Interaction Length Scale Research Articles

Scale-free correlations and potential criticality in weakly ordered populations of brain cancer cells.

Collective behavior spans several orders of magnitude of biological organization, from cell colonies to flocks of birds. We used time-resolved tracking of individual glioblastoma cells to investigate collective motion in an ex vivo model of glioblastoma. At the population level, glioblastoma cells display weakly polarized motion in the (directional) velocities of single cells. Unexpectedly, fluctuations in velocities are correlated over distances many times the size of a cell. Correlation lengths scale linearly with the maximum end-to-end length of the population, indicating that they are scale-free and lack a characteristic decay scale other than the size of the system. Last, a data-driven maximum entropy model captures statistical features of the experimental data with only two free parameters: the effective length scale (nc) and strength (J) of local pairwise interactions between tumor cells. These results show that glioblastoma assemblies exhibit scale-free correlations in the absence of polarization, suggesting that they may be poised near a critical point.

Comprehensive analysis on the effect of ionic size and size disorder parameter in high entropy stabilized ferromagnetic manganite perovskite

A series of high entropy manganites, $(5{A}_{0.2}){\mathrm{MnO}}_{3}$, were prepared with varying the average ionic radius, $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}$, and cationic size disorder, ${\ensuremath{\sigma}}^{2}$, on the $A$ site. All the samples were synthesized using the citrate sol-gel method. In all the compounds, the manganese valence was kept unaltered with reference to the conventional manganite ${\mathrm{La}}_{0.6}{\mathrm{Sr}}_{0.4}{\mathrm{MnO}}_{3}$, which is ferromagnetic with ${T}_{C}\ensuremath{\sim}365$ K. The ratio of manganese valance is found to be unaltered as confirmed using x-ray photoelectron studies. The samples were characterized by powder x-ray diffraction, field-emission scanning electron microscopy (FE-SEM), energy dispersive x-ray analysis, elemental mapping, and magnetization measurements. These high entropy oxides show the variation in Curie temperature over a wide range from 85 to 273 K depending on the average $A$-site ionic radius, $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}$. A drastic drop down in the ferromagnetic transition temperature of ${T}_{C}=365$ K for ${\mathrm{La}}_{0.6}{\mathrm{Sr}}_{0.4}{\mathrm{MnO}}_{3}$ with $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}=1.2536\phantom{\rule{0.16em}{0ex}}\AA{}$ to ${T}_{C}=137\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ for (${\mathrm{La}}_{0.2}{\mathrm{Nd}}_{0.2}{\mathrm{Gd}}_{0.2}{\mathrm{Sr}}_{0.2}{\mathrm{Ba}}_{0.2}$)${\mathrm{MnO}}_{3}$ of comparable $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}=1.2532\phantom{\rule{0.16em}{0ex}}\AA{}$ can be attributed to the high entropy and/or cationic size disorder effect. The variation of ${T}_{C}$ with $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}$ for the whole series of high entropy manganites does not follow the expected linear behavior; rather, it follows opposite traces of the variation in ${\ensuremath{\sigma}}^{2}$ with $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}$. However, ${T}_{C}$ shows almost linear behavior with ${\ensuremath{\sigma}}^{2}$ except for the sample with lowest $\ensuremath{\langle}{r}_{A}\ensuremath{\rangle}$. This result suggests that the local cationic disordering is more important than the average cationic size in ferromagnetic high entropy manganites. Unlike the conventional system in these high entropy oxides, the ferromagnetic state is not suppressed; only the length scale of the double exchange mediated long-range ferromagnetic interaction is transformed to localized ferromagnetic clusters without losing the ferromagnetic identity. The presence of multiple $A$-site cations in high entropy oxides results in a local deformation of the ${\mathrm{MnO}}_{6}$ octahedra. This possibly increases the carrier localization followed by reducing the length scale of the double exchange interaction.

Soft fundamental measure theory functional for the Weeks-Chandler-Andersen repulsive potential.

We introduce a soft fundamental measure theory functional for the purely repulsive Weeks-Chandler-Andersen (WCA) fluid. This classical density functional could serve as a reference fluid for functionals created using thermodynamic perturbation theory instead of the hard-sphere fluid. Our functional incorporates temperature-dependent parameters describing the length scale and effective softness of the particle interaction, and which reproduce the second virial coefficient of the WCA fluid. We find that this approach is comparable in accuracy to the Barker-Henderson approach combined with the White Bear density functional for the hard-sphere fluid.

