arXiv subjects

V. M. Kendon

Publications and source records attributed to V. M. Kendon.

8 recordsLinked to original sources

arXiv2025

Quantum smoothed particle hydrodynamics algorithm inspired by quantum walks

Recent years have seen great progress in quantum computing, providing opportunities to overcome computational bottlenecks in many scientific applications. In particular, the intersection of computational fluid dynamics (CFD) and quantum computing has become an active area of research with exponential computational speedup as an ultimate goal. In this work, we propose a quantum algorithm for the time-dependent smoothed particle hydrodynamics (SPH) method. Our algorithm uses concepts from discrete-time quantum walks to solve the one-dimensional advection partial differential equation via an SPH formalism. Hence, we construct a quantum circuit to carry out the calculations for a two-particle system over one, two and three timesteps. We compare its outputs with results from the classical SPH algorithm and show there is excellent agreement. The methodology and findings here are a key step towards developing a more general quantum SPH algorithm for solving practical engineering problems on gate-based quantum computers.

quant-ph↗

arXiv2014

Nonreversal and nonrepeating quantum walks

We introduce a variation of the discrete time quantum walk, the nonreversal quantum walk, which does not step back onto a position which it has just occupied. This allows us to simulate a dimer and we achieve it by introducing a new type of coin operator. The nonrepeating walk, which never moves in the same direction in consecutive time steps, arises by a permutation of this coin operator. We describe the basic properties of both walks and prove that the even-order joint moments of the nonrepeating walker are independent of the initial condition, being determined by five parameters derived from the coin instead. Numerical evidence suggests that the same is the case for the nonreversal walk. This contrasts strongly with previously studied coins, such as the Grover operator, where the initial condition can be used to control the standard deviation of the walker.

quant-ph↗

arXiv2002

Quantum random walks in optical lattices

We propose an experimental realization of discrete quantum random walks using neutral atoms trapped in optical lattices. The random walk is taking place in position space and experimental implementation with present day technology --even using existing set-ups-- seems feasible. We analyze the influence of possible imperfections in the experiment and investigate the transition from a quantum random walk to the classical random walk for increasing errors and decoherence.

quant-ph↗

arXiv2001

Thermal concurrence mixing in a 1D Ising model

We investigate the entanglement arising naturally in a 1D Ising chain in a magnetic field in an arbitrary direction. We find that for different temperatures, different orientations of the magnetic field give maximum entanglement. In the high temperature limit, this optimal orientation corresponds to the magnetic field being perpendicular to the Ising orientation (z direction). In the low temperature limit, we find that varying the angle of the magnetic field very slightly from the z direction leads to a rapid rise in entanglement. We also find that the orientation of the magnetic field for maximum entanglement varies with the field amplitude. Furthermore, we have derived a simple rule for the mixing of concurrences (a measure of entanglement) due to mixing of pure states satisfying certain conditions.

quant-ph↗

arXiv2000

Inertial effects in three dimensional spinodal decomposition of a symmetric binary fluid mixture: A lattice Boltzmann study

The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamicaly consistent lattice Boltzmann method. We combine results from simulations with different numerical parameters to obtain an unprecendented range of length and time scales when expressed in reduced physical units. Using eight large (256^3) runs, the resulting composite graph of reduced domain size l against reduced time t covers 1 < l < 10^5, 10 < t < 10^8. Our data is consistent with the dynamical scaling hypothesis, that l(t) is a universal scaling curve. We give the first detailed statistical analysis of fluid motion, rather than just domain evolution, in simulations of this kind, and introduce scaling plots for several quantities derived from the fluid velocity and velocity gradient fields.

cond-mat↗

arXiv1999

Persistence exponents in a 3D symmetric binary fluid mixture

The persistence exponent, theta, is defined by N_F sim t^theta, where t is the time since the start of the coarsening process and the "no-flip fraction", N_F, is the number of points that have not seen a change of "color" since t=0. Here we investigate numerically the persistence exponent for a binary fluid system where the coarsening is dominated by hydrodynamic transport. We find that N_F follows a power law decay (as opposed to exponential) with the value of theta somewhat dependent on the domain growth rate (L sim t^alpha, where L is the average domain size), in the range theta=1.23 +-0.1 (alpha = 2/3) to theta=1.37 +-0.2 (alpha=1). These alpha values correspond to the inertial and viscous hydrodynamic regimes respectively.

cond-mat↗

arXiv1999

Inertia, coarsening and fluid motion in binary mixtures

Symmetric binary fluids, quenched into a regime of immiscibility, undergo phase separation by spinodal decomposition. In the late stages, the fluids are separated by sharply defined, but curved, interfaces: the resulting Laplace pressure drives fluid flow. Scaling ideas (of Siggia and of Furukawa) predict that, ultimately, this flow should become turbulent as inertial effects dominate over viscous ones. The physics here is complex: mesoscale simulation methods (such as Lattice Boltzmann and Dissipative Particle Dynamics) can play an essential role in its elucidation, as we describe. Likewise, it is a matter of experience that immiscible fluids will mix, on some lengthscale at least, if stirred vigorously enough. A scaling theory (of Doi and Ohta) predicts the dependence of a steady state domain size on shear rate, but assumes low Reynolds number (inertia is neglected). Our preliminary simulation results (three-dimensional, so far only on small systems) show little sign of the kind of steady state envisaged by Doi and Ohta; they raise instead the possibility of an oriented domain texture which can continue to coarsen until either inertial effects, or (in our simulations) finite size effects, come into play.

cond-mat↗

arXiv1999

3D Spinodal Decomposition in the Inertial Regime

We simulate late-stage coarsening of a 3D symmetric binary fluid using a lattice Boltzmann method. With reduced lengths and times l and t respectively (scales set by viscosity, density and surface tension) our data sets cover 1 < l < 10^5, 10 < t < 10^8. We achieve Reynolds numbers approaching 350. At Re > 100 we find clear evidence of Furukawa's inertial scaling (l ~ t^{2/3}), although the crossover from the viscous regime (l ~ t) is very broad. Though it cannot be ruled out, we find no indication that Re is self-limiting (l ~ t^{1/2}) as proposed by M. Grant and K. R. Elder [Phys. Rev. Lett. 82, 14 (1999)].

cond-mat↗