Tensegrity and Motor-Driven Effective Interactions in a Model Cytoskeleton

Actomyosin networks are major structural components of the cell. They provide mechanical integrity and allow dynamic remodeling of eukaryotic cells, self-organizing into the diverse patterns essential for development. We provide a theoretical framework to investigate the intricate interplay between local force generation, network connectivity and collective action of molecular motors. This framework is capable of accommodating both regular and heterogeneous pattern formation, arrested coarsening and macroscopic contraction in a unified manner. We model the actomyosin system as a motorized cat's cradle consisting of a crosslinked network of nonlinear elastic filaments subjected to spatially anti-correlated motor kicks acting on motorized (fibril) crosslinks. The phase diagram suggests there can be arrested phase separation which provides a natural explanation for the aggregation and coalescence of actomyosin condensates. Simulation studies confirm the theoretical picture that a nonequilibrium many-body system driven by correlated motor kicks can behave as if it were at an effective equilibrium, but with modified interactions that account for the correlation of the motor driven motions of the actively bonded nodes. Regular aster patterns are observed both in Brownian dynamics simulations at effective equilibrium and in the complete stochastic simulations. The results show that large-scale contraction requires correlated kicking.Comment: 38 pages, 13 figure

A Strong Maximum Principle for Weak Solutions of Quasi-Linear Elliptic Equations with Applications to Lorentzian and Riemannian Geometry

The strong maximum principle is proved to hold for weak (in the sense of support functions) sub- and super-solutions to a class of quasi-linear elliptic equations that includes the mean curvature equation for $C^0$ spacelike hypersurfaces in a Lorentzian manifold. As one application a Lorentzian warped product splitting theorem is given.Comment: 37 pages, 1 figure, ams-latex using eepi

Exchange rate overvaluation and trade protection - lessons from experience

Despite a trend toward more flexible rates, more than half the world's countries maintain fixed or managed exchange rates. In the 1980s and 1990s, developing countries as a group progressively liberalized their trade regimes, but some governments defend their exchange rate in actions that run counter to long-run plans for liberalization. Without discussing the relative merits of fixed and flexible exchange rate systems, the authors note that exchange rate management in many countries has resulted in overvaluation of the real exchange rate. Roughly twenty five percent of the countries for which data are available have overvalued exchange rates, with black market premiums from 10 percent to more than 100 percent. After surveying the literature, the authors present lessons from experience about what has worked (or not) in response to crises involving external shocks and external trade deficits - and why. Trying to defend an overvalued exchange rate with protectionist trade policies is a classic pattern, but experience shows such protection does significantly retard the country's growth, and delay its integration into the world trading community. In fact, and overvalued exchange rate is often the root cause of protection, preventing the country from returning to more liberal trade policies that allow growth and integration into the world community without exchange rate adjustment. Most developing countries have downward price and wage rigidities and, with an external trade deficit, require some form of nominal exchange rate adjustment to restore external equilibrium. The authors present cross-country econometric and case study evidence - citing examples from Argentina, Chile, Ghana, The Republic of Korea, Malaysia, Turkey, Uruguay, and Sub-Saharan Africa (including the CFA zone) - that overvalued exchange rates reduce economic growth. Defending the exchange rate, they show, has nor no medium-term benefits, since falling reserves will eventually force devaluation. Better to have devaluation occur without further debilitating losses in reserves and lost productivity because of import controls. After devaluation the exchange rate will reach a new equilibrium, strongly influenced by government and central bank policies.ICT Policy and Strategies,Environmental Economics&Policies,Fiscal&Monetary Policy,Payment Systems&Infrastructure,Economic Theory&Research,Macroeconomic Management,Environmental Economics&Policies,Achieving Shared Growth,Economic Stabilization,Economic Theory&Research

Applications of Subleading-color Amplitudes in N=4 SYM Theory

A number of features and applications of subleading color amplitudes of N=4 SYM theory are reviewed. Particular attention is given to the IR divergences of the subleading-color amplitudes, the relationships of N=4 SYM theory to N=8 supergravity, and to geometric interpretations of one-loop subleading color and N^k MHV amplitudes of N=4 SYM theory.Comment: 39 pages; v2: minor correction

Direct measurements and analysis of skin friction and cooling downstream of multiple flush-slot injection into a turbulent Mach 6 boundary layer

Experiments were conducted to determine the reduction in surface skin friction and the effectiveness of surface cooling downstream of one to four successive flush slots injecting cold air at an angle of 10 deg into a turbulent Mach 6 boundary layer. Data were obtained by direct measurement of surface shear and equilibrium temperatures, respectively. Increasing the number of slots decreased the skin friction, but the incremental improvement in skin-friction reduction decreased as the number of slots was increased. Cooling effectiveness was found to improve, for a given total mass injection, as the number of slots was increased from one to four. Comparison with previously reported step-slot data, however, indicated that step slots with tangential injection are more effective for both reducing skin friction and cooling than the present flush-slot configuration. Finite-difference predictions are in reasonable agreement with skin-friction data and with boundary-layer profile data

Subleading-color contributions to gluon-gluon scattering in N=4 SYM theory and relations to N=8 supergravity

We study the subleading-color (nonplanar) contributions to the four-gluon scattering amplitudes in N=4 supersymmetric SU(N) Yang-Mills theory. Using the formalisms of Catani and of Sterman and Tejeda-Yeomans, we develop explicit expressions for the infrared-divergent contributions of all the subleading-color L-loop amplitudes up to three loops, and make some conjectures for the IR behavior for arbitrary L. We also derive several intriguing relations between the subleading-color one- and two-loop four-gluon amplitudes and the four-graviton amplitudes of N=8 supergravity. The exact one- and two-loop N=8 supergravity amplitudes can be expressed in terms of the one- and two-loop N-independent N=4 SYM amplitudes respectively, but the natural generalization to higher loops fails, despite having a simple interpretation in terms of the 't Hooft picture. We also find that, at least through two loops, the subleading-color amplitudes of N=4 SYM theory have uniform transcendentality (as do the leading-color amplitudes). Moreover, the N=4 SYM Catani operators, which express the IR-divergent contributions of loop amplitudes in terms of lower-loop amplitudes, are also shown to have uniform transcendentality, and to be the maximum transcendentality piece of the QCD Catani operators.Comment: 30 pages; v2: corrections in sec. 6, minor addition in sec. 3.

All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes

The infrared singularities of gravitational amplitudes are one-loop exact, in that higher-loop divergences are characterized by the exponential of the one-loop divergence. We show that the contributions to SU(N) gauge-theory amplitudes that are most-subleading in the 1/N expansion are also one-loop exact, provided that the dipole conjecture holds. Possible corrections to the dipole conjecture, beginning at three loops, could violate one-loop-exactness, though would still maintain the absence of collinear divergences. We also demonstrate a relation between L-loop four-point N=8 supergravity and most-subleading-color N=4 SYM amplitudes that holds for the two leading IR divergences, O(1/\epsilon^L) and O(1/\epsilon^{L-1}), but breaks down at O(1/\epsilon^{L-2}).Comment: 23 pages, no figure