A direct primitive variable recovery scheme for hyperbolic conservative equations: the case of relativistic hydrodynamics

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.Comment: 19 pages, 6 figures, 2 tables. Accepted for publication in PLOS ON

Collapse of Flexible Polyelectrolytes in Multivalent Salt Solutions

The collapse of flexible polyelectrolytes in a solution of multivalent counterions is studied by means of a two state model. The states correspond to rod-like and spherically collapsed conformations respectively. We focus on the very dilute monomer concentration regime where the collapse transition is found to occur when the charge of the multivalent salt is comparable (but smaller) to that of the monomers. The main contribution to the free energy of the collapsed conformation is linear in the number of monomers $N$, since the internal state of the collapsed polymer approaches that of an amorphous ionic solid. The free energy of the rod-like state grows as $N\ln N$, due to the electrostatic energy associated with that shape. We show that practically all multivalent counterions added to the system are condensed into the polymer chain, even before the collapse.Comment: LaTeX-revtex, psfig file, 4 figure

Heteroskedasticity in Multiple Regression Analysis: What it is, How to Detect it and How to Solve it with Applications in R and SPSS

Within psychology and the social sciences, Ordinary Least Squares (OLS) regression is one of the most popular techniques for data analysis. In order to ensure the inferences from the use of this method are appropriate, several assumptions must be satisfied, including the one of constant error variance (i.e. homoskedasticity). Most of the training received by social scientists with respect to homoskedasticity is limited to graphical displays for detection and data transformations as solution, giving little recourse if none of these two approaches work. Borrowing from the econometrics literature, this tutorial aims to present a clear description of what heteroskedasticity is, how to measure it through statistical tests designed for it and how to address it through the use of heteroskedastic-consistent standard errors and the wild bootstrap. A step-by-step solution to obtain these errors in SPSS is presented without the need to load additional macros or syntax. Emphasis is placed on the fact that non-constant error variance is a population-defined, model-dependent feature and different types of heteroskedasticity can arise depending on what one is willing to assume about the data. Accessed 4,952 times on https://pareonline.net from January 11, 2019 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Holographic fabrication of three-dimensional orthorhombic and tetragonal photonic crystal templates using a diffractive optical element

We report the fabrication of both orthorhombic and tetragonal photonic crystal templates using a phase mask technique. Three-dimensional photonic crystal structures were formed by a double exposure of SU8 to three-beam interference patterns generated by a phase mask. Lattice structures and photonic band gap can be controlled by rotational angles of the phase mask between two exposures. Band gap computation predicts that photonic crystal structures with the optimized band gap can be realized when the rotational angle is set between 50° and 70°. A photonic crystal template with 60° phase mask rotation was fabricated, showing improved lattice structures required for the band gap opening. © 2007 American Institute of Physics

Pattern formation on the surface of cationic-anionic cylindrical aggregates

Charged pattern formation on the surfaces of self--assembled cylindrical micelles formed from oppositely charged heterogeneous molecules such as cationic and anionic peptide amphiphiles is investigated. The net incompatibility $\chi$ among different components results in the formation of segregated domains, whose growth is inhibited by electrostatics. The transition to striped phases proceeds through an intermediate structure governed by fluctuations, followed by states with various lamellar orientations, which depend on cylinder radius $R_c$ and $\chi$. We analyze the specific heat, susceptibility $S(q^*)$, domain size $\Lambda=2\pi/q^*$ and morphology as a function of $R_c$ and $\chi$.Comment: Sent to PRL 11Jan05 Transferred from PRL to PRE 10Jun0

Non-monotonic swelling of surface grafted hydrogels induced by pH and/or salt concentration

We use a molecular theory to study the thermodynamics of a weak-polyacid hydrogel film that is chemically grafted to a solid surface. We investigate the response of the material to changes in the pH and salt concentration of the buffer solution. Our results show that the pH-triggered swelling of the hydrogel film has a non-monotonic dependence on the acidity of the bath solution. At most salt concentrations, the thickness of the hydrogel film presents a maximum when the pH of the solution is increased from acidic values. The quantitative details of such swelling behavior, which is not observed when the film is physically deposited on the surface, depend on the molecular architecture of the polymer network. This swelling-deswelling transition is the consequence of the complex interplay between the chemical free energy (acid-base equilibrium), the electrostatic repulsions between charged monomers, which are both modulated by the absorption of ions, and the ability of the polymer network to regulate charge and control its volume (molecular organization). In the absence of such competition, for example, for high salt concentrations, the film swells monotonically with increasing pH. A deswelling-swelling transition is similarly predicted as a function of the salt concentration at intermediate pH values. This reentrant behavior, which is due to the coupling between charge regulation and the two opposing effects triggered by salt concentration (screening electrostatic interactions and charging/discharging the acid groups), is similar to that found in end-grafted weak polyelectrolyte layers. Understanding how to control the response of the material to different stimuli, in terms of its molecular structure and local chemical composition, can help the targeted design of applications with extended functionality. We describe the response of the material to an applied pressure and an electric potential. We present profiles that outline the local chemical composition of the hydrogel, which can be useful information when designing applications that pursue or require the absorption of biomolecules or pH-sensitive molecules within different regions of the film.Fil: Longo, Gabriel Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentina. Northwestern University. Department of Biomedical Engineering; Estados Unidos. Northwestern University. Chemistry of Life Processes Institute; Estados UnidosFil: Olvera de la Cruz, Monica. Northwestern University; Estados UnidosFil: Szleifer, Igal. Northwestern University; Estados Unido