Phase transitions and non-equilibrium relaxation in kinetic models of opinion formation

We review in details some recently proposed kinetic models of opinion dynamics. We discuss the several variants including a generalised model. We provide mean field estimates for the critical points, which are numerically supported with reasonable accuracy. Using non-equilibrium relaxation techniques, we also investigate the nature of phase transitions observed in these models. We study the nature of correlations as the critical points are approached, and comment on the universality of the phase transitions observed.Comment: 11 pages, 8 eps figures, 1 table. Contribution for proceedings of Statphys-Kolkata-VII 26-30 November, 201

Continuous transition of social efficiencies in the stochastic strategy Minority Game

We show that in a variant of the Minority Game problem, the agents can reach a state of maximum social efficiency, where the fluctuation between the two choices is minimum, by following a simple stochastic strategy. By imagining a social scenario where the agents can only guess about the number of excess people in the majority, we show that as long as the guess value is sufficiently close to the reality, the system can reach a state of full efficiency or minimum fluctuation. A continuous transition to less efficient condition is observed when the guess value becomes worse. Hence, people can optimize their guess value for excess population to optimize the period of being in the majority state. We also consider the situation where a finite fraction of agents always decide completely randomly (random trader) as opposed to the rest of the population that follow a certain strategy (chartist). For a single random trader the system becomes fully efficient with majority-minority crossover occurring every two-days interval on average. For just two random traders, all the agents have equal gain with arbitrarily small fluctuations.Comment: 8 pages, 6 fig

Disorder induced phase transition in kinetic models of opinion dynamics

We propose a model of continuous opinion dynamics, where mutual interactions can be both positive and negative. Different types of distributions for the interactions, all characterized by a single parameter $p$ denoting the fraction of negative interactions, are considered. Results from exact calculation of a discrete version and numerical simulations of the continuous version of the model indicate the existence of a universal continuous phase transition at p=p_c below which a consensus is reached. Although the order-disorder transition is analogous to a ferromagnetic-paramagnetic phase transition with comparable critical exponents, the model is characterized by some distinctive features relevant to a social system.Comment: 10 pages, 5 eps fig

Fire-Retardant, Self-Extinguishing Inorganic/Polymer Composite Memory Foams

Polymeric foams used in furniture and automotive and aircraft seating applications rely on the incorporation of environmentally hazardous fire-retardant additives to meet fire safety norms. This has occasioned significant interest in novel approaches to the elimination of fire-retardant additives. Foams based on polymer nanocomposites or based on fire-retardant coatings show compromised mechanical performance and require additional processing steps. Here, we demonstrate a one-step preparation of a fire-retardant ice-templated inorganic/polymer hybrid that does not incorporate fire-retardant additives. The hybrid foams exhibit excellent mechanical properties. They are elastic to large compressional strain, despite the high inorganic content. They also exhibit tunable mechanical recovery, including viscoelastic “memory”. These hybrid foams are prepared using ice-templating that relies on a green solvent, water, as a porogen. Because these foams are predominantly comprised of inorganic components, they exhibit exceptional fire retardance in torch burn tests and are self-extinguishing. After being subjected to a flame, the foam retains its porous structure and does not drip or collapse. In micro-combustion calorimetry, the hybrid foams show a peak heat release rate that is only 25% that of a commercial fire-retardant polyurethanes. Finally, we demonstrate that we can use ice-templating to prepare hybrid foams with different inorganic colloids, including cheap commercial materials. We also demonstrate that ice-templating is amenable to scale up, without loss of mechanical performance or fire-retardant properties

