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In colloid and nanoparticle chemistry, particle size, shape, crystallinity, surface morphology and composition are controlled by employing the mechanisms of burst nucleation, diffusional growth, aggregation, or their combinations. Here we review and survey practical examples of recently developed methods for preparing metal colloids and nanoparticles for industrial applications such as photovoltaics, catalysis, and consumer electronics. We discuss relevant theoretical models, many of which are general, and identify growth mechanisms that play a major role in other systems and applications as well.

The present study aims at integrating drug-releasing materials with signal-processing biocomputing systems. Enzymes alanine transaminase (ALT) and aspartate transaminase (AST)---biomarkers for liver injury---were logically processed by a biocatalytic cascade realizing Boolean AND gate. Citrate produced in the system was used to trigger a drug-mimicking release from alginate microspheres. In order to differentiate low vs. high concentration signals, the microspheres were coated with a protective shell composed of layer-by-layer adsorbed poly(L-lysine) and alginate. The alginate core of the microspheres was prepared from (Fe3+)-cross-linked alginate loaded with rhodamine 6G dye mimicking a drug. Dye release from the core occurred only when both biomarkers, ALT and AST, appeared at their high pathophysiological concentrations jointly indicative of liver injury. The signal-triggered response was studied at the level of a single microsphere, yielding information on the dye release kinetics.

Growth of nanoclusters and nanopillars is considered in a model of surface deposition of building blocks (atoms) diffusionally transported from solution to the forming surface structure. Processes of surface restructuring are also accounted for in the model, which then yields morphologies of interest in catalysis applications. Kinetic Monte Carlo numerical approach is utilized to explore the emergence of FCC-symmetry surface features in Pt-type metal nanostructures. Available results exemplify evaluation of the fraction of the resulting active sites with desirable properties for catalysis, such as (111)-like coordination, as well as suggest optimal growth regimes.

We review results on evaluation of loss of information in quantum registers due to their interactions with the environment. It is demonstrated that an optimal measure of the level of quantum noise effects can be introduced via the maximal absolute eigenvalue norm of deviation of the density matrix of a quantum register from that of ideal, noiseless dynamics. For a semiconductor quantum dot charge qubits interacting with acoustic phonons, explicit expressions for this measure are derived. For a broad class of environmental modes, this measure is shown to have the property that for small levels of quantum noise it is additive and scales linearly with the size of the quantum register.

We study the self-healing process of materials with embedded "glue"-carrying cells, in the regime of the onset of the initial fatigue. Three-dimensional numerical simulations within the percolation-model approach are reported. The main numerical challenge taken up in the present work, has been to extend the calculation of the conductance to three-dimensional lattices. Our results confirm the general features of the process: The onset of the material fatigue is delayed, by developing a plateau-like time-dependence of the material quality. We demonstrate that in this low-damage regime, the changes in the conductance and thus, in similar transport/response properties of the material can be used as measures of the material quality degradation. A new feature found for three dimensions, where it is much more profound than in earlier-studied two-dimensional systems, is the competition between the healing cells. Even for low initial densities of the healing cells, they interfere with each other and reduce each other's effective healing efficiency., Comment: 15 pages in PDF, with 6 figures

We report an experimental evaluation of the "input-output surface" for a biochemical AND gate. The obtained data are modeled within the rate-equation approach, with the aim to map out the gate function and cast it in the language of logic variables appropriate for analysis of Boolean logic for scalability. In order to minimize "analog" noise, we consider a theoretical approach for determining an optimal set for the process parameters to minimize "analog" noise amplification for gate concatenation. We establish that under optimized conditions, presently studied biochemical gates can be concatenated for up to order 10 processing steps. Beyond that, new paradigms for avoiding noise build-up will have to be developed. We offer a general discussion of the ideas and possible future challenges for both experimental and theoretical research for advancing scalable biochemical computing.

