Semiflexible polymer in a strip

We study the thermodynamic properties of a semiflexible polymer confined inside strips of widths L<=9 defined on a square lattice. The polymer is modeled as a self-avoiding walk and a short range interaction between the monomers and the walls is included through an energy e associated to each monomer placed on one of the walls. Also, an additional energy is associated to each elementary bend of the walk. The free energy of the model is obtained exactly through a transfer matrix formalism. The profile of the monomer density and the force on the walls are obtained. We notice that as the bending energy is decreased, the range of values of e for which the density profile is neither convex nor concave increases, and for sufficiently attracting walls (e<0) we find that in general the attractive force is maximum for situations where the bends are favored.Comment: 5 pages, 6 figure

Nature of the collapse transition in interacting self-avoiding trails

We study the interacting self-avoiding trail (ISAT) model on a Bethe lattice of general coordination $q$ and on a Husimi lattice built with squares and coordination $q=4$. The exact grand-canonical solutions of the model are obtained, considering that up to $K$ monomers can be placed on a site and associating a weight $\omega_i$ for a $i$-fold visited site. Very rich phase diagrams are found with non-polymerized (NP), regular polymerized (P) and dense polymerized (DP) phases separated by lines (or surfaces) of continuous and discontinuous transitions. For Bethe lattice with $q=4$ and $K=2$, the collapse transition is identified with a bicritical point and the collapsed phase is associated to the dense polymerized phase (solid-like) instead of the regular polymerized phase (liquid-like). A similar result is found for the Husimi lattice, which may explain the difference between the collapse transition for ISAT's and for interacting self-avoiding walks on the square lattice. For $q=6$ and $K=3$ (studied on the Bethe lattice only), a more complex phase diagram is found, with two critical planes and two coexistence surfaces, separated by two tricritical and two critical end-point lines meeting at a multicritical point. The mapping of the phase diagrams in the canonical ensemble is discussed and compared with simulational results for regular lattices.Comment: 12 pages, 13 figure

A general creation-annihilation model with absorbing states

A one dimensional non-equilibrium stochastic model is proposed where each site of the lattice is occupied by a particle, which may be of type A or B. The time evolution of the model occurs through three processes: autocatalytic generation of A and B particles and spontaneous conversion A to B. The two-parameter phase diagram of the model is obtained in one- and two-site mean field approximations, as well as through numerical simulations and exact solution of finite systems extrapolated to the thermodynamic limit. A continuous line of transitions between an active and an absorbing phase is found. This critical line starts at a point where the model is equivalent to the contact process and ends at a point which corresponds to the voter model, where two absorbing states coexist. Thus, the critical line ends at a point where the transition is discontinuous. Estimates of critical exponents are obtained through the simulations and finite-size-scaling extrapolations, and the crossover between universality classes as the voter model transition is approached is studied.Comment: 9 pages and 17 figure

The nature of attraction between like charged rods

Comment on the paper of Ha and Liu (Phys. Rev. Lett. {\bf 79}, 1289 (1997)) regarding the nature of attraction between like charged rods. We demostrate that their results do not produce the correct low temperature limit.Comment: Comment to appear in Phys. Rev. Let

Parallel Computation in Econometrics: A Simplified Approach

Parallel computation has a long history in econometric computing, but is not at all wide spread. We believe that a major impediment is the labour cost of coding for parallel architectures. Moreover, programs for specific hardware often become obsolete quite quickly. Our approach is to take a popular matrix programming language (Ox), and implement a message-passing interface using MPI. Next, object-oriented programming allows us to hide the specific parallelization code, so that a program does not need to be rewritten when it is ported from the desktop to a distributed network of computers. Our focus is on so-called embarrassingly parallel computations, and we address the issue of parallel random number generation.Code optimization; Econometrics; High-performance computing; Matrix-programming language; Monte Carlo; MPI; Ox; Parallel computing; Random number generation.

Computationally-intensive Econometrics using a Distributed Matrix-programming Language

This paper reviews the need for powerful facilities in econometrics, focusing on concrete problems which arise in financial economics and in macroeconomics. We argue that the profession is being held back by the lack of easy to use generic software which is able to exploit the availability of cheap clusters of distributed computers. Our response is to extend, in a number of directions, the well known matrix-programming interpreted language Ox developed by the first author. We note three possible levels of extensions: (i) Ox with parallelization explicit in the Ox code; (ii) Ox with a parallelized run-time library; (iii) Ox with a parallelized interpreter. This paper studies and implements the first case, emphasizing the need for deterministic computing in science. We give examples in the context of financial economics and time-series modelling.Distributed computing; Econometrics; High-performance computing; Matrix-programming language

Workshop on Observations of Recent Comets (1990)

Potential interpretations are presented for observations of four comets: Brorsen-Metcalf (1989o), Okazaki-Levy-Rudenko (1989r), Aarseth-Brewington (1989a1), and Austin (1989o1). The relationship of minor species with each other and possible parents as well as with dust are being pursued in a number of investigations. Of particular interest are the abundance ratios of CH4 to CO and NH3 to N2. The need for closer collaboration betwen observing teams and modelers is examined. The need for dust size distribution as a function of cometocentric distance to be analyzed in closer collaboration between observers and modelers is discussed

Cooperative gas adsorption without a phase transition in metal-organic frameworks

Cooperative adsorption of gases by porous frameworks permits more efficient uptake and removal than does the more usual non-cooperative (Langmuir-type) adsorption. Cooperativity, signaled by a step-like isotherm, is usually attributed to a phase transition of the framework. However, the class of metal-organic frameworks mmen-M$_2$(dobpdc) exhibit cooperative adsorption of CO2 but show no evidence of a phase transition. Here we show how cooperativity emerges in these frameworks in the absence of a phase transition. We use a combination of quantum and statistical mechanics to show that cooperativity results from a sharp but finite increase, with pressure, of the mean length of chains of CO2 molecules that polymerize within the framework. Our study provides microscopic understanding of the emergent features of cooperative binding, including the position, slope and height of the isotherm step, and indicates how to optimize gas storage and separation in these materials.Comment: 18 pages, 11 figure

Forecasting the UK top 1% income share in a shifting world

UK top income shares have varied hugely over the past two centuries, ranging from more than 30% to less than 7% of pre-tax national income allocated to the top 1 percentile. We build a congruent dynamic linear regression model of the top 1% income share allowing for economic, political and social factors. Saturation estimation is used to model outliers and trend breaks, proxying underlying structural changes driving income inequality in the UK. We use the model to forecast the top 1% income share over the last 15 years, and compare to a range of forecast devices. Despite a well-specified constant parameter model conditioning on significant explanatory variables, the best performing forecasts are obtained from a random walk and a smoothed random walk. These results are explained by the presence of shifts in the income share over the forecast period, resulting in forecasts from equilibrium correction models converging to the wrong equilibrium. Our best prediction for 2026 based on the most recent data from 2021 (a 5-year ahead projection) is that the pre-tax top 1% income share will remain at the most recent realized value of 12.7%, but there is a large degree of uncertainty, with a 95% confidence band ranging from 10% to 15.7%