The Mechanism of Our Jury System Should be Adjusted and Lubricated

When the colonists came to America, they brought with them the right of trial by jury. To preserve and protect this right for them and their descendants, it was incorporated in the Bill of Rights of the Virginias, and it is now firmly entrenched in the judiciary system of West Virginia. The citizens of our state have ever zealously guarded this as a sacred right, and looked to it as a bulwark of protection when their rights have been invaded, or their liberties jeopardized. Notwithstanding all the recognized defects and imperfections of the jury system, experience has demonstrated that trial by a jury of twelve good men and true is the best machinery yet devised for arriving at a true result. Through the ages, our jury system has repelled vicious assaults of its enemies. It would be folly for one to now advocate that trial by jury be supplanted by any other method of determining an issue of fact. In this treatise, neither the abolishment of trial by jury, nor any radical and revolutionary changes in that system will be advocated; but an endeavor will be made to examine the mechanics of the jury system of West Virginia to determine whether it can be developed into a smoother running machine by adjustments and lubrication. By so doing, we may find that the machinery of the jury system is properly designed and fabricated to do the work prescribed for it, but, because of the lack of necessary adjustments and lubrication, and inefficient and careless engineers, it has developed some piston knocks that have unjustly relegated it to the graveyard of used and useless machinery, in which the public is losing confidence

Mechanics and force transmission in soft composites of rods in elastic gels

We report detailed theoretical investigations of the micro-mechanics and bulk elastic properties of composites consisting of randomly distributed stiff fibers embedded in an elastic matrix in two and three dimensions. Recent experiments published in Physical Review Letters [102, 188303 (2009)] have suggested that the inclusion of stiff microtubules in a softer, nearly incompressible biopolymer matrix can lead to emergent compressibility. This can be understood in terms of the enhancement of the compressibility of the composite relative to its shear compliance as a result of the addition of stiff rod-like inclusions. We show that the Poisson's ratio $\nu$ of such a composite evolves with increasing rod density towards a particular value, or {\em fixed point}, independent of the material properties of the matrix, so long as it has a finite initial compressibility. This fixed point is $\nu=1/4$ in three dimensions and $\nu=1/3$ in two dimensions. Our results suggest an important role for stiff filaments such as microtubules and stress fibers in cell mechanics. At the same time, our work has a wider elasticity context, with potential applications to composite elastic media with a wide separation of scales in stiffness of its constituents such as carbon nanotube-polymer composites, which have been shown to have highly tunable mechanics.Comment: 10 pages, 8 figure

Persistence in the zero-temperature dynamics of the QQ-states Potts model on undirected-directed Barab\'asi-Albert networks and Erd\"os-R\'enyi random graphs

The zero-temperature Glauber dynamics is used to investigate the persistence probability $P(t)$ in the Potts model with $Q=3,4,5,7,9,12,24,64, 128$, $256, 512, 1024,4096,16384$,..., $2^{30}$ states on {\it directed} and {\it undirected} Barab\'asi-Albert networks and Erd\"os-R\'enyi random graphs. In this model it is found that $P(t)$ decays exponentially to zero in short times for {\it directed} and {\it undirected} Erd\"os-R\'enyi random graphs. For {\it directed} and {\it undirected} Barab\'asi-Albert networks, in contrast it decays exponentially to a constant value for long times, i.e, $P(\infty)$ is different from zero for all $Q$ values (here studied) from $Q=3,4,5,..., 2^{30}$; this shows "blocking" for all these $Q$ values. Except that for $Q=2^{30}$ in the {\it undirected} case $P(t)$ tends exponentially to zero; this could be just a finite-size effect since in the other "blocking" cases you may have only a few unchanged spins.Comment: 14 pages, 8 figures for IJM

Actively Contracting Bundles of Polar Filaments

We introduce a phenomenological model to study the properties of bundles of polar filaments which interact via active elements. The stability of the homogeneous state, the attractors of the dynamics in the unstable regime and the tensile stress generated in the bundle are discussed. We find that the interaction of parallel filaments can induce unstable behavior and is responsible for active contraction and tension in the bundle. Interaction between antiparallel filaments leads to filament sorting. Our model could apply to simple contractile structures in cells such as stress fibers.Comment: 4 pages, 4 figures, RevTex, to appear in Phys. Rev. Let

