_S(\omega))=\pi v^{2}S\delta(\omega). The thermal Drude weight is, universally, v^{2}S. This gives a way to measure the entropy density directly.Comment: 2005 paper published 2017 in Kadanoff memorial issue of J Stat Phys with revisions for clarity following referee's suggestions, arguments and results unchanged, cross-posting now to quant-ph, 27 page

Microscopic Selection of Fluid Fingering Pattern

We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accord with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.Comment: 6 pages, 5 figure

Cyclic dinucleotides bind the C-linker of HCN4 to control channel cAMP responsiveness

cAMP mediates autonomic regulation of heart rate by means of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which underlie the pacemaker current If. cAMP binding to the C-terminal cyclic nucleotide binding domain enhances HCN open probability through a conformational change that reaches the pore via the C-linker. Using structural and functional analysis, we identified a binding pocket in the C-linker of HCN4. Cyclic dinucleotides, an emerging class of second messengers in mammals, bind the C-linker pocket (CLP) and antagonize cAMP regulation of the channel. Accordingly, cyclic dinucleotides prevent cAMP regulation of If in sinoatrial node myocytes, reducing heart rate by 30%. Occupancy of the CLP hence constitutes an efficient mechanism to hinder β-adrenergic stimulation on If. Our results highlight the regulative role of the C-linker and identify a potential drug target in HCN4. Furthermore, these data extend the signaling scope of cyclic dinucleotides in mammals beyond their first reported role in innate immune system

Boundary states for a free boson defined on finite geometries

Langlands recently constructed a map that factorizes the partition function of a free boson on a cylinder with boundary condition given by two arbitrary functions in the form of a scalar product of boundary states. We rewrite these boundary states in a compact form, getting rid of technical assumptions necessary in his construction. This simpler form allows us to show explicitly that the map between boundary conditions and states commutes with conformal transformations preserving the boundary and the reality condition on the scalar field.Comment: 16 pages, LaTeX (uses AMS components). Revised version; an analogy with string theory computations is discussed and references adde

Algebraic Structures and Eigenstates for Integrable Collective Field Theories

Conditions for the construction of polynomial eigen--operators for the Hamiltonian of collective string field theories are explored. Such eigen--operators arise for only one monomial potential $v(x) = \mu x^2$ in the collective field theory. They form a $w_{\infty}$--algebra isomorphic to the algebra of vertex operators in 2d gravity. Polynomial potentials of orders only strictly larger or smaller than 2 have no non--zero--energy polynomial eigen--operators. This analysis leads us to consider a particular potential $v(x)= \mu x^2 + g/x^2$. A Lie algebra of polynomial eigen--operators is then constructed for this potential. It is a symmetric 2--index Lie algebra, also represented as a sub--algebra of $U (s\ell (2)).$Comment: 27 page

Efficient Numerical Schemes for Computing Cardiac Electrical Activation over Realistic Purkinje Networks: Method and Verification

We present a numerical solver for the fast conduction system in the heart using both a CPU and a hybrid CPU/GPU implementation. To verify both implementations, we construct analytical solutions and show that the L2-error is similar in both implementations and decreases linearly with the spatial step size. Finally, we test the performance of the implementations with networks of varying complexity, where the hybrid implementation is, on average, 5.8 times faster

Amprenavir and efavirenz pharmacokinetics before and after the addition of nelfinavir, indinavir, ritonavir, or saquinavir in seronegative individuals

Adult AIDS Clinical Trials Group 5043 examined pharmacokinetic (PK) interactions between amprenavir (APV) and efavirenz (EFV) both by themselves and when nelfinavir (NFV), indinavir (IDV), ritonavir (RTV), or saquinavir (SQV) is added. A PK study was conducted after the administration of single doses of APV (day 0). Subjects (n = 56) received 600 mg of EFV every 24 h (q24h) for 10 days and restarted APV with EFV for days 11 to 13 with a PK study on day 14. A second protease inhibitor (PI) (NFV, 1,250 mg, q12h; IDV, 1,200 mg, q12h; RTV, 100 mg, q12h; or SQV, 1,600 mg, q12h) was added to APV and EFV on day 15, and a PK study was conducted on day 21. Controls continued APV and EFV without a second PI. Among subjects, the APV areas under the curve (AUCs) on days 0, 14, and 21 were compared using the Wilcoxon signed-rank test. Ninety-percent confidence intervals around the geometric mean ratios (GMR) were calculated. APV AUCs were 46% to 61% lower (median percentage of AUC) with EFV (day 14 versus day 0; P values of <0.05). In the NFV, IDV, and RTV groups, day 21 APV AUCs with EFV were higher than AUCs for EFV alone. Ninety-percent confidence intervals around the GMR were 3.5 to 5.3 for NFV (P < 0.001), 2.8 to 4.5 for IDV (P < 0.001), and 7.8 to 11.5 for RTV (P = 0.004). Saquinavir modestly increased the APV AUCs (GMR, 1.0 to 1.4; P = 0.106). Control group AUCs were lower on day 21 compared to those on day 14 (GMR, 0.7 to 1.0; P = 0.042). African-American non-Hispanics had higher day 14 efavirenz AUCs than white non-Hispanics. We conclude that EFV lowered APV AUCs, but nelfinavir, indinavir, or ritonavir compensated for EFV induction