Multibody Interactions Research Articles

Structures of cationic and anionic polyelectrolytes in aqueous solutions: the sign effect.

In this study, we use molecular dynamics simulation to explore the structures of anionic and cationic polyelectrolytes in aqueous solutions. We first confirm the significantly stronger solvation effects of single anions compared to cations in water at the fixed ion radii, due to the reversal orientations of asymmetric dipolar H2O molecules around the ions. Based on this, we demonstrate that the solvation discrepancy of cations/anions and electrostatic correlations of ionic species can synergistically cause the nontrivial structural difference between single anionic and cationic polyelectrolytes. The cationic polyelectrolyte shows an extended structure whereas the anionic polyelectrolyte exhibits a collapsed structure, and their structural differences decline with increasing the counterion size. Furthermore, we corroborate that multiple cationic polyelectrolytes or multiple anionic polyelectrolytes can exhibit largely differential molecular architectures in aqueous solutions. In the solvation dominant regime, the polyelectrolyte solutions exhibit uniform structures; whereas, in the electrostatic correlation dominant regime, the polyelectrolyte solutions exhibit heterogeneous structures, in which the likely charged chains microscopically aggregate through counterion condensations. Increasing the intrinsic chain rigidity causes polyelectrolyte extension and hence moderately weakens the inter-chain clustering. Our work highlights the various, unique structures and molecular architectures of polyelectrolytes in solutions caused by the multi-body correlations between polyelectrolytes, counterions and asymmetric dipolar solvent molecules, which provides insights into the fundamental understanding of ion-containing polymers.

Efficient learning of discrete graphical models* *This article is an updated version of: Vuffray M, Misra S and Lokhov A 2020 Efficient Learning of Discrete Graphical Models Advances in Neural Information Processing Systems vol 33 eds H Larochelle, M Ranzato, R Hadsell, M F Balcan and H Lin (New York: Curran Associates) pp 13575–85.

Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for learning graphical models with least amount of data remains an active research topic. Reconstruction of graphical models that describe the statistics of discrete variables is a particularly challenging problem, for which the maximum likelihood approach is intractable. In this work, we provide the first sample-efficient method based on the interaction screening framework that allows one to provably learn fully general discrete factor models with node-specific discrete alphabets and multi-body interactions, specified in an arbitrary basis. We identify a single condition related to model parametrization that leads to rigorous guarantees on the recovery of model structure and parameters in any error norm, and is readily verifiable for a large class of models. Importantly, our bounds make explicit distinction between parameters that are proper to the model and priors used as an input to the algorithm. Finally, we show that the interaction screening framework includes all models previously considered in the literature as special cases, and for which our analysis shows a systematic improvement in sample complexity.

Analyzing the quasi-oscillatory nature of electrical parameters with the concentration of sucrose in aqueous solution at room temperature

The impedance, capacitance and conductance of aqueous sucrose polar solution are measured by employing impedance spectroscopy method and the current passing through the system for different DC voltages are measured implementing I-V method. The variation of electrical parameters with sucrose content in such solution exhibits a quasi-oscillatory nature, which is attributed to the random orientation of water and sucrose dipoles in the solution and their mutual interactions at the molecular level, including water-water, water-sucrose and sucrose-sucrose dipole interactions. To justify the quasi-oscillatory nature from analytical point of view, a theoretical model is developed on the basis of multi-body dipolar interactions of randomly distributed molecular dipoles. The experimental data agrees well with those obtained from the analytical model. The measurement of electrical parameters is performed within a frequency window of 100 Hz to 4 MHz for volume fractions of sucrose with respect to water, ranging from 0.1 to 0.6. The impedance, capacitance and conductance are obtained to be in the range of 0.907 k – 281 k, 38 pF – 266 pF, and 3 µS – 55 µS respectively for the sucrose volume fraction range considered. Current voltage measurements for the same concentration range are performed for a voltage swing between ±5 V and the obtained values vary from +20 µA to -25 µA. The study represents a deterministic approach to analyze the effective nature of a sucrose solution in terms of dielectric polarization of the system which finds application in sucrose quality assessments.