Fire-Retardant, Self-Extinguishing Inorganic/Polymer Composite Memory Foams

Polymeric foams used in furniture and automotive and aircraft seating applications rely on the incorporation of environmentally hazardous fire-retardant additives to meet fire safety norms. This has occasioned significant interest in novel approaches to the elimination of fire-retardant additives. Foams based on polymer nanocomposites or based on fire-retardant coatings show compromised mechanical performance and require additional processing steps. Here, we demonstrate a one-step preparation of a fire-retardant ice-templated inorganic/polymer hybrid that does not incorporate fire-retardant additives. The hybrid foams exhibit excellent mechanical properties. They are elastic to large compressional strain, despite the high inorganic content. They also exhibit tunable mechanical recovery, including viscoelastic “memory”. These hybrid foams are prepared using ice-templating that relies on a green solvent, water, as a porogen. Because these foams are predominantly comprised of inorganic components, they exhibit exceptional fire retardance in torch burn tests and are self-extinguishing. After being subjected to a flame, the foam retains its porous structure and does not drip or collapse. In micro-combustion calorimetry, the hybrid foams show a peak heat release rate that is only 25% that of a commercial fire-retardant polyurethanes. Finally, we demonstrate that we can use ice-templating to prepare hybrid foams with different inorganic colloids, including cheap commercial materials. We also demonstrate that ice-templating is amenable to scale up, without loss of mechanical performance or fire-retardant properties

Omniphilic Polymeric Sponges by Ice Templating

Sponges that absorb a large quantity of solvent relative to their weight, independent of the solvent polarity, represent useful universal absorbents for laboratory and industrial spills. We report the preparation of macroporous polymer sponges by ice templating of polyethylenimine aqueous solutions and their cross-linking in the frozen state. The as-prepared monolith is hydrophilic and absorbs over 30-fold its weight in water. Modification of this sponge using valeroyl chloride renders it omniphilic; viz., a modified sponge absorbs over 10-fold its dry weight of either water or hexane. Modification using palmitoyl chloride that has a longer chain length results in the preparation of a hydrophobic sponge with a water contact angle around 130°, which retains its oleophilicity underwater. The solvent absorbed in these sponges can be simply squeezed out, and the sponges are stable to several hundred cycles of compression. The large pore sizes of these sponges allow rapid absorption of even high viscosity solvents such as pump oil. Finally, we demonstrate that these sponges are also able to separate apolar oils that are emulsified in water using surfactants. These high porosity sponges with controllable solvophilicity represent inexpensive, high performance universal absorbents for general solvent spills

Elastic Compressible Energy Storage Devices from Ice Templated Polymer Gels treated with Polyphenols

Design and fabrication of rechargeable energy storage devices that are robust to mechanical deformation is essential for wearable electronics. We report the preparation of compressible supercapacitors that retain their specific capacitance after large compression and that recover elastically after at least a hundred compression–expansion cycles. Compressible supercapacitors are prepared using a facile, scalable method that readily yields centimeter-scale macroporous objects. We ice template a solution of polyethylenimine in green tea extract to prepare a macroporous cross-linked polymer gel (PG) whose walls are impregnated with green tea derived polyphenols. As the PG is insulating, we impart conductivity by deposition of gold on it. Gold deposition is done in two steps: first, silver nanoparticles are formed on the PG walls by in situ reduction by polyphenols and then gold films are deposited on these walls. Gold coated PGs (GPGs) were used as electrodes to deposit poly­(3,4-ethylenedioxythiophene) as a pseudocapacitive material. The specific capacitance of PEDOT coated GPGs (PGPG) was found to be 253 F/g at 1 A/g. PGPG could be compressed and expanded over a hundred cycles without any suffering mechanical failure or loss of capacitative performance. The capacitance was found to be 243 F/g upon compressing the device to 25% of its original size (viz. compressive strain = 75%). Thus, even large compression does not affect the device performance. This device shows power and energy densities of 2715 W/kg and 22 Wh/kg, respectively, in the uncompressed state. The macroporous nature of PGPG makes it possible to fill the PGPG pores with gel electrolyte. We report that the gel electrolyte filled supercapacitor exhibited a specific capacitance of 200 F/g, which increased by 4% upon 75% compression