Random Landscape Research Articles

Effects of long-range disorder and electronic interactions on the optical properties of graphene quantum dots

We theoretically investigate the effects of long-range disorder and electron-electron interactions on the optical properties of hexagonal armchair graphene quantum dots consisting of up to 10806 atoms. The numerical calculations are performed using a combination of tight-binding, mean-field Hubbard and configuration interaction methods. Imperfections in the graphene quantum dots are modelled as a long-range random potential landscape, giving rise to electron-hole puddles. We show that, when the electron-hole puddles are present, tight-binding method gives a poor description of the low-energy absorption spectra compared to meanfield and configuration interaction calculation results. As the size of the graphene quantum dot is increased, the universal optical conductivity limit can be observed in the absorption spectrum. When disorder is present, calculated absorption spectrum approaches the experimental results for isolated monolayer of graphene sheet.

The rich phase structure of a mutator model.

We propose a modification of the Crow-Kimura and Eigen models of biological molecular evolution to include a mutator gene that causes both an increase in the mutation rate and a change in the fitness landscape. This mutator effect relates to a wide range of biomedical problems. There are three possible phases: mutator phase, mixed phase and non-selective phase. We calculate the phase structure, the mean fitness and the fraction of the mutator allele in the population, which can be applied to describe cancer development and RNA viruses. We find that depending on the genome length, either the normal or the mutator allele dominates in the mixed phase. We analytically solve the model for a general fitness function. We conclude that the random fitness landscape is an appropriate choice for describing the observed mutator phenomenon in the case of a small fraction of mutators. It is shown that the increase in the mutation rates in the regular and the mutator parts of the genome should be set independently; only some combinations of these increases can push the complex biomedical system to the non-selective phase, potentially related to the eradication of tumors.

Colloids exposed to random potential energy landscapes: From particle number density to particle-potential and particle-particle interactions.

Colloidal particles were exposed to a random potential energy landscape that has been created optically via a speckle pattern. The mean particle density as well as the potential roughness, i.e., the disorder strength, were varied. The local probability density of the particles as well as its main characteristics were determined. For the first time, the disorder-averaged pair density correlation function g((1))(r) and an analogue of the Edwards-Anderson order parameter g((2))(r), which quantifies the correlation of the mean local density among disorder realisations, were measured experimentally and shown to be consistent with replica liquid state theory results.

Active dynamics of colloidal particles in time-varying laser speckle patterns.

Colloidal particles immersed in a dynamic speckle pattern experience an optical force that fluctuates both in space and time. The resulting dynamics presents many interesting analogies with a broad class of non-equilibrium systems like: active colloids, self propelled microorganisms, transport in dynamical intracellular environments. Here we show that the use of a spatial light modulator allows to generate light fields that fluctuate with controllable space and time correlations and a prescribed average intensity profile. In particular we generate ring-shaped random patterns that can confine a colloidal particle over a quasi one-dimensional random energy landscape. We find a mean square displacement that is diffusive at both short and long times, while a superdiffusive or subdiffusive behavior is observed at intermediate times depending on the value of the speckles correlation time. We propose two alternative models for the mean square displacement in the two limiting cases of a short or long speckles correlation time. A simple interpolation formula is shown to account for the full phenomenology observed in the mean square displacement across the entire range from fast to slow fluctuating speckles.

Hartree–Fock mean-field theory for trapped dirty bosons

Here we work out in detail a non-perturbative approach to the dirty boson problem, which relies on the Hartree–Fock theory and the replica method. For a weakly interacting Bose gas within a trapped confinement and a delta-correlated disorder potential at finite temperature, we determine the underlying free energy. From it we determine via extremization self-consistency equations for the three components of the particle density, namely the condensate density, the thermal density, and the density of fragmented local Bose–Einstein condensates within the respective minima of the random potential landscape. Solving these self-consistency equations in one and three dimensions in two other publications has revealed how these three densities change for increasing disorder strength.