Effects of Gap Resonance on the Hydrodynamics and Dynamics of a Multi-Module Floating System with Narrow Gaps

Multi-module floating system has attracted much attention in recent years as ocean space utilization becomes more demanding. This type of structural system has potential applications in the design and construction of floating piers, floating airports and Mobile Offshore Bases (MOBs) generally consists of multiple modules with narrow gaps in which hydrodynamic interactions play a non-neglected role. This study considers a numerical model consisting of several rectangular modules to study the hydrodynamics and dynamics of the multi-module floating system subjected to the waves. Based on ANSYS-AQWA, both frequency-domain and time-domain simulations are performed to analyze the complex multi-body hydrodynamic interactions by introducing artificial damping on the gap surfaces. Parametric studies are carried out to investigate the effects of the gap width, shielding effects of the multi-body system, artificial damping ratio on the gap surface, and the dependency of the hydrodynamic interaction effect on wave headings is clarified. Based on the results, it is found that the numerical analysis based on the potential flow theory with artificial damping introduced can produce accurate results for the normal wave period range. In addition, the effects of artificial damping on the dynamics and connector loads are investigated by using a simplified RMFC model. For the case of adding an artificial damping ratio of 0.2, the relative heave and pitch motions are found to be reduced by 33% and 50%, respectively. In addition, the maximum cable and fender forces are found to be reduced by 50%, compared with the case without viscosity correction.

Waveguide-QED platform for synthetic quantum matter

An exciting frontier in quantum information science is the realization and control of complex quantum many-body systems. The hybrid nanophotonic system with cold atoms has emerged as a paradigmatic platform for realizing long-range spin models from the bottom up, exploiting their modal geometry and group dispersion for tailored interactions. An important challenge is the physical limitation imposed by the photonic bath, constraining the types of local Hamiltonians that decompose the available physical models and restricting the spatial dimensions to that of the dielectric media. However, at the nanoscopic scale, atom-field interaction inherently accompanies significant driven-dissipative quantum forces that may be tamed as a new form of a mediator for controlling the atomic internal states. Here we formulate a quantum optics toolbox for constructing universal quantum matter with individual atoms in the vicinity of one-dimensional photonic crystal waveguides. The enabling platform synthesizes analog quantum materials of universal 2-local Hamiltonian graphs mediated by phononic superfluids of the trapped atoms. We generalize our microscopic theory of an analog universal quantum simulator to the development of dynamical gauge fields. In the spirit of gauge theories, we investigate emergent lattice models of arbitrary graphs, for which strongly coupled $\mathrm{SU}(n)$ excitations are driven by an underlying multibody interaction. As a minimal model in the infrared, we explore the realization of an archetypical strong-coupling quantum field theory, the $\mathrm{SU}(n)$ Wess-Zumino-Witten model, and discuss a diagnostic tool to map the conformal data of the field theory to the static and dynamical correlators of the fluctuating photons in the guided mode.

Scanning-probe and information-concealing machine learning intermediate hexatic phase and critical scaling of solid-hexatic phase transition in deformable particles

We investigate the two-dimensional melting of deformable polymeric particles with multi-body interactions described by the Voronoi model. We report machine learning evidence for the existence of the intermediate hexatic phase in this system, and extract the critical exponent for the divergence of the correlation length of the associated solid-hexatic phase transition. Moreover, we clarify the discontinuous nature of the hexatic-liquid phase transition in this system. These findings are achieved by directly analyzing system's spatial configurations with two generic machine learning approaches developed in this work, dubbed “scanning-probe” via which the possible existence of intermediate phases can be efficiently detected, and “information-concealing” via which the critical scaling of the correlation length in the vicinity of generic continuous phase transition can be extracted. Our work provides new physical insights into the fundamental nature of the two-dimensional melting of deformable particles, and establishes a new type of generic toolbox to investigate fundamental properties of phase transitions in various complex systems.

Tridynamic model of the beam with transverse shear deformation

Tridynamics is a nonlocal approach to describe lower-scale multi-body interactions at the macroscopic level. Although such a description is sometimes crucial to model the response of a body (for instance carbon nanotube), the computational cost might be very high in the analysis of large structures. Therefore the introduction of basic elements such as beam and plate in this framework could significantly reduce the computational cost. Through this study, we present a set of meaningful and physical quantities that explain the deformation of the beam in this framework. However, the introduced quantities have the potential in describing the variation of field variable in other mechanical problems such as thermal problems. Starting from the kinematic of the beam, a tridynamics beam model (with no restriction on the height of the beam) is developed by using the Lagrangian of the system. The nonlocal parameters are calibrated by carrying out the material correspondences with the classical equations. To see the credibility of the model, a dispersion analysis from low to high wave numbers is performed, and the results are compared with the local and nonlocal models available in the literature.