Multiscale voter model on real networks

We introduce the Multiscale Voter Model (MVM) to investigate clan influence at multiple scales—family, neighborhood, political party…—in opinion formation on real complex networks. Clans, consisting of similar nodes, are constructed using a coarse-graining procedure on network embeddings that allows us to control for the length scale of interactions. We ran numerical simulations to monitor the evolution of MVM dynamics in real and synthetic networks, and identified a transition between a final stage of full consensus and one with mixed binary opinions. The transition depends on the scale of the clans and on the strength of their influence. We found that enhancing group diversity promotes consensus while strong kinship yields to metastable clusters of same opinion. The segregated domains, which signal opinion polarization, are discernible as spatial patterns in the hyperbolic embeddings of the networks. Our multiscale framework can be easily applied to other dynamical processes affected by scale and group influence.

Analytical model for predicting the length scale of shock/boundary layer interaction with curvature

In practical aerodynamic problems, curved shock/boundary layer interaction (CSBLI) is more frequently encountered than the canonical shock/boundary layer interaction (SBLI). Owing to the topological complexity of the flow field brought about by shock curvature, accurate prediction of the interaction length scale of CSBLI is a challenging task. In this work, streamwise and spanwise curvatures are introduced, in turn, with the aim of establishing an analytical model for the interaction length scale of CSBLI based on conservation of mass. The validity and universality of the model are verified, which reveal the impact of the shock curvatures on the interaction, acting as the form of non-uniformity. As an example, the CSBLI with different curvatures is compared, demonstrating that a streamwise curvature of 0.071 will bring a reduction of about 16.5% of the interaction length. The proposed method can be regarded as providing a foundation for further research on CSBLI, opening new perspectives for the investigation of SBLI flow structures.

Emergence of biaxiality in nematic liquid crystals with magnetic inclusions: Some theoretical insights.

The biaxial phase in nematic liquid crystals has been elusive for several decades after its prediction in the 1970s. A recent experimental breakthrough was achieved by Liu etal. [Proc. Natl. Acad. Sci. USA 113, 10479 (2016)0027-842410.1073/pnas.1601235113] in a liquid-crystalline medium with magnetic nanoparticles. They exploited the different length scales of dipolar and magnetonematic interactions to obtain an equilibrium state where the magnetic moments are at an angle to the nematic director. This tilt introduces a second distinguished direction for orientational ordering or biaxiality in the two-component system. Using coarse-grained Ginzburg-Landau free-energy models for the nematic and magnetic fields, we provide a theoretical framework which allows for the manipulation of morphologies and quantitative estimates of biaxial order.

Slow and fast minimal speed traveling waves of the FKPP equation with chemotaxis

We examine a general model for the Fisher-KPP (FKPP) equation with nonlocal advection. The main interpretation of this model is as describing a diffusing and logistically growing population that is also influenced by intraspecific attraction or repulsion. For a particular choice of parameters, this specializes to the Keller-Segel-Fisher equation for chemotaxis. Our interest is in the effect of chemotaxis on the speed of traveling waves. We prove that there is a threshold such that, when interactions are weaker and more localized than this, chemotaxis, despite being non-trivial, does not influence the speed of traveling waves; that is, the minimal speed traveling wave has speed 2 as in the FKPP case. On the other hand, when the interaction is repulsive, we show that the minimal traveling wave speed is arbitrarily large in a certain asymptotic regime in which the interaction strength and length scale tend to infinity.

Tau depolarization at very high energies for neutrino telescopes

The neutrino interaction length scales with energy, and becomes comparable to Earth's diameter above 10's of TeV energies. Over terrestrial distances, the tau's short lifetime leads to an energetic regenerated tau neutrino flux, tau neutrino to tau to tau neutrino, within the Earth. The next generation of neutrino experiments aim to detect ultra-high energy neutrinos. Many of them rely on detecting either the regenerated tau neutrino, or a tau decay shower. Both of these signatures can be affected by the polarization of the tau through the energy distribution of the secondary particles produced from the tau's decay. While taus produced in weak interactions are nearly 100 percent polarized, it is expected that taus experience some depolarization due to electromagnetic interactions in the Earth. In this paper, for the first time we quantify the depolarization of taus in electromagnetic energy loss. We find that tau depolarization has only small effects on the final energy of tau neutrinos or taus produced by high energy tau neutrinos incident on the Earth. Tau depolarization can be directly implemented in Monte Carlo simulations such as nuPyProp and TauRunner.

