Tension dynamics and viscoelasticity of extensible wormlike chains

The dynamic response of prestressed semiflexible biopolymers is characterized by the propagation and relaxation of tension, which arises due to the near inextensibility of a stiff backbone. It is coupled to the dynamics of contour length stored in thermal undulations, but also to the local relaxation of elongational strain. We present a systematic theory of tension dynamics for stiff yet extensible wormlike chains. Our results show that even moderate prestress gives rise to distinct Rouse-like extensibility signatures in the high-frequency viscoelastic response.Comment: 4 pages, 1 figure; corrected typo

The Martian crustal dichotomy: Product of accretion and not a specific event?

Attempts to explain the fundamental crustal dichotomy on Mars range from purely endogenic to extreme exogenic processes, but to date no satisfactory theory has evolved. What is accepted is: (1) the dichotomy is an ancient feature of the Martian crust, and (2) the boundary between the cratered highlands and northern plains which marks the dichotomy in parts of Mars has undergone significant and variable modification during the observable parts of Martian history. Some ascribe it to a single mega-impact event, essentially an instantaneous rearrangement of the crustal structures (topography and lithospheric thickness). Others prefer an internal mechanism: a period of vigorous convection subcrustally erodes the northern one third of Mars, causing foundering and isostatic lowering of that part of Mars. The evidence for each theory is reviewed, with the conclusion that there is little to recommend either. An alternative is suggested: the formation of the crustal dichotomy on Mars was not a specific tectonic event but a byproduct of the accretionary process and therefore a primordial characteristic of the Martian crust, predating the oldest recognizable landforms

Probing the qudit depolarizing channel

For the quantum depolarizing channel with any finite dimension, we compare three schemes for channel identification: unentangled probes, probes maximally entangled with an external ancilla, and maximally entangled probe pairs. This comparison includes cases where the ancilla is itself depolarizing and where the probe is circulated back through the channel before measurement. Compared on the basis of (quantum Fisher) information gained per channel use, we find broadly that entanglement with an ancilla dominates the other two schemes, but only if entanglement is cheap relative to the cost per channel use and only if the external ancilla is well shielded from depolarization. We arrive at these results by a relatively simple analytical means. A separate, more complicated analysis for partially entangled probes shows for the qudit depolarizing channel that any amount of probe entanglement is advantageous and that the greatest advantage comes with maximal entanglement

Optimal execution strategies in limit order books with general shape functions

We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modeling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e., of the volume of the LOB, or the exponential recovery of the bid-ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type

Studying top quark decay into the polarized W-boson in the TC2 model

We study the decay mode of top quark decaying into Wb in the TC2 model where the top quark is distinguished from other fermions by participating in a strong interaction. We find that the TC2 correction to the decay width $\Gamma (t \to b W)$ is generally several percent and maximum value can reach 8% for the currently allowed parameters. The magnitude of such correction is comparable with QCD correction and larger than that of minimal supersymmetric model. Such correction might be observable in the future colliders. We also study the TC2 correction to the branching ratio of top quark decay into the polarized W bosons and find the correction is below $1$. After considering the TC2 correction, we find that our theoretical predictions about the decay branching ratio are also consistent with the experimental data.Comment: 8 pages, 4 figure

Mechanics of bundled semiflexible polymer networks

While actin bundles are used by living cells for structural fortification, the microscopic origin of the elasticity of bundled networks is not understood. Here, we show that above a critical concentration of the actin binding protein fascin, a solution of actin filaments organizes into a pure network of bundles. While the elasticity of weakly crosslinked networks is dominated by the affine deformation of tubes, the network of bundles can be fully understood in terms of non-affine bending undulations.Comment: 5 pages, 3 figures, final version as publishe

Elasticity of Stiff Polymer Networks

We study the elasticity of a two-dimensional random network of rigid rods (``Mikado model''). The essential features incorporated into the model are the anisotropic elasticity of the rods and the random geometry of the network. We show that there are three distinct scaling regimes, characterized by two distinct length scales on the elastic backbone. In addition to a critical rigidiy percolation region and a homogeneously elastic regime we find a novel intermediate scaling regime, where elasticity is dominated by bending deformations.Comment: 4 pages, 4 figure

Validity of the Law of Mass Action in Three-Dimensional Coagulation Processes

Diffusion-limited reactions are studied in detail on the classical coalescing process. We demonstrate how, with the aid of a recent renormalization group approach, fluctuations can be integrated systematically. We thereby obtain an exact relation between the microscopic physics (lattice structure and particle shape and size) and the macroscopic decay rate in the law of mass action. Moreover, we find a strong violation of the law of mass action. The corresponding term in the kinetic equations originates in longwavelength fluctuations and is a universal function of the macroscopic decay rate