An implicit spin lattice dynamics integrator in LAMMPS

An iterative implicit solver is implemented in LAMMPS for spin lattice dynamics simulations. An approach to treat multibody interactions, specifically in metallic materials described by the embedded atom method, is presented for the first time in an implicit solver. Magnetization is extremely well preserved in this integrator, with fluctuations eight orders of magnitude smaller than those observed using a timestep of 0.1 fs in the explicit solver currently in LAMMPS. This is true even when larger timesteps than 0.1 fs are used in the implicit integrator, enabling the implicit integrator in some cases to have smaller magnetization error and shorter runtime than the explicit solver for the same overall simulation time. The integrator also conserves energy well. Energy error comparable to or lower than that of the explicit solver is achieved for implicit timesteps up to five times larger than the explicit timestep, with minimal increase in runtime. Errors in energy grow as timestep cubed, while errors in magnetization remain unchanged as timestep increases.

Modeling stress–strain response of shape memory alloys during reorientation of self-accommodated martensites with different morphologies

The shape memory effect observed in many alloys arises due to stress induced transformation between variants of the martensitic phase. It is difficult to study this process in detail using continuum approaches and particle based methods are eminently more suitable. In this work, we study detwinning, which is the transformation between martensite variants due to applied stress using a novel discrete particle model. The approach uses a novel multibody interparticle interaction defined directly using a non-convex free energy potential pertinent to such material behavior. This model is able to describe simultaneously occurring multiple microscale events during the detwinning process: nucleation and propagation of ledges along twin boundary. Due to these underlying microscale events the plateau region of stress–strain response shows a jerky nature. The effect of temperature and morphology on the stress–strain behavior of the self-accommodated martensite microstructure is studied in detail. From the simulations, we identify the morphological features affecting the transformation stress for detwinning. The critical parameters are found to be the length and number of twin and macro-twin boundaries and the number of mobile ledges.

DISTRIBUTION AND EVOLUTION OF FREE VOLUME OF ELLIPSOIDAL PARTICLE SYSTEMS DURING SHEARING

Granular material is a complex multi-body interaction system which is composed of a large number of discrete particles and their surrounding free volume. Although the correlation between free volume and the mechanical properties as well as the deformation characteristics of granular materials has been proved, the local free volume of non-spherical particles is not fully understood at present due to the difficulties in characterizing. In this paper, the combined finite and discrete element method (FDEM) is used to simulate the triaxial tests of ellipsoidal particles with different principal axis lengths, and the Set Voronoi tessellation method is applied to construct the Voronoi cells of the particles during shearing. The statistical distribution and evolution of the local free volume of the granular systems during shearing are analyzed, and the influence of particle shape on the evolution of free volume is studied. Our results show the anisotropy of Voronoi cells gradually increases during shearing, and the degree of anisotropy increase will be intensified with the increase of particle shape asphericity, which means the granular assembly with a larger asphericity will experience more intense rearrangement during shearing. The local void ratio of ellipsoidal particle systems with different asphericity statistically complies with a k-gamma distribution, which is controlled by the global void ratio of granular assembly and not affected by particle shape and shear state. The local void ratio fluctuations follow an Asymmetric Laplace Distribution (ALD), and its asymmetric parameter which has a linear relationship with the global void ratio of granular assembly describes the competition between contraction and dilatation of local free volume.

Modelling, simulation and control of a novel structure varying quadrotor

In this work, a novel structure of a Quadrotor Unmanned Aerial Vehicle (UAV) is proposed to change the dynamics during flight. The proposed mechanism is presented which consists of extendable plates that move along the horizontal axes from the body frame respectively. Essentially, the main goal behind this novel architecture is to enhance performance and improve flight duration in reaching the desired position. The Euler dynamic model is derived to represent the multirotor equation of motion. Basic PID controllers were implemented to demonstrate the concept and to analyse the vehicle behaviour as the structure is altered during flight. A physical modelling software is also used to study the multi-body interactions of rigid bodies as well as the dynamic response. By comparing the performance between the proposed system and the traditional version, the paper reveals improved flight performance for attitude and position tracking. The mathematical representation of the dynamic system was also verified using Msc ADAMS as identical control inputs where simultaneously applied.

Dynamics of majority rule on hypergraphs.

