Two-dimensional Setting Research Articles

On the Variance of the Optimal Alignments Score for Binary Random Words and an Asymmetric Scoring Function

We investigate the order of the variance of the optimal alignments score of two independent iid binary random words having the same length. The letters are equiprobable, but the scoring function is such that one letter has a larger score than the other. In this setting, we prove that the order of variance is linear in the common length. Optimal alignments constitute a generalization of longest common subsequences, they can be represented as optimal paths in a two-dimensional last passage percolation setting with dependent weights.

Le système de Vlasov–Poisson effectif pour les plasmas fortement magnétisés

We study the finite Larmor radius regime for the Vlasov–Poisson system. The magnetic field is assumed to be uniform. We investigate this non-linear problem in the two-dimensional setting. We derive the limit model by appealing to gyro-average methods (cf. [1,2]). We indicate the explicit expression of the effective advection field, entering the Vlasov equation, after substituting the self-consistent electric field, obtained by the resolution of the averaged (with respect to the cyclotronic time scale) Poisson equation. We emphasize the Hamiltonian structure of the limit model and present its properties: conservation of mass, of kinetic energy, of electric energy, etc.

On the power of uniform power: capacity of wireless networks with bounded resources

The throughput capacity of arbitrary wireless networks under the physical Signal to Interference Plus Noise Ratio (SINR) model has received much attention in recent years. In this paper, we investigate the question of how much the worst-case performance of uniform and non-uniform power assignments differ under constraints such as a bound on the area where nodes are distributed or restrictions on the maximum power available. We determine the maximum factor by which a non-uniform power assignment can outperform the uniform case in the SINR model. More precisely, we prove that in one-dimensional settings the capacity of a non-uniform assignment exceeds a uniform assignment by at most a factor of O(logL max ) when the length of the network is L max . In two-dimensional settings, the uniform assignment is at most a factor of O(logP max ) worse than the non-uniform assignment if the maximum power is P max . We provide algorithms that reach this capacity in both cases. Due to lower bound examples in previous work, these results are tight in the sense that there are networks where the lack of power control causes a performance loss in the order of these factors. As a consequence, engineers and researchers may prefer the uniform model due to its simplicity if this degree of performance deterioration is acceptable.

Pressure-Dependent Viscosity Model for Granular Media Obtained from Compressible Navier–Stokes Equations

The aim of this article is to justify mathematically, in the two-dimensional periodic setting, a generalization of a two-phase model with pressure dependent viscosity first proposed by A. Lefebvre-Lepot and B. Maury to describe a system in one dimension of aligned spheres interacting through lubrication forces. This model involves an adhesion potential, apparent only on the congested domain, which keeps track of history of the flow. The solutions are constructed (through a singular limit) from a compressible Navier-Stokes system with viscosity and pressure both singular close to a maximal volume fraction. Interestingly, this study can be seen as the first mathematical connection between models of granular flows and models of suspensions. As a by-product of this result, we also obtain global existence of weak solutions for a system of incompressible Navier-Stokes equations with pressure dependent viscosity, the adhesion potential playing a crucial role in this result.

Sublinear signal production in a two-dimensional Keller–Segel–Stokes system

We study the chemotaxis–fluid system {nt=Δn−∇⋅(n∇c)−u⋅∇n,x∈Ω,t>0,ct=Δc−c+f(n)−u⋅∇c,x∈Ω,t>0,ut=Δu+∇P+n∇ϕ,x∈Ω,t>0,∇⋅u=0,x∈Ω,t>0, where Ω⊂R2 is a bounded and convex domain with smooth boundary, ϕ∈W2,∞(Ω) and f∈C1([0,∞)) satisfies 0≤f(s)≤K0sα for all s∈[0,∞), with K0>0 and α∈(0,1]. This system models the chemotactic movement of actively communicating cells in slow moving liquid.We will show that in the two-dimensional setting for any α∈(0,1) the classical solution to this Keller–Segel–Stokes-system is global and remains bounded for all times.

Engineering pancreatic tissues from stem cells towards therapy.