The random sequential adsorption (RSA) model is modified to describe damage and crack accumulation. The exclusion for object deposition (for damaged region formation) is not for the whole object, as in the standard RSA, but only for the initial point (or higher-dimensional defect) from which the damaged region or crack initiates. The one-dimensional variant of the model is solved exactly., Comment: 12 pages in ReVTeX, with 2 EPS figures

The phenomenon of burst nucleation in solution, in which a period of apparent chemical inactivity is followed by a sudden and explosive growth of nucleated particles from a solute species, has been given a widely accepted qualitative explanation by LaMer and co-workers. Here, we present a model with the assumptions of instantaneous thermalization below the critical nucleus size and irreversible diffusive growth above the critical size, which for the first time formulates LaMer's explanation of burst nucleation in a manner allowing quantitative calculations. The behavior of the model at large times is derived, with the result that the average cluster size, as measured by the number of atoms, grows linearly with time, while the width of the cluster distribution grows as the square root of time. We develop an effective numerical scheme to integrate the equations of the model and compare the asymptotic expressions to results from numerical simulation. Finally, we discuss the physical effects which cause real nucleation processes in solution to deviate from the behavior of the model., Comment: accepted by Langmuir; 15 pages, w/ 16 figures; 3 supplemental info files included in PDF

We offer a theoretical design of new systems that show promise for digital biochemical computing, including realizations of error correction by utilizing redundancy, as well as signal rectification. The approach includes information processing using encoded DNA sequences, DNAzyme biocatalyzed reactions and the use of DNA-functionalized magnetic nanoparticles. Digital XOR and NAND logic gates and copying (fanout) are designed using the same components., Comment: 14 pages in PDF

We present a review of our recent results for the comparative evaluation of the induced exchange interaction and quantum noise mediated by the bosonic environment in two-qubit systems. We report new calculations for P-donor-electron spins in Si-Ge type materials. Challenges and open problems are discussed., Comment: Invited Review, 17 pages in LaTeX, with 4 EPS figures

We outline different approaches to define and quantify decoherence. We argue that a measure based on a properly defined norm of deviation of the density matrix is appropriate for quantifying decoherence in quantum registers. For a semiconductor double quantum dot qubit, evaluation of this measure is reviewed. For a general class of decoherence processes, including those occurring in semiconductor qubits, we argue that this measure is additive: It scales linearly with the number of qubits., Comment: Revised version, 26 pages, in LaTeX, 3 EPS figures

We summarize semiclassical modeling methods, including drift-diffusion, kinetic transport equation and Monte Carlo simulation approaches, utilized in studies of spin dynamics and transport in semiconductor structures. As a review of the work by our group, several examples of applications of these modeling techniques are presented., Comment: 31 pages, 9 figures

We demonstrate by an explicit model calculation that the decay of entanglement of two two-state systems (two qubits) is governed by the product of the factors that measure the degree of decoherence of each of the qubits, subject to independent sources of quantum noise. This demonstrates an important physical property that separated open quantum systems can evolve quantum mechanically on time scales larger than the times for which they remain entangled., Comment: 4 pages, 1 figure

We report the first theoretical estimate of the nuclear-spin dephasing time T_2 owing to the spin interaction with the two-dimensional electron gas, when the latter is in the integer quantum Hall state, in a two-dimensional heterojunction or quantum well at low temperature and in large applied magnetic field. We establish that the leading mechanism of dephasing is due to the impurity potentials that influence the dynamics of the spin via virtual magnetic spin-exciton scattering. Implications of our results for implementation of nuclear spins as quantum bits (qubits) for quantum computing are discussed., Comment: 19 pages in plain TeX

We study a general quantum system interacting with environment modeled by the bosonic heat bath of Caldeira and Leggett type. General interaction Hamiltonians are considered that commute with the system's Hamiltonian so that there is no energy exchange between the system and bath. We argue that this model provides an appropriate description of adiabatic quantum decoherence, i.e., loss of entanglement on time scales short compared to those of thermal relaxation processes associated with energy exchange with the bath. The interaction Hamiltonian is then proportional to a conserved "pointer observable." Calculation of the elements of the reduced density matrix of the system is carried out exactly, and time-dependence of decoherence is identified, similar to recent results for related models. Our key finding is that the decoherence process is controlled by spectral properties of the interaction rather than system's Hamiltonian., Comment: 29 pages in TeX

We describe a quantum information processor (quantum computer) based on the hyperfine interactions between the conduction electrons and nuclear spins embedded in a two-dimensional electron system in the quantum-Hall regime. Nuclear spins can be controlled individually by electromagnetic pulses. Their interactions, which are of the spin-exchange type, can be possibly switched on and off pair-wise dynamically, for nearest neighbors, by controlling impurities. We also propose the way to feed in the initial data and explore ideas for reading off the final results., Comment: 12 pages in LaTeX + 1 PostScript figure