Identifying Categorical Land Use Transition and Land Degradation in Northwestern Drylands of Ethiopia

Land use transition in dryland ecosystems is one of the major driving forces to landscape change that directly impacts the welfare of humans. In this study, the support vector machine (SVM) classification algorithm and cross tabulation matrix analysis are used to identify systematic and random processes of change. The magnitude and prevailing signals of land use transitions are assessed taking into account net change and swap change. Moreover, spatiotemporal patterns and the relationship of precipitation and the Normalized Difference Vegetation Index (NDVI) are explored to evaluate landscape degradation. The assessment showed that 44% of net change and about 54% of total change occurred during the study period, with the latter being due to swap change. The conversion of over 39% of woodland to cropland accounts for the existence of the highest loss of valuable ecosystem of the region. The spatial relationship of NDVI and precipitation also showed R2 of below 0.5 over 55% of the landscape with no significant changes in the precipitation trend, thus representing an indicative symptom of land degradation. This in-depth analysis of random and systematic landscape change is crucial for designing policy intervention to halt woodland degradation in this fragile environment.

Vacuum statistics and stability in axionic landscapes

We investigate vacuum statistics and stability in random axionic landscapes. For this purpose we developed an algorithm for a quick evaluation of the tunneling action, which in most cases is accurate within 10%. We find that stability of a vacuum is strongly correlated with its energy density, with lifetime rapidly growing as the energy density is decreased. On the other hand, the probability P(B) for a vacuum to have a tunneling action B greater than a given value declines as a slow power law in B. This is in sharp contrast with the studies of random quartic potentials, which found a fast exponential decline of P(B). Our results suggest that the total number of relatively stable vacua (say, with B>100) grows exponentially with the number of fields N and can get extremely large for N≳ 100. The problem with this kind of model is that the stable vacua are concentrated near the absolute minimum of the potential, so the observed value of the cosmological constant cannot be explained without fine-tuning. To address this difficulty, we consider a modification of the model, where the axions acquire a quadratic mass term, due to their mixing with 4-form fields. This results in a larger landscape with a much broader distribution of vacuum energies. The number of relatively stable vacua in such models can still be extremely large.

Brownian motion on random dynamical landscapes

We present a study of overdamped Brownian particles moving on a random landscape of dynamic and deformable obstacles (spatio-temporal disorder). The obstacles move randomly, assemble, and dissociate following their own dynamics. This landscape may account for a soft matter or liquid environment in which large obstacles, such as macromolecules and organelles in the cytoplasm of a living cell, or colloids or polymers in a liquid, move slowly leading to crowding effects. This representation also constitutes a novel approach to the macroscopic dynamics exhibited by active matter media. We present numerical results on the transport and diffusion properties of Brownian particles under this disorder biased by a constant external force. The landscape dynamics are characterized by a Gaussian spatio-temporal correlation, with fixed time and spatial scales, and controlled obstacle concentrations.

Experimental creation and characterization of random potential-energy landscapes exploiting speckle patterns

The concept of potential energy landscapes is applied in many areas of science. We experimentally realize a random potential energy landscape (rPEL) to which colloids are exposed. This is achieved exploiting the interaction of matter with light. The optical set-up is based on a special diffuser, which creates a top-hat beam containing a speckle pattern. This is imposed on colloids. The effect of the speckle pattern on the colloids can be described by a rPEL. The speckle pattern as well as the rPEL are quantitatively characterized. The distributions of both, intensity and potential energy values, can be approximated by Gamma distributions. They can be tuned from exponential to approximately Gaussian with variable standard deviation, which determines the contrast of the speckles and the roughness of the rPEL. Moreover, the characteristic length scales, e.g. the speckle size, can be controlled. By rotating the diffuser, furthermore, a flat potential can be created and hence only radiation pressure exerted on the particles.

