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High-resolution single-shot nonrelativistic ultrafast electron microscopy (UEM) relies on adaptive optics to compress high-intensity bunches using radio frequency (RF) cavities. We present a comprehensive discussion of the analytic approaches available to characterize bunch dynamics as an electron bunch goes through a longitudinal focal point after an RF cavity where space charge effects can be large. Methods drawn from the Coulomb explosion literature, the accelerator physics literature, and the analytic Gaussian model developed for UEM are compared, utilized, and extended in some cases. In particular the longitudinal focus may occur in two different regimes, a bounce-back regime and a crossover regime; and we characterize the critical point separating these regimes in the zero-emittance model. Results from N-particle simulations using efficient multipole methods are compared to the theoretical models revealing features requiring extensions of the analytic approaches; and in particular mechanisms for emittance growth and transfer are discussed.

Understanding and controlling ultrafast charge carrier dynamics is of fundamental importance in diverse fields of (quantum) science and technology. Here, we create a three-dimensional hot electron gas through two-photon photoemission from a copper surface in vacuum. We employ an ultrafast electron microscope to record movies of the subsequent electron dynamics on the picosecond-nanosecond time scale. After a prompt Coulomb explosion, the subsequent dynamics is characterized by a rapid oblate-to-prolate shape transformation of the electron gas, and periodic and long-lived electron cyclotron oscillations inside the magnetic field of the objective lens. In this regime, the collective behavior of the oscillating electrons causes a transient, mean-field lensing effect and pronounced distortions in the images. We derive an analytical expression for the time-dependent focal length of the electron-gas lens, and perform numerical electron dynamics and probe image simulations to determine the role of Coulomb self-fields and image charges. This work inspires the visualization of cyclotron dynamics inside two-dimensional electron-gas materials and enables the elucidation of electron/plasma dynamics and properties that could benefit the development of high-brightness electron and X-ray sources.

A frontier challenge in implementing femtosecond electron microscopy is to gain precise optical control of intense beams to mitigate collective space charge effects for significantly improving the throughput. Here, we explore the flexible uses of an RF cavity as a longitudinal lens in a high-intensity beam column for condensing the electron beams both temporally and spectrally, relevant to the design of ultrafast electron microscopy. Through the introduction of a novel atomic grating approach for characterization of electron bunch phase space and control optics, we elucidate the principles for predicting and controlling the phase space dynamics to reach optimal compressions at various electron densities and generating conditions. We provide strategies to identify high-brightness modes, achieving ∼100 fs and ∼1 eV resolutions with 10 6 electrons per bunch, and establish the scaling of performance for different bunch charges. These results benchmark the sensitivity and resolution from the fundamental beam brightness perspective and also validate the adaptive optics concept to enable delicate control of the density-dependent phase space structures to optimize the performance, including delivering ultrashort, monochromatic, high-dose, or coherent electron bunches.

The study presents an algorithm, ParSCAPE, for model-independent extraction of peak positions and intensities from atomic pair distribution functions (PDFs). It provides a statistically motivated method for determining parsimony of extracted peak models using the information-theoretic Akaike information criterion (AIC) applied to plausible models generated within an iterative framework of clustering and chi-square fitting. All parameters the algorithm uses are in principle known or estimable from experiment, though careful judgment must be applied when estimating the PDF baseline of nanostructured materials. ParSCAPE has been implemented in the Python program SrMise. Algorithm performance is examined on synchrotron X-ray PDFs of 16 bulk crystals and two nanoparticles using AIC-based multimodeling techniques, and particularly the impact of experimental uncertainties on extracted models. It is quite resistant to misidentification of spurious peaks coming from noise and termination effects, even in the absence of a constraining structural model. Structure solution from automatically extracted peaks using the Liga algorithm is demonstrated for 14 crystals and for C60. Special attention is given to the information content of the PDF, theory and practice of the AIC, as well as the algorithm's limitations.