A broad range of dynamical systems involve multibody interactions, or group interactions, which may not be encoded in traditional graphical structures. In this work, we focus on a canonical example from opinion dynamics, namely the majority rule, and we investigate the possibility to represent and analyze the system by means of hypergraphs. We explore the formation of consensus, and we restrict our attention to interaction groups of size 3 in order to simplify our analysis from a combinatorial perspective. We propose different types of hypergraph models, incorporating modular structure or mean-field heterogeneity, and we recast the dynamics in terms of Fokker-Planck equations, which allows us to predict the transient dynamics toward consensus. Numerical simulations show a very good agreement between the stochastic dynamics and theoretical predictions for large population sizes.

Scattering-type multi-probe scanning thermal microscope based on near-field thermal radiation

As one of the most potential applications of near-field thermal radiation, near-field scanning thermal microscope has its own advantage compared with commercial near-field scanning optical microscope, which takes the thermally excited near-field radiation as light source and does not need external illumination. However, the signal of near-field scanning thermal microscope is very weak. Ones have to heat the tip or sample to improve the signal, or apply a sensitive detector. In this work, we describe a scattering-type multi-probe scanning thermal microscope (s-m-SThM) based on near-field thermal radiation which is configured with multi-probe to improve the signal, and present a theory to determine its far-field signal. The theoretical model is based on dipole approximation and consider the multibody mutual interactions between the probes and the sample. The results demonstrate that multibody mutual interactions between the probes and the sample can effectively improve the far-filed signal of s-m-SThM. For a three-probe (Au) configuration, the results show that the far field signal has been increased more than 200 times compared with a single probe (Au) configuration. This work will help to improve the applicability of scanning thermal microscope based on near-field thermal radiation.

DP-MPM: Domain partitioning material point method for evolving multi-body thermal–mechanical contacts during dynamic fracture and fragmentation

We propose a material point method (MPM) to model the evolving multi-body contacts due to crack growth and fragmentation of thermo-elastic bodies. By representing particle interface with an implicit function, we adopt the gradient partition techniques introduced by Homel and Herbold (2017) to identify the separation between a pair of distinct material surfaces. This treatment allows us to replicate the frictional heating of the evolving interfaces and predict the energy dissipation more precisely in the fragmentation process. By storing the temperature at material points, the resultant MPM model captures the thermal advection–diffusion in a Lagrangian frame during the fragmentation, which in return affects the structural heating and dissipation across the frictional interfaces. The resultant model is capable of replicating the crack growth and fragmentation without requiring dynamic adaptation of data structures or insertion of interface elements. A staggered algorithm is adopted to integrate the displacement and temperature sequentially. Numerical experiments are employed to validate the diffusion between the thermal contact, the multi-body contact interactions and demonstrate how these thermo-mechanical processes affect the path-dependent behaviors of the multi-body systems.

Kinetic SIR equations and particle limits

We present and analyze two simple N -particle systems for the spread of an infection, respectively with binary and with multi-body interactions. We establish a convergence result, as N\to\infty , to a set of kinetic equations, providing a mathematical justification of related numerical schemes. We analyze rigorously the time asymptotics of these equations, and compare the models numerically.

Experimental investigation on continuous load transfer process of twin-barge float-over installation

The objective of the present study is to investigate the dynamic motions and impact loads of twin-barge float-over installation with the model tests, which involve multi-body interactions between wave-induced vessel motions and constraint components. A particular contribution of the model tests is that a novel remote rapid (de)ballasting system based on an intelligent algorithm is provided to change the draft of transportation and installation barges continuously, and the load transfer process of twin-barge float-over installation can be simulated in a continuous manner. In addition, several shock absorbers with adjustable constraint components, including the deck support units (DSUs), leg mating units (LMUs), surge and sway fenders, are carefully designed to smooth the continuous load transfer process. The impact loads between topside, barges and substructure can be captured accurately and efficiently. Two typical cases in the mating phase of twin-barge float-over installation, namely Case B2B where the topside is transferred from transportation barge to installation barges, and Case B2J where the topside is transferred from installation barges to pre-installed jacket, are simulated in the model tests. Results indicate that the impact loads on the DSUs of transportation barge increase and those on the DSUs of installation barges decrease continuously as the draft of transportation barge increases in Case B2B. Furthermore, the impact loads on the DSUs of installation barges decrease and the impact loads on the LUMs of Jacket increase continuously as the draft of installation barges increases in Case B2J. The relative motions and impact loads between the topside, barges, and jacket are within an acceptable limit in the investigated conditions. In addition, two particular phenomena are captured in the model tests. One is that the load transfer rate of the topside is closely related to the trim angle of the transportation barge, and another one is that the separations between stabbing pins of topside and receptor cones of DSUs are asynchronous. These phenomena have never been observed in conventional simulation methods.