Proposal for the search for new spin interactions at the micrometer scale using diamond quantum sensors

For decades, searches for exotic spin interactions have used increasingly-precise laboratory measurements to test various theoretical models of particle physics. However, most searches have focused on interaction length scales greater than 1 mm, corresponding to hypothetical boson masses less than 0.2 meV. Recently, quantum sensors based on Nitrogen-Vacancy (NV) centers in diamond have emerged as a promising platform to probe spin interactions at the micrometer scale, opening the door to explore new physics at this length scale. Here, we propose experiments to search for several hypothetical interactions between NV electron spins and moving masses. We focus on potential interactions involving the coupling of NV spin ensembles to both spin-polarized and unpolarized masses attached to vibrating mechanical oscillators. For each interaction, we estimate the sensitivity, identify optimal experimental conditions, and analyze potential systematic errors. Using multi-pulse quantum sensing protocols with NV spin ensembles to improve sensitivity, we project new constraints that are ~5 orders-of-magnitude improvement over previous constraints at the micrometer scale. We also identify a spin-polarized test mass, based on hyperpolarized 13C nuclear spins in a thin diamond membrane, which offers a favorable combination of high spin density and low stray magnetic fields. Our analysis is timely in light of a recent preprint (arXiv:2010.15667) reporting a surprising non-zero result of micrometer-scale spin-velocity interactions.

Electric field induced parametric excitation of exchange magnons in a CoFeB/MgO junction

Inspired by the success of field-effect transistors in electronics, electric field controlled magnetization dynamics has emerged as an important integrant in low-power spintronic devices. Here, we demonstrate electric field induced parametric excitation for CoFeB/MgO junctions by using interfacial in-plane magnetic anisotropy (IMA). When the IMA and the external magnetic field are parallel to each other, magnons are efficiently excited by electric field induced parametric resonance. The corresponding wavelengths are estimated to be tuned down to exchange interaction length scales by changing the input power and frequency of the applied voltage. A generalized phenomenological model is developed to explain the underlying role of the electric field torque. Electric field control of IMA is shown to be the origin for excitation of both uniform and parametric resonance modes in the in-plane magnetized sample, a crucial element for purely electric field induced magnetization dynamics. Electric field excitation of exchange magnons, with no Joule heating, offers a good opportunity for developing nanoscale magnonic devices and exploring various nonlinear dynamics in nanomagnetic systems.

Superglass formation in an atomic BEC with competing long-range interactions

The complex dynamical phases of quantum systems are dictated by atomic interactions that usually evoke an emergent periodic order. Here, we study a quantum many-body system with two competing and substantially different long-range interaction potentials where the dynamical instability towards density order can give way to a superglass phase, i. e., a superfluid disordered amorphous solid, which exhibits local density modulations but no long-range periodic order. We consider a two-dimensional BEC in the Rydberg-dressing regime coupled to an optical standing wave resonator. The dynamic pattern formation in this system is governed by the competition between the two involved interaction potentials: repulsive soft-core interactions arising due to Rydberg dressing and infinite-range sign changing interactions induced by the cavity photons. The superglass phase is found when the two interaction potentials introduce incommensurate length scales. The dynamic formation of this peculiar phase without any externally added disorder is driven by quantum fluctuations and can be attributed to frustration induced by the two competing interaction energies and length scales.

Ab-Initio Investigation of Finite Size Effects in Rutile Titania Nanoparticles with Semilocal and Nonlocal Density Functionals

In this work, we employ hybrid and generalized gradient approximation (GGA) level density functional theory (DFT) calculations to investigate the convergence of surface properties and the electronic gap of rutile titania (TiO2) nanoparticles with particle size. The surface energies and electronic gaps are calculated for cuboidal particles with minimum dimension ranging from 3.7 Å (24 atoms) to 10.3 Å (384 atoms) using a highly parallel real-space DFT code to enable hybrid-level DFT calculations of larger nanoparticles than are typically practical. We deconvolute the geometric and electronic finite size effects in surface energy and evaluate the influence of defects on the electronic gap and density of states (DOS). The electronic finite size effects in surface energy vanish when the minimum length scale of the nanoparticles becomes greater than 10 Å. We show that this length scale is consistent with a computationally efficient numerical analysis of the characteristic length scale of electronic interactions. The surface energy of nanoparticles having a minimum dimension beyond this characteristic length can be approximated using slab calculations that account for the geometric defects. In contrast, the finite size effects on the electronic gap and DOS are highly dependent on the shape and size of these particles. The DOS for cuboidal particles and more realistic particles constructed using the Wulff algorithm reveal that defect states within the electronic gap play a key role in determining the eigenvalue distribution of nanoparticles and the electronic gap does not converge to the bulk limit for the particle sizes investigated.