Characterizing and understanding the emergence of multiple macroscopically ordered electronic phases through subtle tuning of temperature, pressure, and chemical doping has been a long-standing central issue for complex materials research. We report the first comprehensive studies of optical doping-induced emergence of stable phases and metastable hidden phases visualized in situ by femtosecond electron crystallography. The electronic phase transitions are triggered by femtosecond infrared pulses, and a temperature-optical density phase diagram is constructed and substantiated with the dynamics of metastable states, highlighting the cooperation and competition through which the macroscopic quantum orders emerge. These results elucidate key pathways of femtosecond electronic switching phenomena and provide an important new avenue to comprehensively investigate optical doping-induced transition states and phase diagrams of complex materials with wide-ranging applications.

Reconstruction of complex structures is an inverse problem arising in virtually all areas of science and technology, from protein structure determination to bulk heterostructure solar cells and the structure of nanoparticles. We cast this problem as a complex network problem where the edges in a network have weights equal to the Euclidean distance between their endpoints. We present a method for reconstruction of the locations of the nodes of the network given only the edge weights of the Euclidean network. The theoretical foundations of the method are based on rigidity theory, which enables derivation of a polynomial bound on its efficiency. An efficient implementation of the method is discussed and timing results indicate that the run time of the algorithm is polynomial in the number of nodes in the network. We have reconstructed Euclidean networks of about 1000 nodes in approximately 24 h on a desktop computer using this implementation. We also reconstruct Euclidean networks corresponding to polymer chains in two dimensions and planar graphene nanoparticles. We have also modified our base algorithm so that it can successfully solve random point sets when the input data are less precise.

We generate percolating fullerene-polymer bulk heterostructures that are consistent with the experimental characterization of a nanostructure, in particular neutron reflectometry and small-angle neutron scattering data from as-cast and annealed poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl C61-butyric acid methyl ester systems. Transport simulations correlate changes in exciton dissociation efficiency and charge collection efficiency with morphological features including characteristic domain size, fullerene concentration profile, degree of fullerene sequestration, and degree of P3HT crystallization.

Using optical, TEM, and ultrafast electron diffraction experiments we find that single crystal VO(2) microbeams gently placed on insulating substrates or metal grids exhibit different behaviors, with structural and metal-insulator transitions occurring at the same temperature for insulating substrates, while for metal substrates a new monoclinic metal phase lies between the insulating monoclinic phase and the metallic rutile phase. The structural and electronic phase transitions in these experiments are strongly first order and we discuss their origins in the context of current understanding of multiorbital splitting, strong correlation effects, and structural distortions that act cooperatively in this system.

Cells are regulated by networks of controllers having many targets, and targets affected by many controllers, in a "many-to-many" control structure. Here we study several of these bipartite (two-layer) networks. We analyze both naturally occurring biological networks (composed of transcription factors controlling genes, microRNAs controlling mRNA transcripts, and protein kinases controlling protein substrates) and a drug-target network composed of kinase inhibitors and of their kinase targets. Certain statistical properties of these biological bipartite structures seem universal across systems and species, suggesting the existence of common control strategies in biology. The number of controllers is ∼8% of targets and the density of links is 2.5%±1.2%. Links per node are predominantly exponentially distributed. We explain the conservation of the mean number of incoming links per target using a mathematical model of control networks, which also indicates that the "many-to-many" structure of biological control has properties of efficient robustness. The drug-target network has many statistical properties similar to the biological networks and we show that drug-target networks with biomimetic features can be obtained. These findings suggest a completely new approach to pharmacological control of biological systems. Molecular tools, such as kinase inhibitors, are now available to test if therapeutic combinations may benefit from being designed with biomimetic properties, such as "many-to-many" targeting, very wide coverage of the target set, and redundancy of incoming links per target.

Effective therapy of complex diseases requires control of highly nonlinear complex networks that remain incompletely characterized. In particular, drug intervention can be seen as control of cellular network activity. Identification of control parameters presents an extreme challenge due to the combinatorial explosion of control possibilities in combination therapy and to the incomplete knowledge of the systems biology of cells. In this review paper, we describe the main current and proposed approaches to the design of combinatorial therapies, including the heuristic methods used now by clinicians and alternative approaches suggested recently by several authors. New approaches for designing combinations arising from systems biology are described. We discuss in special detail the design of algorithms that identify optimal control parameters in cellular networks based on a quantitative characterization of control landscapes, maximizing utilization of incomplete knowledge of the state and structure of intracellular networks. The use of new technology for high-throughput measurements is key to these new approaches to combination therapy and essential for the characterization of control landscapes and implementation of the algorithms. Combinatorial optimization in medical therapy is also compared with the combinatorial optimization of engineering and materials science and similarities and differences are delineated.

