Multibody Interactions Research Articles

Directional transport of active particles in the two-dimensional asymmetric ratchet potential field

Relationship between matter and energy transport has always been one of the key issues that researchers have been searching for in statistical physics and complexity science. In many transport phenomena, the active transport with zero or even no external force in life activities has attracted extensive attention of scholars. As a special kind of active particles, active Brownian particles have received the attention of physicists and biophysicists. These active particles are natural or artificially designed particles, whose scale is in the order of micrometer or nanometer. Different from the traditional passive Brownian particles driven by the equilibrium heat wave generated by the random collision of the surrounding fluid molecules, active Brownian particles can extract energy from their own environment to drive their own motion. Here, directional transport process of active particles in the two-dimensional asymmetric ratchet potential field is analyzed. Both the overdamped medium and the critically damped one are emphasized. Langevin equations with inertia term are introduced to describe the impacts of the self-driven force, friction coefficient, etc. on the directional motion. Then, the average particle speed is found. Thereafter, the relationships between the speed and critical parameters like self-driven force, friction coefficient, etc. are obtained. Two different dynamical domination mechanisms are found, which are expressed as the random collision domination and the self-driven force domination, respectively. Furthermore, the random collision domination is found to correspond to the much higher peak of the two-dimensional asymmetric Brownian rachet potential field, while the self-driven force domination is found to correspond to the much lower peak of the introduced potential. The study will be helpful for discovering the stochastic thermodynamics mechanisms in nonlinear dynamics and nonlinear properties of such multibody interaction system in statistical physics and complex system science.

A joint data and model driven method for study diatomic vibrational spectra including dissociation behavior.

The details of quantum multi-body interactions are so rich and subtle which make it difficult to accurately model for some situations such as the behavior of diatomic long-range vibrations. In recent years, data-driven machine learning has made remarkable achievements in capturing complex relationships that are subtle. Combining the characteristics of these two fields, we propose a joint machine learning method to obtain reliable diatomic vibrational spectra including dissociation energy by using accessible heterogeneous micro/macro information such as low lying vibrational energy levels and heat capacity. Applications of this method to CO and Br2 in the ground state yield their state of the art of vibrational spectra including dissociation limit. The strategy introduced here is an exploration of combining the model-driven and data-driven method to cover subtle physical details that are difficult to study in a single way.

(Invited) Quantum Multi-Body Interactions in Semiconducting WSe2 and C60-Graphene Hybrids for High-Performance Photodetectors

In this work we will discuss the use of halide-assisted low-pressure chemical vapour deposition (HA-LPCVD) with NaCl to help facilitate the growth of monolayer WSe2 at low growth temperatures of ~ 750oC, which is lower than the typical temperatures needed with conventional CVD for realizing 1L WSe2. Moreover, we experimentally probed the quantum multi-body interactions in 1L WSe2 ascribed to excitons, trions and other localized states by analyzing the temperature-dependent photoluminescence spectra. A 1L WSe2 based photodetector was fabricated using Al contacts, which shows a high photoresponsivity, and the interface state trap density of the Al/WSe2 junction was computed to be extremely low. Hybrids of two-dimensional (2D) graphene with fullerene (C60) molecules were also fabricated using electrophoretic deposition, where the C60 clusters are electrically charged upon the application of an external bias in a polar solvent. A low energy shift in the Fermi level EF ~ 140 meV was calculated for the hybrids. When the hybrid devices were irradiated with a broadband white light source and a tunable laser source (with wavelength λ ranging from ~ 400-1100 nm), a strong photoresponse was evident, in contrast to the bare graphene devices which appeared unresponsive. We will discuss the strong photo-response of the C60-graphene hybrids reported here which we attribute to the doping enhancement arising in the graphene upon the adsorption of C60.