Time- and ensemble-averages in evolving systems: the case of Brownian particles in random potentials

Anomalous diffusion is a ubiquitous phenomenon in complex systems. It is often quantified using time- and ensemble-averages to improve statistics, although time averages represent a non-local measure in time and hence can be difficult to interpret. We present a detailed analysis of the influence of time- and ensemble-averages on dynamical quantities by investigating Brownian particles in a rough potential energy landscape (PEL). Initially, the particle ensemble is randomly distributed, but the occupancy of energy values evolves towards the equilibrium distribution. This relaxation manifests itself in the time evolution of time- and ensemble-averaged dynamical measures. We use Monte Carlo simulations to study particle dynamics in a potential with a Gaussian distribution of energy values, where the long-time limit of the diffusion coefficient is known from theory. In our experiments, individual colloidal particles are exposed to a laser speckle pattern inducing a non-Gaussian roughness and are followed by optical microscopy. The relaxation depends on the kind and degree of roughness of the PEL. It can be followed and quantified by the time- and ensemble-averaged mean squared displacement. Moreover, the heterogeneity of the dynamics is characterized using single-trajectory analysis. The results of this work are relevant for the correct interpretation of single-particle tracking experiments in general.

A Ground-Nesting Galliform's Response to Thermal Heterogeneity: Implications for Ground-Dwelling Birds.

The habitat selection choices that individuals make in response to thermal environments influence both survival and reproduction. Importantly, the way that organisms behaviorally respond to thermal environments depends on the availability and juxtaposition of sites affording tolerable or preferred microclimates. Although, ground nesting birds are especially susceptible to heat extremes across many reproductive stages (i.e., breeding, nesting, brood rearing), the mechanistic drivers of nest site selection for these species are not well established from a thermal perspective. Our goal was to assess nest site selection relative to the configuration of the thermal landscape by quantifying thermal environments available to a ground-nesting bird species inhabiting a climatically stressful environment. Using northern bobwhite (Colinus virginanus) as a model species, we measured black bulb temperature (Tbb) and vegetation parameters at 87 nests, 87 paired sites and 205 random landscape sites in Western Oklahoma during spring and summer 2013 and 2014. We found that thermal space within the study area exhibited differences in Tbb of up to 40°C during peak diurnal heating, resulting in a diverse thermal landscape available to ground-nesting birds. Within this thermally heterogeneous landscape, nest sites moderated Tbb by more than 12°C compared to random landscape sites. Furthermore, successful nests remained on average 6°C cooler than unsuccessful nests on days experiencing ambient temperatures ≥ 39°C. Models of future Tbb associated with 2080 climate change projections indicate that nesting bobwhites will face substantially greater Tbb throughout the landscape for longer durations, placing an even greater importance on thermal choices for nest sites in the future. These results highlight the capacity of landscape features to act as moderators of thermal extremes and demonstrate how thermal complexity at organism-specific scales can dictate habitat selection.

Thermal patterns constrain diurnal behavior of a ground‐dwelling bird

Recently, gaining knowledge about thermal refuges for vulnerable species has been a major focal point of ecological studies, and this focus has been heightened by predicted temperature increases associated with global climate change. To better understand how organisms respond to thermal landscapes and extremes, we investigated the thermal ecology of a gallinaceous bird species (northern bobwhite; Colinus virginianus, hereafter bobwhite) during a key life history period. Specifically, our study focused on the brood‐rearing period of precocial bobwhite chicks associated with brood‐attending adults. We measured site‐specific black bulb temperatures (Tbb) and vegetation characteristics across 38 brood tracking days and 68 random landscape sites to assess thermal patterns at scales relevant to broods. We observed that the landscape was thermally heterogeneous, exhibiting variation in Tbb up to 40°C during peak diurnal heating demonstrating a wide array of thermal choices available to broods. At 15:00 h, broods selected thermal refuges that moderated Tbb on average up to 10.4°C more than landscape sites. Moreover, broods exhibited behavioral thermoregulation through reduced movement and by occupying more moderate microclimates that afforded taller vegetation structure during high heat. Modeled climate projections suggest that future Tbb in thermal refuges will approach those currently avoided on the landscape, emphasizing the need for future conservation plans that acknowledge fine scale thermal space in climate change scenarios. These findings underline that studying both abiotic and biotic factors at scales relevant to organisms can increase our understanding of how thermally heterogeneous landscapes provide thermal choices under extreme conditions.