Computational techniques for nanostructure determination of substances that resist standard crystallographic methods are often laborious processes starting from initial guess solutions not derived from experimental data. The Liga algorithm can create nanostructures using only lists of lengths or distances between atom pairs, providing an experimental basis for starting structures. These distance lists may be extracted from a variety of experimental probes and we illustrate the procedure with distances determined from the pair distribution function. Candidate subclusters that are a subset of a structure's atoms compete based on adherence to the length list. Atoms are added to well performing candidates and removed from poor ones, until a complete structure with sufficient agreement to the length list emerges. The Liga algorithm is shown to reliably recreate Lennard-Jones clusters from ideal length lists and the C60 structure from neutron-scattering data. The correct fullerene structure was obtained with experimental data which missed several distances and had loosened constraints on distance multiplicity. This suggests that the Liga algorithm may have robust applicability for a wide range of nanostructures even in the absence of ideal data.

The dimensions of individual deuterated polystyrene (d-PS) chains in a well-dispersed mixture of protonated polystyrene and chemically identical nanoparticles was determined by neutron scattering. A 10%-20% increase in the radius of gyration of d-PS was found when the nanoparticles are homogeneously dispersed in the polymer, an effect that occurs only when the radius of gyration of the polymer is larger than the nanoparticle radius. These results are reconciled with the existing literature.

Background: Selective control in a population is the ability to control a member of the population while leaving the other members relatively unaffected. The concept of selective control is developed using cell death or apoptosis in heterogeneous cell populations as an example. Control of apoptosis is essential in a variety of therapeutic environments, including cancer where cancer cell death is a desired outcome and Alzheimer's disease where neuron survival is the desired outcome. However, in both cases these responses must occur with minimal response in other cells exposed to treatment; that is, the response must be selective., Methodology and Principal Findings: Apoptosis signaling in heterogeneous cells is described by an ensemble of gene networks with identical topology but different link strengths. Selective control depends on the statistics of signaling in the ensemble of networks, and we analyze the effects of superposition, non-linearity and feedback on these statistics. Parallel pathways promote normal statistics while series pathways promote skew distributions, which in the most extreme cases become log-normal. We also show that feedback and non-linearity can produce bimodal signaling statistics, as can discreteness and non-linearity. Two methods for optimizing selective control are presented. The first is an exhaustive search method and the second is a linear programming based approach. Though control of a single gene in the signaling network yields little selectivity, control of a few genes typically yields higher levels of selectivity. The statistics of gene combinations susceptible to selective control in heterogeneous apoptosis networks is studied and is used to identify general control strategies., Conclusions and Significance: We have explored two methods for the study of selectivity in cell populations. The first is an exhaustive search method limited to three node perturbations. The second is an effective linear model, based on interpolation of single node sensitivity, in which the selective combinations can be found by linear programming optimization. We found that selectivity is promoted by acting on the least sensitive nodes in the case of weak populations, while selective control of robust populations is optimized through perturbations of more sensitive nodes. High throughput experiments with heterogeneous cell lines could be designed in an analogous manner, with the further possibility of incorporating the selectivity optimization process into a closed-loop control system.

We show it is possible to assemble nanoparticle-polymer layers in a controllable manner dictated by the difference in nano-object morphology and dielectric properties. A thin (10-100 nm) layer of the two components is spin coated onto a solid substrate and the system thermally aged to activate a cross-linking process between polymer molecules. The nanoparticles segregate to the solid substrate prior to complete cross-linking if entropic forces are dominant or to the air interface if dielectric (surface energy) forces are properly tuned. Subsequent layers are then spin coated onto the layer below, and the process is repeated to create layered structures with nanometer accuracy useful for tandem solar cells, sensors, optical coatings, etc. Unlike other self-assembly techniques the layer thicknesses are dictated by the spin coating conditions and relative concentration of the two components.