We develop an analytical diffusion-equation-type approximation scheme for the one-dimensional coagulation reaction A+A->A with partial reaction probability on particle encounters which are otherwise hard-core. The new approximation describes the crossover from the mean-field rate-equation behavior at short times to the universal, fluctuation-dominated behavior at large times. The approximation becomes quantitatively accurate when the system is initially close to the continuum behavior, i.e., for small initial density and fast reaction. For large initial density and slow reaction, lattice effects are nonnegligible for an extended initial time interval. In such cases our approximation provides the correct description of the initial mean-field as well as the asymptotic large-time, fluctuation-dominated behavior. However, the intermediate-time crossover between the two regimes is described only semiquantitatively., Comment: 21 pages, plain TeX

Random sequential adsorption (RSA) models have been studied due to their relevance to deposition processes on surfaces. The depositing particles are represented by hard-core extended objects; they are not allowed to overlap. Numerical Monte Carlo studies and analytical considerations are reported for 1D and 2D models of multilayer adsorption processes. Deposition without screening is investigated, in certain models the density may actually increase away from the substrate. Analytical studies of the late stage coverage behavior show the crossover from exponential time dependence for the lattice case to the power law behavior in the continuum deposition. 2D lattice and continuum simulations rule out some "exact" conjectures for the jamming coverage. For the deposition of dimers on a 1D lattice with diffusional relaxation we find that the limiting coverage (100%) is approached according to the ~1/t**0.5 power-law preceded, for fast diffusion, by the mean-field crossover regime with the intermediate ~1/t behavior. In case of k-mer deposition (k>3) with diffusion the void fraction decreases according to the power-law t**[-1/(k-1)]. In the case of RSA of lattice hard squares in 2D with diffusional relaxation the approach to the full coverage is ~t**(-0.5)., Comment: 5 pages (plain LaTeX)

We review recent numerical studies and the phenomenology of spatially synchronized collective states in many-body dynamical systems. These states exhibit thermodynamic noise superimposed on the collective, quasiperiodic order parameter evolution with typically one basic irrational frequency. We concentrate on the description of the global temporal properties in terms of second-order difference equations., Comment: 11 pages (plain TeX), 4 figures (PostScript), preprint OUTP-92-51S

We study by Monte Carlo computer simulations random sequential adsorption (RSA) with diffusional relaxation, of lattice hard squares in two dimensions. While for RSA without diffusion the coverage approaches its maximum jamming value (large-time fractional coverage) exponentially, added diffusion allows the deposition process to proceed to the full coverage. The approach to the full coverage is consistent with the t**(-1/2) power law reminiscent of the equilibrium cluster coarsening in models with nonconserved order-parameter dynamics., Comment: 11 pages (plain TeX), 4 figures (PostScript)

We derive an improved mean-field approximation for k-body annihilation reactions kA --> inert, for hard-core diffusing particles on a line, annihilating in groups of k neighbors with probability 0 < q <= 1. The hopping and annihilation processes are correlated to mimic chemical reactions. Our new mean-field theory accounts for hard-core particle properties and has a larger region of applicability than the standard chemical rate equation especially for large k values. Criteria for validity of the mean-field theory and its use in phenomenological data fits are derived. Numerical tests are reported for k=3,4,5,6., Comment: 16 pages, TeX (plain)

We report numerical simulation of the deposition of spherical particles on a planar surface, by ballistic, straight-line trajectory transport, and assuming irreversible adhesion on contact with the surface or previously deposited particles. Our data indicate that the deposit formed has a loosely layered structure within few diameters from the surface. This structure can be explained by a model of growth via chain formation. Away from the surface we found evidence of a monotonic, power-law approach to the bulk density. Both density and contact-statistics results suggest that the deposit formed is sparse: the space-filling fraction is about 15%, and the average number of contacts is 2. The morphology of the deposit both near the surface and in the bulk seems to be a result of competition of screening and branching; nearly half of all the spheres are either single-contact dangling ends, or branching nodes with more than two contacts., Comment: 20 pages, TeX (plain)