Pancreatic islet transplantation is performed as a potential treatment for type 1 diabetes mellitus. However, this approach is significantly limited due to the critical shortage of islet sources. Recently, a number of publications have developed protocols for directed β-cell differentiation of pluripotent cells, such as embryonic stem (ES) or induced pluripotent stem (iPS) cells. Decades of studies have led to the development of modified protocols that recapitulate molecular developmental cues by combining various growth factors and small molecules with improved efficiency. However, the later step of pancreatic differentiation into functional β-cells has yet to be satisfactory in vitro, highlighting alternative approach by recapitulating spatiotemporal multicellular interaction in three-dimensional (3D) culture. Here, we summarize recent progress in the directed differentiation into pancreatic β-cells with a focus on both two-dimensional (2D) and 3D differentiation settings. We also discuss the potential transplantation strategies in combination with current bioengineering approaches towards diabetes therapy.

A Novel Scheme for Liouville’s Equation with a Discontinuous Hamiltonian and Applications to Geometrical Optics

A novel scheme is developed that computes numerical solutions of Liouville’s equation with a discontinuous Hamiltonian. It is assumed that the underlying Hamiltonian system has well-defined behaviour even when the Hamiltonian is discontinuous. In the case of geometrical optics such a discontinuity yields the familiar Snell’s law or the law of specular reflection. Solutions to Liouville’s equation should be constant along curves defined by the Hamiltonian system when the right-hand side is zero, i.e., no absorption or collisions. This consideration allows us to derive a new jump condition, enabling us to construct a first-order accurate scheme. Essentially, the correct physics is built into the solver. The scheme is tested in a two-dimensional optical setting with two test cases, the first using a single jump in the refractive index and the second a compound parabolic concentrator. For these two situations, the scheme outperforms the more conventional method of Monte Carlo ray tracing.

A jigsaw puzzle framework for homogenization of high porosity foams

An approach to homogenization of high porosity metallic foams is explored. The emphasis is on the Alporas® foam and its representation by means of two-dimensional wire-frame models. The guaranteed upper and lower bounds on the effective stiffness coefficients are derived by the first-order homogenization with the Uniform and Minimal Kinematic Boundary Conditions at heart. This is combined with the method of Wang tilings to generate sufficiently large material samples along with their finite element discretization. The obtained results are compared to experimental and numerical data available in literature and the suitability of the two-dimensional setting itself is discussed.

Short-range cytokine gradients to mimic paracrine cell interactions in vitro

Cell fate decisions in many physiological processes, including embryogenesis, stem cell niche homeostasis and wound healing, are regulated by secretion of small signaling proteins, called cytokines, from source cells to their neighbors or into the environment. Concentration level and steepness of the resulting paracrine gradients elicit different cell responses, including proliferation, differentiation or chemotaxis. For an in-depth analysis of underlying mechanisms, in vitro models are required to mimic in vivo cytokine gradients. We set up a microparticle-based system to establish short-range cytokine gradients in a three-dimensional extracellular matrix context. To provide native binding sites for cytokines, agarose microparticles were functionalized with different glycosaminoglycans (GAG). After protein was loaded onto microparticles, its slow release was quantified by confocal microscopy and fluorescence correlation spectroscopy. Besides the model protein lysozyme, SDF-1 was used as a relevant chemokine for hematopoietic stem and progenitor cell (HSPC) chemotaxis. For both proteins we found gradients ranging up to 50μm from the microparticle surface and concentrations in the order of nM to pM in dependence on loading concentration and affinity modulation by the GAG functionalization. Directed chemotactic migration of cells from a hematopoietic cell line (FDCPmix) and primary murine HSPC (Sca-1+ CD150+ CD48−) toward the SDF-1-laden microparticles proved functional short-range gradients in a two-dimensional and three-dimensional setting over time periods of many hours. The approach has the potential to be applied to other cytokines mimicking paracrine cell–cell interactions in vitro.

Homogenization Model for Aberrant Crypt Foci

Several explanations can be found in the literature about the origin of colorectal cancer. There is, however, some agreement on the fact that the carcinogenic process is a result of several genetic mutations of normal cells. The colon epithelium is characterized by millions of invaginations, very small cavities, called crypts, where most of the cellular activity occurs. It is agreed in the medical community that a potential first manifestation of the carcinogenic process, observed in conventional colonoscopy images, is the appearance of aberrant crypt foci (ACF). These are clusters of abnormal crypts, morphologically characterized by an atypical behavior of the cells that populate the crypts. In this work a homogenization model is proposed for representing the cellular dynamics in the colon epithelium. The goal is to simulate and predict, in silico, the spread and evolution of ACF, as it can be observed in colonoscopy images. By assuming that the colon is a heterogeneous medium, exhibiting a periodic distribution of crypts, we start this work by describing a periodic model that represents the ACF cell-dynamics in a two-dimensional setting. Then, homogenization techniques are applied to this periodic model to find a simpler model, whose solution symbolizes the averaged behavior of ACF at the tissue level. Some theoretical results concerning the existence of solution of the homogenized model are proved, applying a fixed point theorem. Numerical results showing the convergence of the periodic model to the homogenized model are presented.