Core percolation and maximum independent set on random graphs have recently been characterized using the methods of statistical physics. Here we present a statistical physics study of these problems on bond diluted triangular lattices. Core percolation critical behavior is found to be consistent with the standard percolation values, though there are strong finite size effects. A transfer matrix method is developed and applied to find accurate values of the density and degeneracy of the maximum independent set on lattices of limited width but large length. An extrapolation of these results to the infinite lattice limit yields high precision results, which are tabulated. These results are compared to results found using both vertex based and edge based local probability recursion algorithms, which have proven useful in the analysis of hard computational problems, such as the satisfiability problem.

Advances in materials science and molecular biology followed rapidly from the ability to characterize atomic structure using single crystals. Structure determination is more difficult if single crystals are not available. Many complex inorganic materials that are of interest in nanotechnology have no periodic long-range order and so their structures cannot be solved using crystallographic methods. Here we demonstrate that ab initio structure solution of these nanostructured materials is feasible using diffraction data in combination with distance geometry methods. Precise, sub-ångström resolution distance data are experimentally available from the atomic pair distribution function (PDF). Current PDF analysis consists of structure refinement from reasonable initial structure guesses and it is not clear, a priori, that sufficient information exists in the PDF to obtain a unique structural solution. Here we present and validate two algorithms for structure reconstruction from precise unassigned interatomic distances for a range of clusters. We then apply the algorithms to find a unique, ab initio, structural solution for C60 from PDF data alone. This opens the door to sub-ångström resolution structure solution of nanomaterials, even when crystallographic methods fail.

Traditionally the dispersion of particles in polymeric materials has proven difficult and frequently results in phase separation and agglomeration. We show that thermodynamically stable dispersion of nanoparticles into a polymeric liquid is enhanced for systems where the radius of gyration of the linear polymer is greater than the radius of the nanoparticle. Dispersed nanoparticles swell the linear polymer chains, resulting in a polymer radius of gyration that grows with the nanoparticle volume fraction. It is proposed that this entropically unfavorable process is offset by an enthalpy gain due to an increase in molecular contacts at dispersed nanoparticle surfaces as compared with the surfaces of phase-separated nanoparticles. Even when the dispersed state is thermodynamically stable, it may be inaccessible unless the correct processing strategy is adopted, which is particularly important for the case of fullerene dispersion into linear polymers.

We study the culling avalanches which occur after the "death" of a single randomly chosen site in a network where sites are unstable, and are culled, if they have coordination less than an integer parameter m. Avalanche distributions are presented for triangular and cubic lattices for values of m where the associated bootstrap transitions are either first or second order. In second order cases, the culling avalanche distribution is found to be exponential, while in first order cases it follows a power law. We present an exact relation between culling avalanches and conventional bootstrap percolation and show that a relation proposed by Manna [Physica A 261, 351 (1998)] can be a good approximation for strongly first order bootstrap transitions but not for continuous bootstrap transitions.