Constitutively informed multi-body interactions for lattice particle models

Discrete particle models have been widely used as an alternative to classical continuum mechanics to describe the mechanical behavior of solids, fluids and granular matter. Lattice particle models (LPM) are a subset of discrete particle models which treat the body as a set of interacting point masses with fixed sets of neighbors. Heretofore, the types of interaction forces considered in LPMs have been very limited; consisting mainly of linear pairwise interactions or empirically motivated generalizations thereof. Thus LPMs have been able to describe a very limited range of macroscopic constitutive behavior and the properties have generally been strongly dependent on the discretization.We present a new paradigm for incorporating multibody interactions in LPMs using a mesoscale analog of the Cauchy–Born rule which relates the deformation of the continuum to that of the underlying atomic lattice. We consider a Delaunay triangulation of an irregular lattice of particles comprising the body in its reference configuration. We calculate linear transformations to map the particle positions of each triangle in the current configuration to its reference configuration. Invoking the analogy of the Cauchy–Born rule, we identify the linear transformations with the continuum deformation gradient. Using this we express the continuum constitutive free energy of the body, which is a function of the deformation gradient, in terms of the current positions of the particles. The neighbor interaction forces on each of the particles are taken to be the gradients of this energy. The equations of motion for each particle are then solved numerically to obtain the particle trajectories and the overall deformation of the body. This model is validated using comparisons with classical results of stress distribution in isotropic and anisotropic material plates with circular holes. We then show how this model is able to describe formation of fine microstructure in two different materials: crack branching in brittle materials and twinning in phase transforming materials.

(Invited) Quantum Multi-Body Interactions in Semiconducting WSe2 and C60-Graphene Hybrids for High-Performance Photodetectors

In this work we will discuss the use of a halide-assisted low-pressure chemical vapor deposition (HA-LPCVD) with NaCl to help facilitate the growth of monolayer WSe2 at low growth temperatures of ~ 750oC, which is lower than the typical temperatures needed with conventional CVD for realizing monolayer (1L) WSe2. Moreover, we experimentally probed the quantum multi-body interactions in 1L WSe2 ascribed to excitons, trions and other localized states by analyzing the temperature-dependent photoluminescence spectra. A 1L WSe2 based photodetector was fabricated using Al contacts, which shows a high photoresponsivity, and the interface state trap density (Dit) of the Al/WSe2 junction was computed to be extremely low. Hybrids of two-dimensional (2D) graphene with fullerene (C60) molecules were also fabricated using electrophoretic deposition, where the C60 clusters are electrically charged upon the application of an external bias in a polar solvent. A low energy shift in the Fermi level EF ~ 140 meV was calculated for the hybrids. When the hybrid devices were irradiated with a broadband white light source and a tunable laser source (with wavelength λ ranging from ~ 400-1100 nm), a strong photoresponse was evident, in contrast to the bare graphene devices which appeared unresponsive. We will discuss the strong photo-response of the C60-graphene hybrids reported here which we attribute to the doping enhancement arising in the graphene upon the adsorption of C60.

Exact solution of the extended dimer Bose–Hubbard model with multi-body interactions

It is shown that the extended one-dimensional dimer Bose–Hubbard model with multi-body interactions can be solved exactly by using the algebraic Bethe ansatz mainly due to the site-permutation S2 symmetry. The solution for the model with up to three-particle hopping and three-body on-site interaction is explicitly shown. As an example of the application, lower part of the excitation energy levels and the ground-state entanglement measure of the standard Bose–Hubbard Hamiltonian with the attractive two-body on-site interaction plus the three-body on-site interaction for 100 bosons with variation of the control parameter are calculated by using the exact solution. It is shown that the attractive three-body on-site interaction reinforces the critical point entanglement of the system, which may be helpful for design of an optical lattice for ultracold atoms or a tuneable superconducting quantum interference device with maximal entanglement.

Multibody interactions and nonlinear consensus dynamics on networked systems.

Multibody interactions can reveal higher-order dynamical effects that are not captured by traditional two-body network models. In this work, we derive and analyze models for consensus dynamics on hypergraphs, where nodes interact in groups rather than in pairs. Our work reveals that multibody dynamical effects that go beyond rescaled pairwise interactions can appear only if the interaction function is nonlinear, regardless of the underlying multibody structure. As a practical application, we introduce a specific nonlinear function to model three-body consensus, which incorporates reinforcing group effects such as peer pressure. Unlike consensus processes on networks, we find that the resulting dynamics can cause shifts away from the average system state. The nature of these shifts depends on a complex interplay between the distribution of the initial states, the underlying structure, and the form of the interaction function. By considering modular hypergraphs, we discover state-dependent, asymmetric dynamics between polarized clusters where multibody interactions make one cluster dominate the other.

