Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as non-Abelian anyons, meaning that they obey non-Abelian braiding statistics. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations that are necessary for quantum computation are carried out by braiding quasiparticles and then measuring the multiquasiparticle states. The fault tolerance of a topological quantum computer arises from the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the $\ensuremath{\nu}=5∕2$ state, although several other prospective candidates have been proposed in systems as disparate as ultracold atoms in optical lattices and thin-film superconductors. In this review article, current research in this field is described, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. Both the mathematical underpinnings of topological quantum computation and the physics of the subject are addressed, using the $\ensuremath{\nu}=5∕2$ fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

Non-Abelian Anyons and Topological Quantum Computation

Topological quantum computation has recently emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of matter whose quasiparticle excitations are neither bosons nor fermions, but are particles known as {it Non-Abelian anyons}, meaning that they obey {it non-Abelian braiding statistics}. Quantum information is stored in states with multiple quasiparticles, which have a topological degeneracy. The unitary gate operations which are necessary for quantum computation are carried out by braiding quasiparticles, and then measuring the multi-quasiparticle states. The fault-tolerance of a topological quantum computer arises from the non-local encoding of the states of the quasiparticles, which makes them immune to errors caused by local perturbations. To date, the only such topological states thought to have been found in nature are fractional quantum Hall states, most prominently the nu=5/2 state, although several other prospective candidates have been proposed in systems as disparate as ultra-cold atoms in optical lattices and thin film superconductors. In this review article, we describe current research in this field, focusing on the general theoretical concepts of non-Abelian statistics as it relates to topological quantum computation, on understanding non-Abelian quantum Hall states, on proposed experiments to detect non-Abelian anyons, and on proposed architectures for a topological quantum computer. We address both the mathematical underpinnings of topological quantum computation and the physics of the subject using the nu=5/2 fractional quantum Hall state as the archetype of a non-Abelian topological state enabling fault-tolerant quantum computation.

Preface 1.General Considerations 2.Basic Processes in Atomization 3.Drop Size Distributions of Sprays 4.Atomizers 5.Flow in Atomizers 6.Atomizer Performance 7.External Spray Charcteristics 8.Drop Evaporation 9.Drop Sizing Methods Index

Atomization and Sprays

In this paper, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible and immiscible displacement processes in reservoir rocks are reviewed and discussed. Both macroscopically homogeneous and heterogeneous rocks are considered. The latter are characterized by large-scale spatial variations and correlations in their effective properties and include rocks that may be characterized by several distinct degrees of porosity, a well-known example of which is a fractured rock with two degrees of porosity---those of the pores and of the fractures. First, the diagenetic processes that give rise to the present reservoir rocks are discussed and a few geometrical models of such processes are described. Then, measurement and characterization of important properties, such as pore-size distribution, pore-space topology, and pore surface roughness, and morphological properties of fracture networks are discussed. It is shown that fractal and percolation concepts play important roles in the characterization of rocks, from the smallest length scale at the pore level to the largest length scales at the fracture and fault scales. Next, various structural models of homogeneous and heterogeneous rock are discussed, and theoretical and computer simulation approaches to flow, dispersion, and displacement in such systems are reviewed. Two different modeling approaches to these phenomena are compared. The first approach is based on the classical equations of transport supplemented with constitutive equations describing the transport and other important coefficients and parameters. These are called the continuum models. The second approach is based on network models of pore space and fractured rocks; it models the phenomena at the smallest scale, a pore or fracture, and then employs large-scale simulation and modern concepts of the statistical physics of disordered systems, such as scaling and universality, to obtain the macroscopic properties of the system. The fundamental roles of the interconnectivity of the rock and its wetting properties in dispersion and two-phase flows, and those of microscopic and macroscopic heterogeneities in miscible displacements are emphasized. Two important conceptual advances for modeling fractured rocks and studying flow phenomena in porous media are also discussed. The first, based on cellular automata, can in principle be used for computing macroscopic properties of flow phenomena in any porous medium, regardless of the complexity of its structure. The second, simulated annealing, borrowed from optimization processes and the statistical mechanics of spin glasses, is used for finding the optimum structure of a fractured reservoir that honors a limited amount of experimental data.