Steady-state MreB helices inside bacteria: dynamics without motors

Within individual bacteria, we combine force-dependent polymerization dynamics of individual MreB protofilaments with an elastic model of protofilament bundles buckled into helical configurations. We use variational techniques and stochastic simulations to relate the pitch of the MreB helix, the total abundance of MreB, and the number of protofilaments. By comparing our simulations with mean-field calculations, we find that stochastic fluctuations are significant. We examine the quasi-static evolution of the helical pitch with cell growth, as well as timescales of helix turnover and denovo establishment. We find that while the body of a polarized MreB helix treadmills towards its slow-growing end, the fast-growing tips of laterally associated protofilaments move towards the opposite fast-growing end of the MreB helix. This offers a possible mechanism for targeted polar localization without cytoplasmic motor proteins.Comment: 7 figures, 1 tabl

Mass-degenerate Higgs bosons at 125 GeV in the Two-Higgs-Doublet Model

The analysis of the Higgs boson data by the ATLAS and CMS Collaborations appears to exhibit an excess of h --> gamma\gamma events above the Standard Model (SM) expectations; whereas no significant excess is observed in h --> ZZ* --> {four lepton} events, albeit with large statistical uncertainty due to the small data sample. These results (assuming they persist with further data) could be explained by a pair of nearly mass-degenerate scalars, one of which is a SM-like Higgs boson and the other is a scalar with suppressed couplings to W+W- and ZZ. In the two Higgs doublet model, the observed \gamma\gamma and ZZ* --> {four lepton} data can be reproduced by an approximately degenerate CP-even (h) and CP-odd (A) Higgs boson for values of \sin(\beta-\alpha) near unity and 0.7 < \tan\beta < 1. An enhanced \gamma\gamma signal can also arise in cases where m_h ~ m_H, m_H ~ m_A, or m_h ~ m_H ~ m_A. Since the ZZ* --> {four lepton} signal derives primarily from a SM-like Higgs boson whereas the \gamma\gamma signal receives contributions from two (or more) nearly mass-degenerate states, one would expect a slightly different invariant mass peak in the ZZ* --> {four lepton} and \gamma\gamma channels. The phenomenological consequences of such models can be tested with additional Higgs data that will be collected at the LHC in the near future.Comment: 18 pages, 19 pdf figures, v2: references added, v3&v4: added refs and explanation

Millimeter-wave diode-grid phase shifters

Monolithic diode grids have been fabricated on 2-cm square gallium-arsenide wafers with 1600 Schottky-barrier varactor diodes. Shorted diodes are detected with a liquid-crystal technique, and the bad diodes are removed with an ultrasonic probe. A small-aperture reflectometer that uses wavefront division interference was developed to measure the reflection coefficient of the grids. A Phase shift of 70° with a 7-dB loss was obtained at 93 GHz when the bias on the diode grid was changed from -3 V to 1 V. A simple transmission-line grid model, together with the measured low-frequency parameters for the diodes, was shown to predict the measured performance over the entire capacitive bias range of the diodes, as well as over the complete reactive tuning range provided by a reflector behind the grid, and over a wide range of frequencies form 33 GHz to 141 GHz. This shows that the transmission-line model and the measured low-frequency diode parameters can be used to design an electronic beam-steering array and to predict its performance. An electronic beam-steering array made of a pair of grids using state-of-the-art diodes with 5-Ω series resistances would have a loss of 1.4 dB at 90 GHz

Millimeter-Wave Diode-Grid Frequency Doubler

Monolithic diode grid were fabricated on 2-cm^2 gallium-arsenide wafers in a proof-of-principle test of a quasi-optical varactor millimeter-wave frequency multiplier array concept. An equivalent circuit model based on a transmission-line analysis of plane wave illumination was applied to predict the array performance. The doubler experiments were performed under far-field illumination conditions. A second-harmonic conversion efficiency of 9.5% and output powers of 0.5 W were achieved at 66 GHz when the diode grid was pumped with a pulsed source at 33 GHz. This grid had 760 Schottky-barrier varactor diodes. The average series resistance was 27 Ω, the minimum capacitance was 18 fF at a reverse breakdown voltage of -3 V. The measurements indicate that the diode grid is a feasible device for generating watt-level powers at millimeter frequencies and that substantial improvement is possible by improving the diode breakdown voltage

The Application of Canonical Correlation to Two-Dimensional Contingency Tables

This paper re-introduces and demonstrates the use of Mickeys (1970) canonical correlation method in analyzing large two-dimensional contingency tables. This method of analysis supplements the traditional analysis using the Pearson chi-square. Examples and a MATLAB source listing are provided