Far tails of the density of states in amorphous organic semiconductors.

Far tails of the density of state (DOS) are calculated for the simple models of organic amorphous material, the model of dipolar glass and model of quadrupolar glass. It was found that in both models far tails are non-Gaussian. In the dipolar glass model, the DOS is symmetric around zero energy, while for the model of quadrupolar glass, the DOS is generally asymmetric and its asymmetry is directly related to the particular geometry of quadrupoles. Far tails of the DOS are relevant for the quasi-equilibrium transport of the charge carriers at low temperature. Asymmetry of DOS in quadrupolar glasses means a principal inequivalence of the random energy landscape for the transport of electrons and holes. Possible effect of the non-Gaussian shape of the far tails of the DOS on the temperature dependence of carrier drift mobility is discussed.

Trade-offs in antibody repertoires to complex antigens.

Pathogens vary in their antigenic complexity. While some pathogens such as measles present a few relatively invariant targets to the immune system, others such as malaria display considerable antigenic diversity. How the immune response copes in the presence of multiple antigens, and whether a trade-off exists between the breadth and efficacy of antibody (Ab)-mediated immune responses, are unsolved problems. We present a theoretical model of affinity maturation of B-cell receptors (BCRs) during a primary infection and examine how variation in the number of accessible antigenic sites alters the Ab repertoire. Naive B cells with randomly generated receptor sequences initiate the germinal centre (GC) reaction. The binding affinity of a BCR to an antigen is quantified via a genotype–phenotype map, based on a random energy landscape, that combines local and distant interactions between residues. In the presence of numerous antigens or epitopes, B-cell clones with different specificities compete for stimulation during rounds of mutation within GCs. We find that the availability of many epitopes reduces the affinity and relative breadth of the Ab repertoire. Despite the stochasticity of somatic hypermutation, patterns of immunodominance are strongly shaped by chance selection of naive B cells with specificities for particular epitopes. Our model provides a mechanistic basis for the diversity of Ab repertoires and the evolutionary advantage of antigenically complex pathogens.

Statistics of stationary points of random finite polynomial potentials

.The stationary points (SPs) of the potential energy landscapes (PELs) of multivariate random potentials (RPs) have found many applications in many areas of Physics, Chemistry and Mathematical Biology. However, there are few reliable methods available which can find all the SPs accurately. Hence, one has to rely on indirect methods such as Random Matrix theory. With a combination of the numerical polynomial homotopy continuation method and a certification method, we obtain all the certified SPs of the most general polynomial RP for each sample chosen from the Gaussian distribution with mean 0 and variance 1. While obtaining many novel results for the finite size case of the RP, we also discuss the implications of our results on mathematics of random systems and string theory landscapes.

Probabilistic Downscaling of Remote Sensing Data with Applications for Multi-Scale Biogeochemical Flux Modeling.

Upscaling ecological information to larger scales in space and downscaling remote sensing observations or model simulations to finer scales remain grand challenges in Earth system science. Downscaling often involves inferring subgrid information from coarse-scale data, and such ill-posed problems are classically addressed using regularization. Here, we apply two-dimensional Tikhonov Regularization (2DTR) to simulate subgrid surface patterns for ecological applications. Specifically, we test the ability of 2DTR to simulate the spatial statistics of high-resolution (4 m) remote sensing observations of the normalized difference vegetation index (NDVI) in a tundra landscape. We find that the 2DTR approach as applied here can capture the major mode of spatial variability of the high-resolution information, but not multiple modes of spatial variability, and that the Lagrange multiplier (γ) used to impose the condition of smoothness across space is related to the range of the experimental semivariogram. We used observed and 2DTR-simulated maps of NDVI to estimate landscape-level leaf area index (LAI) and gross primary productivity (GPP). NDVI maps simulated using a γ value that approximates the range of observed NDVI result in a landscape-level GPP estimate that differs by ca 2% from those created using observed NDVI. Following findings that GPP per unit LAI is lower near vegetation patch edges, we simulated vegetation patch edges using multiple approaches and found that simulated GPP declined by up to 12% as a result. 2DTR can generate random landscapes rapidly and can be applied to disaggregate ecological information and compare of spatial observations against simulated landscapes.