Flow phenomena in rocks : from continuum models to fractals, percolation, cellular automata, and simulated annealing

Droplet based microfluidics is a rapidly growing interdisciplinary field of research combining soft matter physics, biochemistry and microsystems engineering. Its applications range from fast analytical systems or the synthesis of advanced materials to protein crystallization and biological assays for living cells. Precise control of droplet volumes and reliable manipulation of individual droplets such as coalescence, mixing of their contents, and sorting in combination with fast analysis tools allow us to perform chemical reactions inside the droplets under defined conditions. In this paper, we will review available drop generation and manipulation techniques. The main focus of this review is not to be comprehensive and explain all techniques in great detail but to identify and shed light on similarities and underlying physical principles. Since geometry and wetting properties of the microfluidic channels are crucial factors for droplet generation, we also briefly describe typical device fabrication methods in droplet based microfluidics. Examples of applications and reaction schemes which rely on the discussed manipulation techniques are also presented, such as the fabrication of special materials and biophysical experiments.

https://iopscience.iop.org/article/10.1088/0034-4885/75/1/016601/pdf

Droplet based microfluidics

The induced electrorheological solid has thick columns in the field direction ({ital z} axis), spreading between two electrodes. The ground state is proposed to be a body-centered tetragonal lattice with {bold a}{sub 1}= {radical}6 {ital a}{bold {cflx x}}, {bold a}{sub 2}= {radical}6 {ital a}{bold {cflx y}}, and {bold a}{sub 3}=2{ital a}{bold {cflx z}}, where {ital a} is the radius of dielectric spheres. This bct lattice can be regarded as a compound of chains of class {ital A} and {ital B}, where chains {ital B} are obtained from chains {ital A} by shifting a distance {ital a} in the {ital z} direction.

Three-dimensional structure of induced electrorheological solid

The yield stress of magnetorheological (MR) fluids depends on the induced solid structure. Since thick columns have a yield stress much higher than a single-chain structure, we improve the yield stress of MR fluids by changing the fluid microstructure. Immediately after a magnetic field is applied, we compress the MR fluid along the field direction. Scanning electron microscopy images show that particle chains are pushed together to form thick columns. The shear force measured after the compression shows that the structure-enhanced static yield stress can reach as high as 800 kPa under a moderate magnetic field, while the same MR fluid has a yield stress of 80 kPa without compression. This improved yield stress increases with the magnetic field and compression pressure and has an upper limit well above 800 kPa. The method may also be useful for electrorheological fluids.

Structure-enhanced yield stress of magnetorheological fluids

Magnetorheological (MR) fluids, which can rapidly be changed from a liquid state to a solid state and vice versa by a magnetic field, have the potential to revolutionize several industrial sectors The key issue is to enhance their yield shear stress This paper reviews the physical mechanism and microstructure of MR fluids It finds that the weak points of the MR microstructure under a shear force are at the chains' ends Hence, a general technique, a compression-assisted-aggregation process, is developed to change the induced MR structure to a structure that consists of robust thick columns with strong ends The scanning electronic micrographic (SEM) images confirm such a structure change With this approach, MR fluids become super-strong The enhanced yield stress of MR fluids reaches 800 kPa at a moderate magnetic field

https://iopscience.iop.org/article/10.1088/0953-8984/13/50/202/pdf

Super-strong magnetorheological fluids

The electric-field-induced structures of small glass spheres in silicone oil produce laser diffraction patterns which verify, for the first time, the body-centered-tetragonal lattice structure predicted by theory. By n mechanism totally unlike that of conventionnl x-ray scattering, the incident laser beam propagates through the lattice of close-packed spheres via stable optic modes along regular arrays of transparent spheres, and then produces diffraction patterns after exiting from the lattice

Laser diffraction determination of the crystalline structure of an electrorheological fluid.

The temporal evolution of three-dimensional structure in an electrorheological (ER) fluid is examined by a computer simulation A parameter B characterizing the ratio of the Brownian force to the dipolar force is introduced For a wide range of B, the ER fluid has a rapid chain formation followed by aggregation of chains into thick columns which has a body-centered tetragonal lattice structure The Peierls-Landau instability of single chains help formation of thick columns If the Brownian force is very small, the ER system may be trapped in some local energy-minimum state

Rongjia Tao

Papers

Three-dimensional structure of induced electrorheological solid

Structure-enhanced yield stress of magnetorheological fluids

Super-strong magnetorheological fluids

Laser diffraction determination of the crystalline structure of an electrorheological fluid.

Simulation of structure formation in an electrorheological fluid.