Percolation theory is now standard in the analysis of polycrystalline materials where the grain boundaries can be divided into two distinct classes, namely "good" boundaries that have favorable properties and "bad" boundaries that seriously degrade the material performance. Grain-boundary engineering (GBE) strives to improve material behavior by engineering the volume fraction c and arrangement of good grain boundaries. Two key percolative processes in GBE materials are the onset of percolation of a strongly connected aggregate of grains, and the onset of a connected path of weak grain boundaries. Using realistic polycrystalline microstructures, we find that in two dimensions the threshold for strong aggregate percolation c(SAP) and the threshold for weak boundary percolation c(WBP) are equivalent and have the value c(SAP) = c(WBP) =0.38 (1) , which is slightly higher than the threshold found for regular hexagonal grain structures, c(RH) =2 sin (pi/18) =0.347... . In three dimensions strong aggregate percolation and weak boundary percolation occur at different locations and we find c(SAP) =0.12 (3) and c(WBP) =0.77 (3) . The critical current in high T(c) materials and the cohesive energy in structural systems are related to the critical manifold problem in statistical physics. We develop a theory of critical manifolds in GBE materials, which has three distinct regimes: (i) low concentrations, where random manifold theory applies, (ii) critical concentrations where percolative scaling theory applies, and (iii) high concentrations, c> c(SAP) , where the theory of periodic elastic media applies. Regime (iii) is perhaps most important practically and is characterized by a critical length L(c) , which is the size of cleavage regions on the critical manifold. In the limit of high contrast epsilon-->0 , we find that in two dimensions L(c) proportional, gc/ (1-c) , while in three dimensions L(c) proportional, g exp [ b(0) c/ (1-c) ] / [c (1-c) ](1/2) , where g is the average grain size, epsilon is the ratio of the bonding energy of the weak boundaries to that of the strong boundaries, and b(0) is a constant which is of order 1. Many of the properties of GBE materials can be related to L(c) , which diverges algebraically on approach to c=1 in two dimensions, but diverges exponentially in that limit in three dimensions. We emphasize that GBE percolation processes and critical manifold behavior are very different in two dimensions as compared to three dimensions. For this reason, the use of two dimensional models to understand the behavior of bulk GBE materials can be misleading.

We study the surfaces of lowest energy through model polycrystalline materials in two and three dimensions. When the grain boundaries are sufficiently weak, these critical manifolds (CM's) lie entirely on grain boundaries, while when the grain boundaries are strong, cleavage occurs. A scaling theory for the intergranular to transgranular transition of CM's is developed. The key parameters are the average grain size g, the ratio of grain boundary to the grain interior energy, epsilon, and the sample size L. The key result is that a critical length scale exists, L(c)(g,epsilon), so that on short length scales lL(c), the critical manifold is rough. We develop a scaling theory for L(c) and find that in two dimensions L(c) approximately gx(y(2)), while in three dimensions L(c) approximately g exp(bx(y(3))), where x=epsilon/(1-epsilon) and b is a constant. Data from realistic polycrystalline grain structures are used to test the scaling theory. The exact lowest energy surface through model grain structures is found using a mapping to the minimum-cut/maximum-flow problem in computer science. As a function of grain-boundary energy, we observe the crossover from grain-boundary rupture to mixed mode failure (a mixture of transgramular and intergranular modes) and finally cleavage and that the two-dimensional data are consistent with y(2) approximately 3.0+/-0.3, while the three-dimensional data are more difficult to analyze, but are consistent with y(3) approximately 3.5+/-1.0.

We present large-scale simulations of the diffusion constant D of a random composite consisting of aligned platelets with aspect ratio a/b>>1 in a matrix (with diffusion constant D0) and find that D/D(0)=1/(1+c(1)x+c(2)x(2)), where x=av(f)/b and v(f) is the platelet volume fraction. We demonstrate that for large aspect ratio platelets the pair term (x(2)) dominates suggesting large property enhancements for these materials. However, a small amount of face-to-face ordering of the platelets markedly degrades the efficiency of platelet reinforcement.

Two attractive and often used ideas, namely, universality and the concept of a zero-temperature fixed point, are violated in the infinite-range random-field Ising model. In the ground state we show that the exponents can depend continuously on the disorder and so are nonuniversal. However, we also show that at finite temperature the thermal order-parameter exponent 1/2 is restored so that temperature is a relevant variable. Broader implications of these results are discussed.

We study at T=0 the minimum energy of a domain wall and its gap to the first excited state, concentrating on two-dimensional random-bond Ising magnets. The average gap scales as deltaE1 approximately L(straight theta)f(N(z)), where f(y) approximately [ln y](-1/2), straight theta is the energy fluctuation exponent, L is the length scale, and N(z) is the number of energy valleys. The logarithmic scaling is due to extremal statistics, which is illustrated by mapping the problem into the Kardar-Parisi-Zhang roughening process. It follows that the susceptibility of domain walls also has a logarithmic dependence on the system size.