EVALUATION OF STABILITY OF PIT IN ROCKY SOIL

In the article the technique of calculation of stability of pit walls, stacked rock soil, taking into account geologostroy characteristics of the rock mass and the spatial position of the zones of weakening in relation to the pit walls. It is shown that, depending on their mutual orientation the objective of pit slope stability can be solved in two-dimensional or threedimensional setting. Examples of calculating the stability of opencast sites, subject to zones of weakening for two-dimensional limiting equilibrium methods and finite elements in threedimensional statement – by the volume of the rock blocks. Described modern criteria of strength, which is recommended for the modeling of the stability of rock landslides. The proposed methodology for stability assessment of pit walls, laid in rocky soil, allow to choose the method of calculation, depending on the joint orientation of the structural plane of the rock mass and the spatial position of the pit walls.

Localized plateau beam resulting from strong nonlocal coupling in a cavity filled by metamaterials and liquid-crystal cells

We investigate the formation of a localized plateau beam in the transverse section of a nonlinear optical ring cavity filled with a metamaterial and a nonlocal medium such as a nematic liquid crystal. We show that, far from the modulational instability regime, localized structures with a varying width may be stable in one and two-dimensional settings. The mechanism of stabilization is related with strong nonlocal coupling mediated by a Lorentzian type of kernel. We show that there exists stable bright and dark localized structures. A reduction of Lugiato--Lefever equation in the regime close to the nascent bistability allows us to analytically derive a simple formula for the width of localized structures in one-dimensional systems. Direct numerical simulations of the dynamical model agree with the analytical predictions.

Global estimates and energy identities for elliptic systems with antisymmetric potentials

ABSTRACTWe derive global estimates in critical scale invariant norms for solutions of elliptic systems with antisymmetric potentials and almost holomorphic Hopf differential in two dimensions. Moreover, we obtain new energy identities in such norms for sequences of solutions of these systems. The results apply to harmonic maps into general target manifolds and surfaces with prescribed mean curvature. In particular, the results confirm a conjecture of Rivière in the two-dimensional setting.

Maximum disorder model for dense steady-state flow of granular materials

A flow model is developed for dense shear-driven granular flow. As described in the geomechanics literature, a critical state condition is reached after sufficient shearing beyond an initial static packing. During further shearing at the critical state, the stress, fabric, and density remain nearly constant, even as particles are being continually rearranged. The paper proposes a predictive framework for critical state flow, viewing it as a condition of maximum disorder at the micro-scale. The flow model is constructed in a two-dimensional setting from the probability density of the motions, forces, and orientations of inter-particle contacts. Constraints are applied to this probability density: constant mean stress, constant volume, consistency of the contact dissipation rate with the stress work, and the fraction of sliding contacts. The differential form of Shannon entropy, a measure of disorder, is applied to the density, and the Jaynes formalism is used to find the density of maximum disorder in the underlying phase space. The resulting distributions of contact force, movement, and orientation are compared with two-dimensional DEM simulations of biaxial compression. The model favorably predicts anisotropies of the contact orientations, contact forces, contact movements, and the orientations of those contacts undergoing slip. The model also predicts the relationships between contact force magnitude and contact motion. The model is an alternative to affine-field descriptions of granular flow.

Diffusion Rates and Dispersal Patterns of Unfed versus Recently Fed Bed Bugs (Cimex lectularius L.).