Metapopulation persistence in random fragmented landscapes.

Habitat destruction and land use change are making the world in which natural populations live increasingly fragmented, often leading to local extinctions. Although local populations might undergo extinction, a metapopulation may still be viable as long as patches of suitable habitat are connected by dispersal, so that empty patches can be recolonized. Thus far, metapopulations models have either taken a mean-field approach, or have modeled empirically-based, realistic landscapes. Here we show that an intermediate level of complexity between these two extremes is to consider random landscapes, in which the patches of suitable habitat are randomly arranged in an area (or volume). Using methods borrowed from the mathematics of Random Geometric Graphs and Euclidean Random Matrices, we derive a simple, analytic criterion for the persistence of the metapopulation in random fragmented landscapes. Our results show how the density of patches, the variability in their value, the shape of the dispersal kernel, and the dimensionality of the landscape all contribute to determining the fate of the metapopulation. Using this framework, we derive sufficient conditions for the population to be spatially localized, such that spatially confined clusters of patches act as a source of dispersal for the whole landscape. Finally, we show that a regular arrangement of the patches is always detrimental for persistence, compared to the random arrangement of the patches. Given the strong parallel between metapopulation models and contact processes, our results are also applicable to models of disease spread on spatial networks.

Phase transition in random adaptive walks on correlated fitness landscapes

We study biological evolution on a random fitness landscape where correlations are introduced through a linear fitness gradient of strength c. When selection is strong and mutations rare the dynamics is a directed uphill walk that terminates at a local fitness maximum. We analytically calculate the dependence of the walk length on the genome size L. When the distribution of the random fitness component has an exponential tail, we find a phase transition of the walk length D between a phase at small c, where walks are short (D∼lnL), and a phase at large c, where walks are long (D∼L). For all other distributions only a single phase exists for any c>0. The considered process is equivalent to a zero temperature Metropolis dynamics for the random energy model in an external magnetic field, thus also providing insight into the aging dynamics of spin glasses.

GradientLand Software: A landscape change gradient generator

In landscape ecology, there is a lack of free software that can simulate sequential processes of habitat loss using neutral landscape models. Such a tool would come to the benefit of our understanding of the effects of landscape changes on ecological processes without the need for finding or manipulating appropriate natural landscapes, something both unfeasible and sometimes unethical. This paper presents a free software, named GradientLand, as a tool for generating simulated sets of habitat loss gradients as random and fractal neutral landscapes. GradientLand is easy to handle, with an intuitive interface to create a wide array of habitat cover gradient arrangements. With this tool, we target students, teachers and researchers interested in landscape ecology and issues related to habitat loss and landscape change.

Pinning time statistics for vortex lines in disordered environments.

We study the pinning dynamics of magnetic flux (vortex) lines in a disordered type-II superconductor. Using numerical simulations of a directed elastic line model, we extract the pinning time distributions of vortex line segments. We compare different model implementations for the disorder in the surrounding medium: discrete, localized pinning potential wells that are either attractive and repulsive or purely attractive, and whose strengths are drawn from a Gaussian distribution; as well as continuous Gaussian random potential landscapes. We find that both schemes yield power-law distributions in the pinned phase as predicted by extreme-event statistics, yet they differ significantly in their effective scaling exponents and their short-time behavior.