Thermal Modeling in Polymer Extrusion

In this paper we consider thermal effects of polymer flows through a cylindrical die. First, we derive a model for the oscillatory behavior of polymer flow in an extruder given a functional relation between the pressure and flow rate. A simple isothermal but temperature dependent model is constructed to find this relation. Unfortunately, the model is shown to be invalid in the physical regime of interest. We present several arguments to suggest that the isothermal assumption is reasonable but that a more detailed understanding of the small-scale molecular dynamics near the boundary may be required. Second, we show that a simplified model for thermoflow multiplicity in a cooled tube is inconsistent, when the stationary non-Newtonian flow is assumed to be incompressible without radial pressure gradients and without radial velocity. This inconsistency can be removed by allowing for weak compressibility effects in the down-steam area

Finite N Index and Angular Momentum Bound from Gravity

We exactly compute the finite N index and BPS partition functions for N=4 SYM theory in a newly proposed maximal angular momentum limit. The new limit is not predicted from the superconformal algebra, but naturally arises from the supergravity dual. We show that the index does not receive any finite N corrections while the free BPS partition function does.Comment: 14 pages, v2: minor revisions, published versio

Modelling and solution to the municipal effluent management problem

The aim of this paper is to analyse the municipal effluent management problem; we also show how to solve a problem of that kind. Municipal effluent economics is a complex problem. There are many agents con-fined to a small area, their capital can change through the investment and dis-investment processes and they can abate pollution in the abatement facilities or '(in-stantaneously" (e.g. by exporting it). The agents pollute a local river. On the other hand, a regional authority would like to preserve the quality of the river's water. The quality can be expressed as a series of constraints to be satisfied locally, globally or on average, in the spatial and temporal sense. For that complicated situation, we propose a multi-criteria hierarchical multilevel optimisation model with a Stackelberg type equilibrium between the leader's and the followers' levels, and a Nash type equi-librium at the followers' level. We outline the procedure necessary for a solution to a problem of that class. We analytically compute a steady state Nash equilibrium solution for the followers, and determine a Stackelberg equilibrium solution for the leader-followers interactions, through a Decision Support Tool

Semantic Hygiene for the Law of Regulatory Takings, Due Process, and Unconstitutional Conditions—Making Use of a Muddy Supreme Court Exactions Case

An unfortunate amount of semantic confusion currently burdens the constitutional process of balancing private property rights and governmental public welfare protections. The Fifth Amendment contains both a general requirement of “due process,” and a corollary protection against unconstitutional “taking” of property. These are two separate protections, not just one. More than a century after the Takings Clause was drafted, an enigmatic decision, Pennsylvania Coal, expanded the clause to say that government regulations could cause such a diminution of private property value that they could unconstitutionally take that property, even with no physical appropriation (which is how the Framers had understood the clause). Having launched the concept of regulatory takings, the Court barely revisited it for another fifty years, while extensively developing general due process doctrine. Then, starting in the 1970s, the Justices began to expand the application of regulatory takings doctrine. But they did little to clarify the distinction between takings and general due process scrutiny. Nor did they clarify the essentially subjective line drawing of the takings inquiry, instead freighting it with new complexities, political agendas, and internal contradictions. One particularly inapt result has emerged in the realm of land use regulatory exaction conditions, where a due process inquiry has been maladroitly commingled with takings test language. The Court began to distinguish the two in 2005, but left the resolution half-baked. Koontz v. St. Johns River Management District, in 2013, demonstrated the current semantic jumble, taking a basic due process exaction question and discussing it as a takings question. The semantics have resulted in unfortunate consequences. Building upon a factual and conceptual autopsy of the Koontz litigation, and noting a strategic semicolon from 1789 in the Fifth Amendment, this Article proposes a number of semantic hygiene clarifications for reviews of exactions and other “unconstitutional conditions”—(1) that judicial review of a permit exaction’s validity typically first must address a takings question—could the permit have been simply denied without excessively diminishing private property value?—if not, no added conditions are justified, but if so, then the further question of the exaction conditions’ constitutionality presents a further, distinct, targeted test based in due process—the Nollan-Dolan test; (2) that further review under Nollan-Dolan, based in substantive due process, applies whenever a landowner challenges the logic of any government-required exaction, whether monetary or not; and (3) recognizing Nollan-Dolan review of exaction conditions as a matter of substantive due process, rather than regulatory takings, fundamentally narrows the remedy options, as well as very usefully clarifies other enduring mysteries of the constitutional balance between public and private rights in property, a core issue of modern democratic governance. To serve these goals, this Article includes a suggested Semantic Lexicon of public/private property rights jurisprudence