Bed bug problems have been increasing since the 1980s, and accordingly, there have been intensive efforts to better understand their biology and behavior for control purposes. Understanding bed bug diffusion rates and dispersal patterns from one site to another (or lack thereof) is a key component in prevention and control campaigns. This study analyzed diffusion rates and dispersal patterns in a population of bed bugs, recently fed and unfed, in both one-dimensional and two-dimensional settings. When placed in the middle of a 71 cm × 2.7 cm artificial lane, approximately half of the bugs regardless of feeding status stayed at or near the release point during the 10 min observation periods, while about a fourth of them walked to the end of the lane. When placed in the middle of an arena measuring 51 cm × 76 cm and allowed to walk in any direction, approximately one-fourth of bed bugs, fed or unfed, still remained near their release point (no significant difference between fed or unfed). As for long-distance dispersal, 11/50 (22%) of recently fed bed bugs moved as far as possible in the arena during the 10 min replications, while only 2/50 (4%) unfed bed bugs moved to the maximum distance. This difference was significantly different (p < 0.0038), and indicates that unfed bed bugs did not move as far as recently fed ones. A mathematical diffusion model was used to quantify bed bug movements and an estimated diffusion rate range of 0.00006 cm2/s to 0.416 cm2/s was determined, which is almost no movement to a predicted root mean squared distance of approximately 19 cm per 10 min. The results of this study suggest that bed bugs, upon initial introduction into a new area, would have a difficult time traversing long distances when left alone to randomly disperse.

The ghost solid methods for the elastic–plastic solid–solid interface and the ϑ-criterion

Two variants of the Ghost Solid Method (GSM), namely the Original GSM (OGSM) and Modified GSM (MGSM), are proposed for the elastic–plastic solid–solid interactions in a Lagrangian framework. It is shown that the OGSM is highly problem related and can lead to large numerical errors under certain material combinations or in the presence of the wave propagation through the solid–solid interface. The ϑ-criterion, previously developed for the elastic–elastic solid–solid interactions [1], has been applied to the OGSM for the elastic–plastic interactions. It is shown that this criterion can successfully detect the onset of these large errors. Moreover, it is shown that it can be used to determine the reliability of the results obtained using the OGSM. The MGSM has been shown to be able to remove the large numerical errors that would normally arise due to the OGSM. Next, the extension of the two variants of the GSM, to two-dimensional settings, is presented for two idealized interface conditions, namely the no-slip condition, and the perfect-slip conditions. Numerous numerical experiments are provided attesting to the effectiveness and viability of the GSMs, for simulating wave propagation at the elastic–plastic solid–solid interface. The applicability of the ϑ-criterion is also studied in the numerical experiments.

Two-dimensional capillary origami

We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid.

The Information Carried by Scattered Waves: Near-Field and Nonasymptotic Regimes

The number of spatial degrees of freedom of the field radiated in a two-dimensional setting by a time-harmonic, arbitrary square-integrable current density and in the presence of a random distribution of scattering elements is determined. It is shown that the active power associated to the $k$ th singular value of the near field in the presence of scatterers external to the cut presents a heavy tail decay as a function of its index, rather than the usual exponential attenuation occurring beyond a critical index term observed in free space. This near-field information gain due to scattering was recently anticipated by Janaswamy using a stochastic source model, it is extended here to arbitrary sources, and it is shown to disappear in the limit of large radiating systems. It is also shown that the same information gain and asymptotic cut-off occurs for the singular values of the field radiating in free space. Collectively, these results show that while the presence of scatterers external to the cut can increase the number of channels that can be exploited for communication by the active power in the near field, they do not change the number of channels associated to the field, nor the asymptotic behavior of the number of degrees of freedom.

An analytical description of the time-integrated Brownian bridge

In animal movement research, the probability density function (PDF) of the time-integrated Brownian bridge (TIBB) is used to delineate important regions on the basis of tracking data. Here, it is assumed that an animal performs a Brownian bridge between the data points. As such, the location at any moment in time of an individual performing a Brownian bridge is described by a normal distribution. The (time-independent) marginal probability density at a given point, i.e., the value of the PDF of the TIBB at that point, is obtained by averaging these normal distributions over time. To the best of our knowledge, the PDF of the TIBB is thus far always computed through the use of numerical integration methods. Here, we demonstrate that it is nevertheless possible to derive its analytical expression. Although the two-dimensional setting is the most interesting one for animal movement studies, also the one- and, in general, the n-dimensional setting are considered.

Stress regularity for a new quasistatic evolution model of perfectly plastic plates

We study some properties of solutions to a quasistatic evolution problem for perfectly plastic plates, that has been recently derived from three-dimensional Prandtl–Reuss plasticity. We prove that the stress tensor has locally square-integrable first derivatives with respect to the space variables. We also exhibit an example showing that the model under consideration has in general a genuinely three-dimensional nature and cannot be reduced to a two-dimensional setting.