Driven inelastic Maxwell gases

We consider the inelastic Maxwell model, which consists of a collection of particles that are characterized by only their velocities, and evolving through binary collisions and external driving. At any instant, a particle is equally likely to collide with any of the remaining particles. The system evolves in continuous time with mutual collisions and driving taken to be point processes with rates $\tau_c^-{1}$ and $\tau_w^{-1}$ respectively. The mutual collisions conserve momentum and are inelastic, with a coefficient of restitution $r$. The velocity change of a particle with velocity $v$, due to driving, is taken to be $\Delta v=-(1+r_w) v+\eta$, mimicking the collision with a vibrating wall, where $r_w$ the coefficient of restitution of the particle with the "wall" and $\eta$ is Gaussian white noise. The Ornstein-Uhlenbeck driving mechanism given by $\frac{dv}{dt}=-\Gamma v+\eta$ is found to be a special case of the driving modeled as a point process. Using both the continuum and discrete versions we show that while the equations for the one-particle and the two-particle velocity distribution functions do not close, the joint evolution equations of the variance and the two-particle velocity correlation functions close. With the exact formula for the variance we find that, for $r_w\ne-1$, the system goes to a steady state. On the other hand, for $r_w=-1$, the system does not have a steady state. Similarly, the system goes to a steady state for the Ornstein-Uhlenbeck driving with $\Gamma\not=0$, whereas for the purely diffusive driving ($\Gamma=0$), the system does not have a steady state.Comment: 9 pages, 4 figure

Fluctuation theorem in quantum heat conduction

We consider steady state heat conduction across a quantum harmonic chain connected to reservoirs modelled by infinite collection of oscillators. The heat, $Q$, flowing across the oscillator in a time interval $\tau$ is a stochastic variable and we study the probability distribution function $P(Q)$. In the large $\tau$ limit we use the formalism of full counting statistics (FCS) to compute the generating function of $P(Q)$ exactly. We show that $P(Q)$ satisfies the steady state fluctuation theorem (SSFT) regardless of the specifics of system, and it is nongaussian with clear exponential tails. The effect of finite $\tau$ and nonlinearity is considered in the classical limit through Langevin simulations. We also obtain predictions of universal heat current fluctuations at low temperatures in clean wires.Comment: 4 pages, 2 figure

Eulerian Walkers as a model of Self-Organised Criticality

We propose a new model of self-organized criticality. A particle is dropped at random on a lattice and moves along directions specified by arrows at each site. As it moves, it changes the direction of the arrows according to fixed rules. On closed graphs these walks generate Euler circuits. On open graphs, the particle eventually leaves the system, and a new particle is then added. The operators corresponding to particle addition generate an abelian group, same as the group for the Abelian Sandpile model on the graph. We determine the critical steady state and some critical exponents exactly, using this equivalence.Comment: 4 pages, RevTex, 4 figure

Mean field analysis of quantum phase transitions in a periodic optical superlattice

In this paper we analyze the various phases exhibited by a system of ultracold bosons in a periodic optical superlattice using the mean field decoupling approximation. We investigate for a wide range of commensurate and incommensurate densities. We find the gapless superfluid phase, the gapped Mott insulator phase, and gapped insulator phases with distinct density wave orders.Comment: 6 pages, 7 figures, 4 table

Quantum Phases of Ultracold Bosonic Atoms in a One Dimensional Optical Superlattice

We analyze various quantum phases of ultracold bosonic atoms in a periodic one dimensional optical superlattice. Our studies have been performed using the finite size density matrix renormalization group (FS-DMRG) method in the framework of the Bose-Hubbard model. Calculations have been carried out for a wide range of densities and the energy shifts due to the superlattice potential. At commensurate fillings, we find the Mott insulator and the superfluid phases as well as Mott insulators induced by the superlattice. At a particular incommensurate density, the system is found to be in the superfluid phase coexisting with density oscillations for a certain range of parameters of the system.Comment: 7 pages, 11 figure

Simultaneous Ejection of Six Electrons at a Constant Potential by Hexakis(4-ferrocenylphenyl)benzene

A simple synthesis of a dendritic hexaferrocenyl electron donor (5) is described in which six ferrocene moieties are connected at the vertices of the propeller of the hexaphenylbenzene core. The molecular structure of 5 is confirmed by X-ray crystallography. An electrochemical analysis along with redox titrations (which are tantamount to coulometry) confirmed that it ejects six electrons at a single potential

I Stood Up: Social Design in Practice

Through practice-based research, we explore how interdisciplinary design projects can function to address social issues concerning environmental and social problems. Using two case studies developed between London in the United Kingdom, and Delhi and Ahmedabad in India, we discuss the importance of engagement with the people who the design ultimately serves. Finally, we argue that design concerned with complex social problems require equally complex, multidimensional responses, informed by bodies of knowledge, practices and approaches that lie outside of traditional design approaches