Critical point for the strong field magnetoresistance of a normal conductor/perfect insulator/perfect conductor composite with a random columnar microstructure

A recently developed self-consistent effective medium approximation, for composites with a columnar microstructure, is applied to such a three-constituent mixture of isotropic normal conductor, perfect insulator, and perfect conductor, where a strong magnetic field {\bf B} is present in the plane perpendicular to the columnar axis. When the insulating and perfectly conducting constituents do not percolate in that plane, the microstructure-induced in-plane magnetoresistance is found to saturate for large {\bf B}, if the volume fraction of the perfect conductor $p_S$ is greater than that of the perfect insulator $p_I$. By contrast, if $p_S<p_I$, that magnetoresistance keeps increasing as ${\bf B}^2$ without ever saturating. This abrupt change in the macroscopic response, which occurs when $p_S=p_I$, is a critical point, with the associated critical exponents and scaling behavior that are characteristic of such points. The physical reasons for the singular behavior of the macroscopic response are discussed. A new type of percolation process is apparently involved in this phenomenon.Comment: 4 pages, 1 figur

Reletting the Abandoned or Defaulted Public Works Project in New York- To Bid or Not to Bid?

The general requirement that contracts for public works be let pursuant to advertisements for bids to the lowest responsible bidder has long been the law in New York and other jurisdictions. After determining that the mandatory statutory pronouncements apply to a particular contract, there is an entire second level problem of the propriety of bids and the awarding of the contract pursuant thereto. Suppose a contractor has defaulted or abandoned a valid public works contract. Must the public entity now readvertise for bids for the completion of the work? The answer in most instances is no, and this raises the disconcerting specter of a single unsupervised public official having the power to let potentially huge contracts. Of course the size of the relet contract is not the prime consideration. The key point is that the laboriously developed bidding laws can be circumvented in default and abandonment situations, resulting in favortism for the contractor and a bad bargain for the taxpayers. However, the other side of the question is equally vexing. An abandoned or defaulted contract may require immediate continuation or remedial action. If such situations do not fit into the public emergency exception, must the public body expend the time, effort, and expense to analyze the supplies needed or work remaining, formulate proposed contracts, and advertise for bids? This article will analyse this difficulty in the context of the confusing and conflicting status of the legal requirements in New York for the reletting of abandoned or defaulted work

Grackles

Numbering in the tens of millions of birds, grackle populations in North America can cause a variety of conflicts with people. Grackles eat agricultural crops and livestock feed, damage property, spread pathogens, and collide with aircraft. Their large roosts can be a nuisance in urban and suburban areas. A combination of dispersal techniques, exclusion, and lethal removal may help to reduce grackle damage. Grackles adapt easily to human-dominated environments, and exploit human food and other features of human landscapes. Thus, an integrated damage management approach to grackle damage focuses on reducing and eliminating the damage, rather than simply controlling grackle populations. Three species of grackles are present in North America: the common grackle, the boat-tailed grackle, and the great-tailed grackle. A fourth species, the greater Antillean grackle (Q. niger) is present in Puerto Rico. All are part of the Family Icteridae that includes blackbirds, orioles, cowbirds, meadowlarks, and bobolinks. The population status of all three grackle species is considered common to overabundant

High field magnetotransport in composite conductors: the effective medium approximation revisited

The self consistent effective medium approximation (SEMA) is used to study three-dimensional random conducting composites under the influence of a strong magnetic field {\bf B}, in the case where all constituents exhibit isotropic response. Asymptotic analysis is used to obtain almost closed form results for the strong field magnetoresistance and Hall resistance in various types of two- and three-constituent isotropic mixtures for the entire range of compositions. Numerical solutions of the SEMA equations are also obtained, in some cases, and compared with those results. In two-constituent free-electron-metal/perfect-insulator mixtures, the magnetoresistance is asymptotically proportional to $|{\bf B}|$ at {\em all concentrations above the percolation threshold}. In three-constituent metal/insulator/superconductor mixtures a line of critical points is found, where the strong field magnetoresistance switches abruptly from saturating to non-saturating dependence on $|{\bf B}|$, at a certain value of the insulator-to-superconductor concentration ratio. This transition appears to be related to the phenomenon of anisotropic percolation.Comment: 16 pages, 3 figure

Magnetoresistance of Three-Constituent Composites: Percolation Near a Critical Line

Scaling theory, duality symmetry, and numerical simulations of a random network model are used to study the magnetoresistance of a metal/insulator/perfect conductor composite with a disordered columnar microstructure. The phase diagram is found to have a critical line which separates regions of saturating and non-saturating magnetoresistance. The percolation problem which describes this line is a generalization of anisotropic percolation. We locate the percolation threshold and determine the t = s = 1.30 +- 0.02, nu = 4/3 +- 0.02, which are the same as in two-constituent 2D isotropic percolation. We also determine the exponents which characterize the critical dependence on magnetic field, and confirm numerically that nu is independent of anisotropy. We propose and test a complete scaling description of the magnetoresistance in the vicinity of the critical line.Comment: Substantially revised version; description of behavior in finite magnetic fields added. 7 pages, 7 figures, submitted to PR

Theory of dissipationless Nernst effects

We develop a theory of transverse thermoelectric (Peltier) conductivity, \alpha_{xy}, in finite magnetic field -- this particular conductivity is often the most important contribution to the Nernst thermopower. We demonstrate that \alpha_{xy} of a free electron gas can be expressed purely and exactly as the entropy per carrier irrespective of temperature (which agrees with seminal Hall bar result of Girvin and Jonson). In two dimensions we prove the universality of this result in the presence of disorder which allows explicit demonstration of a number features of interest to experiments on graphene and other two-dimensional materials. We also exploit this relationship in the low field regime and to analyze the rich singularity structure in \alpha_{xy}(B, T) in three dimensions; we discuss its possible experimental implications.Comment: 4.5 pages, 2 figure

A Note on Intersecting and Fluctuating Solitons in 4D Noncommutative Field Theory

We examine the intersections, fluctuations and deformations of codimension two solitons in field theory on noncommutative $R^4$, in the limit of large noncommutativity. We find that holomorphic deformations are zero modes of flat branes, and we show that there is a zero mode localized at the intersection of two solitons.Comment: 19pp LaTeX, refs adde

On the Bergman-Milton bounds for the homogenization of dielectric composite materials

The Bergman-Milton bounds provide limits on the effective permittivity of a composite material comprising two isotropic dielectric materials. These provide tight bounds for composites arising from many conventional materials. We reconsider the Bergman-Milton bounds in light of the recent emergence of metamaterials, in which unconventional parameter ranges for relative permittivities are encountered. Specifically, it is demonstrated that: (a) for nondissipative materials the bounds may be unlimited if the constituent materials have relative permittivities of opposite signs; (b) for weakly dissipative materials characterized by relative permittivities with real parts of opposite signs, the bounds may be exceedingly large