Cross-correlation spectra in interacting quantum dot systems

Two-color spin-noise spectroscopy of interacting electron spins in singly charged semiconductor quantum dots provides information on the interquantum dot interactions. We investigate the spin cross-correlation function in a quantum dot ensemble employing a modified semiclassical approach. Spin-correlation functions are calculated using a Hamilton quaternion approach that maintains local quantum mechanical properties of the spins. This method takes into account the effects of the nuclear-electric quadrupolar interactions, the randomness of the coupling constants, and the variation of the electron $g$ factor on the spin-noise power spectra. We demonstrate that the quantum dot ensemble can be mapped on an effective two-quantum dot problem and discuss how the characteristic length scale of the interdot interaction modifies the low-frequency cross-correlation spectrum. We argue that details on the interaction strength distribution can be extracted from the cross-correlation spectrum when applying a longitudinal or a transversal external magnetic field.

Defined core–shell particles as the key to complex interfacial self-assembly

The two-dimensional self-assembly of colloidal particles serves as a model system for fundamental studies of structure formation and as a powerful tool to fabricate functional materials and surfaces. However, the prevalence of hexagonal symmetries in such self-assembling systems limits its structural versatility. More than two decades ago, Jagla demonstrated that core-shell particles with two interaction length scales can form complex, nonhexagonal minimum energy configurations. Based on such Jagla potentials, a wide variety of phases including cluster lattices, chains, and quasicrystals have been theoretically discovered. Despite the elegance of this approach, its experimental realization has remained largely elusive. Here, we capitalize on the distinct interfacial morphology of soft particles to design two-dimensional assemblies with structural complexity. We find that core-shell particles consisting of a silica core surface functionalized with a noncrosslinked polymer shell efficiently spread at a liquid interface to form a two-dimensional polymer corona surrounding the core. We controllably grow such shells by iniferter-type controlled radical polymerization. Upon interfacial compression, the resulting core-shell particles arrange in well-defined dimer, trimer, and tetramer lattices before transitioning into complex chain and cluster phases. The experimental phase behavior is accurately reproduced by Monte Carlo simulations and minimum energy calculations, suggesting that the interfacial assembly interacts via a pairwise-additive Jagla-type potential. By comparing theory, simulation, and experiment, we narrow the Jagla g-parameter of the system to between 0.9 and 2. The possibility to control the interaction potential via the interfacial morphology provides a framework to realize structural features with unprecedented complexity from a simple, one-component system.

Spatial alanine metabolism determines local growth dynamics of Escherichia coli colonies.

Bacteria commonly live in spatially structured biofilm assemblages, which are encased by an extracellular matrix. Metabolic activity of the cells inside biofilms causes gradients in local environmental conditions, which leads to the emergence of physiologically differentiated subpopulations. Information about the properties and spatial arrangement of such metabolic subpopulations, as well as their interaction strength and interaction length scales are lacking, even for model systems like Escherichia coli colony biofilms grown on agar-solidified media. Here, we use an unbiased approach, based on temporal and spatial transcriptome and metabolome data acquired during E. coli colony biofilm growth, to study the spatial organization of metabolism. We discovered that alanine displays a unique pattern among amino acids and that alanine metabolism is spatially and temporally heterogeneous. At the anoxic base of the colony, where carbon and nitrogen sources are abundant, cells secrete alanine via the transporter AlaE. In contrast, cells utilize alanine as a carbon and nitrogen source in the oxic nutrient-deprived region at the colony mid-height, via the enzymes DadA and DadX. This spatially structured alanine cross-feeding influences cellular viability and growth in the cross-feeding-dependent region, which shapes the overall colony morphology. More generally, our results on this precisely controllable biofilm model system demonstrate a remarkable spatiotemporal complexity of metabolism in biofilms. A better characterization of the spatiotemporal metabolic heterogeneities and dependencies is essential for understanding the physiology, architecture, and function of biofilms.

DLVO Interactions between Particles and Rough Surfaces: An Extended Surface Element Integration Method.