How choosing random-walk model and network representation matters for flow-based community detection in hypergraphs

Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to hypergraphs and studied the multibody effects on flow-based centrality measures. Mapping the large-scale structure of those flows requires effective community detection methods applied to cogent network representations. For different hypergraph data and research questions, which combination of random-walk model and network representation is best? We define unipartite, bipartite, and multilayer network representations of hypergraph flows and explore how they and the underlying random-walk model change the number, size, depth, and overlap of identified multilevel communities. These results help researchers choose the appropriate modelling approach when mapping flows on hypergraphs.

Formation rate of extreme mass ratio inspirals in active galactic nuclei

Extreme mass ratio inspirals (EMRIs) are important sources for space-borne gravitational wave detectors, such as the laser interferometer space antenna and TianQin. Previous EMRI rate studies have focused on the ``loss cone'' scenario, where stellar-mass black holes (sBHs) are scattered into highly eccentric orbits near the central massive black hole (MBH) via multibody interaction. In this work, we calculate the rate of EMRIs of an alternative formation channel: EMRI formation assisted by the accretion flow around accreting massive black holes. In this scenario, sBHs and stars on inclined orbits are captured by the accretion disk, and then subsequently migrate towards the MBH, under the influence of density wave generation and head wind. By solving the Fokker-Planck equation incorporating both sBH-sBH--sBH-star scatterings and sBH--star-disk interactions, we find that an accretion disk usually boosts the EMRI formation rate per individual MBH by $\mathcal{O}({10}^{1}--{10}^{3})$ compared with the canonical loss cone formation channel. Taking into account that the fraction of active Galactic nuclei (AGNs) is $\ensuremath{\sim}\mathcal{O}({10}^{\ensuremath{-}2}\ensuremath{-}{10}^{\ensuremath{-}1})$, where the MBHs are expected to be rapidly accreting, we expect EMRI formation assisted by AGN disks to be an important channel for all EMRIs observed by space-borne gravitational wave detectors. These two channels also predict distinct distributions of EMRI eccentricities and orbit inclinations with respect to the MBH spin equatorial plane, which can be tested by future gravitational wave observations.

Numerical investigation on the multi-body hydrodynamic interactions under Caspian Sea environmental conditions

Floating production storage and offloading (FPSO) platforms are among the most important platforms in the offshore oil and gas industry. These platforms are generally anchored to the seabed through mooring lines. Usually, the FPSO and the oil tanker are nearby before starting the offloading operation. In this research, the hydrodynamic interactions between a turret-moored FPSO and shuttle tanker were examined using the boundary element method for coupled time-domain dynamic analyses. To apply the sea conditions, the environmental conditions of the Caspian Sea were considered. In this regard, considering the values of hydrodynamic forces on the shuttle tanker, the main purpose of this study was to evaluate the most appropriate vertical position of the shuttle tanker in the vicinity of FPSO. Therefore, 19 vertical center-to-center distances with steps of 20 m (from 80 m to 440 m) were considered between the two vessels. A comprehensive assessment of the dynamic responses of the two floating vessels was then conducted at different angular positions of the shuttle tanker relative to the FPSO. The numerical results indicated that the minimum hydrodynamic force was applied to the shuttle tanker for the distance of 400 m between the centers of the vessels. Also, the 60-degree position of the shuttle tanker relative to the FPSO within a 400-m radius was the most critical position in terms of hydrodynamic forces on the shuttle tanker.

Multi-body effects in a coarse-grained protein force field

The use of coarse-grained (CG) models is a popular approach to study complex biomolecular systems. By reducing the number of degrees of freedom, a CG model can explore long time- and length-scales inaccessible to computational models at higher resolution. If a CG model is designed by formally integrating out some of the system's degrees of freedom, one expects multi-body interactions to emerge in the effective CG model's energy function. In practice, it has been shown that the inclusion of multi-body terms indeed improves the accuracy of a CG model. However, no general approach has been proposed to systematically construct a CG effective energy that includes arbitrary orders of multi-body terms. In this work, we propose a neural network based approach to address this point and construct a CG model as a multi-body expansion. By applying this approach to a small protein, we evaluate the relative importance of the different multi-body terms in the definition of an accurate model. We observe a slow convergence in the multi-body expansion, where up to five-body interactions are needed to reproduce the free energy of an atomistic model.