We show that the geometry of minimum spanning trees (MST) on random graphs is universal. Because of this geometric universality, we are able to characterize the energy of MST using a scaling distribution [P(epsilon)] found using uniform disorder. We show that the MST energy for other disorder distributions is simply related to P(epsilon). We discuss the relationship to invasion percolation, to the directed polymer in a random media, to uniform spanning trees, and also the implications for the broader issue of universality in disordered systems.

We analyze intermittence and roughening of an elastic interface or domain wall pinned in a periodic potential, in the presence of random-bond disorder in 1+1 and 2+1 dimensions. Though the ensemble average behavior is smooth, the typical behavior of a large sample is intermittent, and does not self-average to a smooth behavior. Instead, large fluctuations occur in the mean location of the interface and the onset of interface roughening is via an extensive fluctuation which leads to a jump in the roughness of order lambda, the period of the potential. Analytical arguments based on extreme statistics are given for the number of the minima of the periodicity visited by the interface and for the roughening crossover, which is confirmed by extensive exact ground state calculations.

We analyze, in both (1+1) and (2+1) dimensions, a periodic elastic medium in which the periodicity is such that at long distances the behavior is always in the random-substrate universality class. This contrasts with the models with an additive periodic potential in which, according to the field-theoretic analysis of Bouchaud and Georges and more recently of Emig and Nattermann, the random manifold class dominates at long distances in (1+1) and (2+1) dimensions. The models we use are random-bond Ising interfaces in hypercubic lattices. The exchange constants are random in a slab of size L(d-1)xlambda and these coupling constants are periodically repeated, with a period lambda, along either 10 or 11 [in (1+1) dimensions] and 100 or 111 [in (2+1) dimensions]. Exact ground-state calculations confirm scaling arguments which predict that the surface roughness w behaves as w approximately L(2/3), L<>L(c) with L(c) approximately lambda(3/2) in (1+1) dimensions, and w approximately L0.42,L<>L(c) with L(c) approximately lambda(2. 38) in (2+1) dimensions.

We introduce an exact algorithm to calculate the distribution of large low energy clusters (droplets) in disordered manifolds and disordered magnets, and we analyze the extent to which these clusters can be treated as independent two-level systems. We show that interfaces in randomly diluted networks always have broad droplet distributions, while diluted antiferromagnets in a field can have either power law or exponential droplet distributions.

We show that the dynamics of the pair correlation function in a step train can pinpoint the dominant relaxation mechanism occurring at a crystal surface. Evaporation-condensation and step-edge diffusion do not produce dynamical correlations between neighboring steps, while terrace diffusion may lead to correlations which fall off like a power law with distance and which are peaked at a characteristic time. We derive these results within a "real space" Langevin formalism which is based on diffusion kernels which are different for each mass transport process. We validate this formalism by reproducing the step fluctuation autocorrelation function. We then derive results on the pair correlation between different steps. Results for solvable limiting cases are summarized in Tables I and II of the paper. As an intermediate step in the analysis we also find expressions for the relaxation time tau(pq) of a mode of wave number q along the steps and wave number p perpendicular to the steps, which we also discuss and compare with prior work.

Simple models play a key role in the microstructural analysis of mechanical failure in composites and other materials with complex and often disordered microstructures. Although equal load-sharing-models are amenable to rigorous statistical analysis, problems with local load enhancements near failed regions of the material have so far resisted exact analysis. Here we show for the first time, that some of the simpler of these local-load - sharing models can be solved exactly using a sub-stochastic matrix method. For diluted fiber bundles with local load sharing, it is possible to find a compact expression for the characteristic equation of the sub-stochastic matrix, and from it obtain an asymptotic expansion for the largest eigenvalue of the matrix. This in turn gives the asymptotic behavior of the size effect and statistics of the fiber-bundle models. We summarize these results, and show that the important features of the exact result can be obtained from a single scaling analysis we had developed previously. We also compare the statistics of fracture with the appropriate limiting extreme-value survival distribution (a Gumbel distribution), and, as previously indicated by Harlow and Phoenix, note that the Gumbel distribution performs quite poorly in this problem. We comment on the physical origin of this discrepancy.