The surface element integration (SEI) method is a computationally facile technique for calculating DLVO interactions between particles and surfaces. This method yields the exact total DLVO interaction between a particle and a flat surface; however, all surfaces have some degree roughness that profoundly affects the interaction. Previously, an ad hoc approximate method has been used to extend the SEI method to interactions between particles and surfaces with arbitrary morphology. Here we derive a more rigorous approximate method based on the fundamental scaling of DLVO interactions, which approaches the exact solution as the separation distance decreases regardless of the particle or surface morphology. We verify this method by comparison to the exact van der Waals energy when roughness is present on the particle and surface. The accuracy of this method at small separations makes it well-suited for the contexts of particle adhesion and deposition in which the length scale of interaction is on the order of angstroms and nanometers, respectively.

The length scale of multivalent interactions is evolutionarily conserved in fungal and vertebrate phase-separating proteins.

One key feature of proteins that form liquid droplets by phase separation inside a cell is multivalency-the presence of multiple sites that mediate interactions with other proteins. We know little about the variation of multivalency on evolutionary time scales. Here, we investigated the long-term evolution (∼600 million years) of multivalency in fungal mRNA decapping subunit 2 protein (Dcp2), and in the FET (FUS, EWS and TAF15) protein family. We found that multivalency varies substantially among the orthologs of these proteins. However, evolution has maintained the length scale at which sequence motifs that enable protein-protein interactions occur. That is, the total number of such motifs per hundred amino acids is higher and less variable than expected by neutral evolution. To help explain this evolutionary conservation, we developed a conformation classifier using machine-learning algorithms. This classifier demonstrates that disordered segments in Dcp2 and FET proteins tend to adopt compact conformations, which is necessary for phase separation. Thus, the evolutionary conservation we detected may help proteins preserve the ability to undergo phase separation. Altogether, our study reveals that the length scale of multivalent interactions is an evolutionarily conserved feature of two classes of phase-separating proteins in fungi and vertebrates.

Scalar structures around the mixing interface of a thermal mixing layer in multiscale-generated decaying turbulent flows visualized using DNS database

This study shows the results for the visualization of a scalar mixing layer in decaying turbulence produced by a multiscale-generated turbulence grid. For this purpose, a thermal mixing layer in the air is used as the scalar mixing layer. A fractal generating grid proposed in the previous study is used for the generation of multiscale-generated turbulence. In addition, a parameter for determining the grid shape is varied. The scalar field is then visualized using a database given by direct numerical simulations. The instantaneous scalar field, the instantaneous scalar fluctuation field, the instantaneous scalar variance field, and the scalar dissipation field are visualized, and the visualization results are discussed using the wake interaction length scale.

Charge Effects Provide Ångström-Level Control of Lipid Bilayer Morphology on Titanium Dioxide Surfaces.

Interfaces between molecular organic architectures and oxidic substrates are a central feature of biosensors and applications of biomimetics in science and technology. For phospholipid bilayers, the large range of pH- and ionic strength-dependent surface charge densities adopted by titanium dioxide and other oxidic surfaces leads to a rich landscape of phenomena that provides exquisite control of membrane interactions with such substrates. Using neutron reflectometry measurements, we report sharp, reversible transitions that occur between closely surface-associated and weakly coupled states. We show that these states arise from a complex interplay of the tunable length scale of electrostatic interactions with the length scale arising from other forces that are independent of solution conditions. A generalized free energy potential, with its inputs only derived from established measurements of surface and bilayer properties, quantitatively describes these and previously reported observations concerning the unbinding of bilayers from supporting substrates.

Reynolds-Averaged Numerical Simulations of Conical Shock-Wave/Boundary-Layer Interactions

We carry out a parametric study of conical shock-wave/turbulent boundary-layer interactions by means of numerical simulation of the Reynolds-averaged Navier–Stokes (RANS) equations, with the eventual goal of establishing the predictive capabilities of standard turbulence models. Preliminary assessment of several linear-eddy-viscosity models for the case of planar interactions shows that the model and its variants as well as the Spalart–Allmaras model yield accurate prediction of the typical interaction length scale. Numerical simulations of conical interactions at high Reynolds numbers under attached and separated flow conditions generally support good capability of RANS to predict the gross flow features, including conditions of incipiently and fully separated flow. Comparison with direct numerical simulation data at low Reynolds numbers suggests that caution should be made because certain turbulence models may yield unrealistic incoming velocity profiles. With this caveat, we again find that RANS models yield satisfactory prediction of the three-dimensional flow organization and associated length scales. The -wave mean wall pressure signature is quantitatively predicted, and accurate information about the fluctuating pressure variance can be obtained from RANS data in a postprocessing stage by extension of correlations developed for low-speed separation bubbles.