Phase transitions and statistical mechanics for BPS Black Holes in AdS/CFT

Using the general framework developed in hep-th/0607056, we study in detail the phase space of BPS Black Holes in AdS, for the case where all three electric charges are equal. Although these solitons are supersymmetric with zero Hawking temperature, it turns out that these Black Holes have rich phase structure with sharp phase transitions associated to a corresponding critical generalized temperature. We are able to rewrite the gravity variables in terms of dual CFT variables and compare the gravity phase diagram with the free dual CFT phase diagram. In particular, the elusive supergravity constraint characteristic of these Black Holes is particulary simple and in fact appears naturally in the dual CFT in the definition of the BPS Index. Armed with this constraint, we find perfect match between BH and free CFT charges up to expected constant factors.Comment: 14 pages, 5 figures, corrected typos and references adde

Information entropy in fragmenting systems

The possibility of facing critical phenomena in nuclear fragmentation is a topic of great interest. Different observables have been proposed to identify such a behavior, in particular, some related to the use of information entropy as a possible signal of critical behavior. In this work we critically examine some of the most widespread used ones comparing its performance in bond percolation and in the analysis of fragmenting Lennard Jones Drops.Comment: 3 pages, 3 figure

Neuro-mechanical determinants of repeated treadmill sprints - Usefulness of an "hypoxic to normoxic recovery" approach.

To improve our understanding of the limiting factors during repeated sprinting, we manipulated hypoxia severity during an initial set and examined the effects on performance and associated neuro-mechanical alterations during a subsequent set performed in normoxia. On separate days, 13 active males performed eight 5-s sprints (recovery = 25 s) on an instrumented treadmill in either normoxia near sea-level (SL; FiO2 = 20.9%), moderate (MH; FiO2 = 16.8%) or severe normobaric hypoxia (SH; FiO2 = 13.3%) followed, 6 min later, by four 5-s sprints (recovery = 25 s) in normoxia. Throughout the first set, along with distance covered [larger sprint decrement score in SH (-8.2%) compared to SL (-5.3%) and MH (-7.2%); P < 0.05], changes in contact time, step frequency and root mean square activity (surface electromyography) of the quadriceps (Rectus femoris muscle) in SH exceeded those in SL and MH (P < 0.05). During first sprint of the subsequent normoxic set, the distance covered (99.6, 96.4, and 98.3% of sprint 1 in SL, MH, and SH, respectively), the main kinetic (mean vertical, horizontal, and resultant forces) and kinematic (contact time and step frequency) variables as well as surface electromyogram of quadriceps and plantar flexor muscles were fully recovered, with no significant difference between conditions. Despite differing hypoxic severity levels during sprints 1-8, performance and neuro-mechanical patterns did not differ during the four sprints of the second set performed in normoxia. In summary, under the circumstances of this study (participant background, exercise-to-rest ratio, hypoxia exposure), sprint mechanical performance and neural alterations were largely influenced by the hypoxia severity in an initial set of repeated sprints. However, hypoxia had no residual effect during a subsequent set performed in normoxia. Hence, the recovery of performance and associated neuro-mechanical alterations was complete after resting for 6 min near sea level, with a similar fatigue pattern across conditions during subsequent repeated sprints in normoxia

A Fermi Surface Model for Large Supersymmetric AdS_5 Black Holes

We identify a large family of 1/16 BPS operators in N=4 SYM that qualitatively reproduce the relations between charge, angular momentum and entropy in regular supersymmetric AdS_5 black holes when the main contribution to their masses is given by their angular momentum.Comment: 32 pages, 6 figures, LaTeX uses JHEP3 class; ver 2- added acknowledgment, minor change

The QCD Phase Diagram at Nonzero Temperature, Baryon and Isospin Chemical Potentials in Random Matrix Theory

We introduce a random matrix model with the symmetries of QCD at finite temperature and chemical potentials for baryon number and isospin. We analyze the phase diagram of this model in the chemical potential plane for different temperatures and quark masses. We find a rich phase structure with five different phases separated by both first and second order lines. The phases are characterized by the pion condensate and the chiral condensate for each of the flavors. In agreement with lattice simulations, we find that in the phase with zero pion condensate the critical temperature depends in the same way on the baryon number chemical potential and on the isospin chemical potential. At nonzero quark mass, we remarkably find that the critical end point at nonzero temperature and baryon chemical potential is split in two by an arbitrarily small isospin chemical potential. As a consequence, there are two crossovers that separate the hadronic phase from the quark-gluon plasma phase at high temperature. Detailed analytical results are obtained at zero temperature and in the chiral limit.Comment: 13 pages, 5 figures, REVTeX