Computational models for active matter

Active matter, which ranges from molecular motors to groups of animals, exists at different length scales and timescales, and various computational models have been proposed to describe and predict its behaviour. The diversity of the methods and the challenges in modelling active matter primarily originate from the out-of-equilibrium character, lack of detailed balance and of time-reversal symmetry, multiscale nature, nonlinearity and multibody interactions. Models exist for both dry active matter and active matter in fluids, and can be agent-based or continuum-level descriptions. They can be generic, emphasizing universal features, or detailed, capturing specific features. We compare various modelling approaches and numerical techniques to illuminate the innovations and challenges in understanding active matter. Active matter consists of energy-consuming units, which self-propel, exert forces on their neighbours and act collectively, resulting in emergent non-equilibrium behaviour. This Review surveys computational models that describe a wide range of active systems, from synthetic microswimmers to animal herds.

Multiparticle Interactions for Ultracold Atoms in Optical Tweezers: Cyclic Ring-Exchange Terms.

Dominant multiparticle interactions can give rise to exotic physical phases with anyonic excitations and phase transitions without local order parameters. In spin systems with a global SU(N) symmetry, cyclic ring-exchange couplings constitute the first higher-order interaction in this class. In this Letter, we propose a protocol showing how SU(N)-invariant multibody interactions can be implemented in optical tweezer arrays. We utilize the flexibility to rearrange the tweezer configuration on short timescales compared to the typical lifetimes, in combination with strong nonlocal Rydberg interactions. As a specific example, we demonstrate how a chiral cyclic ring-exchange Hamiltonian can be implemented in a two-leg ladder geometry. We study its phase diagram using density-matrix renormalization group simulations and identify phases with dominant vector chirality, a ferromagnet, and an emergent spin-1 Haldane phase. We also discuss how the proposed protocol can be utilized to implement the strongly frustrated J-Q model, acandidate for hosting a deconfined quantum critical point.

Random walks on hypergraphs.

In the past 20 years network science has proven its strength in modeling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Nevertheless, in many relevant cases, interactions are not pairwise but involve larger sets of nodes at a time. These systems are thus better described in the framework of hypergraphs, whose hyperedges effectively account for multibody interactions. Here we propose and study a class of random walks defined on such higher-order structures and grounded on a microscopic physical model where multibody proximity is associated with highly probable exchanges among agents belonging to the same hyperedge. We provide an analytical characterization of the process, deriving a general solution for the stationary distribution of the walkers. The dynamics is ultimately driven by a generalized random-walk Laplace operator that reduces to the standard random-walk Laplacian when all the hyperedges have size 2 and are thus meant to describe pairwise couplings. We illustrate our results on synthetic models for which we have full control of the high-order structures and on real-world networks where higher-order interactions are at play. As the first application of the method, we compare the behavior of random walkers on hypergraphs to that of traditional random walkers on the corresponding projected networks, drawing interesting conclusions on node rankings in collaboration networks. As the second application, we show how information derived from the random walk on hypergraphs can be successfully used for classification tasks involving objects with several features, each one represented by a hyperedge. Taken together, our work contributes to unraveling the effect of higher-order interactions on diffusive processes in higher-order networks, shedding light on mechanisms at the heart of biased information spreading in complex networked systems.

Surrogate modeling of hydrodynamic forces between multiple floating bodies through a hierarchical interaction decomposition

Efficient estimation of wave interactions between multiple floating bodies (diffraction forces and radiation coefficients) is of importance to many applications, with a key one being the layout optimization of arrays of wave energy converter. The computational complexity for this estimation dramatically increases for configurations with large number of bodies. To address this challenge, a data-driven surrogate modeling implementation is discussed in this paper. The foundation of the approach is an innovative application of the many-body expansion principle that overcomes the curse of dimensionality for the surrogate model development. Instead of using a single surrogate model to predict the hydrodynamic characteristics of the multi-body configuration, multiple surrogate models corresponding to clusters with fewer bodies are employed. These lower-order surrogate models can be developed at a substantial smaller computational cost, especially for the first terms of the many-body expansion that contribute dominantly to the total hydrodynamic characteristics. Additional enhancements for the surrogate modeling implementation pertain to the characterization of the surrogate model input and output, exploiting symmetry and invariance principles for the hydrodynamic problem. Using Kriging as surrogate model, the approach is demonstrated for predicting the hydrodynamic characteristics for an array of vertical axisymmetric bodies, but it is extendable to similar multi-body interaction problems or other surrogate modeling techniques. Several numerical case studies are finally presented, showcasing the computational efficiency and prediction accuracy of the proposed method, as well as its scalability to arrays of large size, and the advantages it can offer within the context of layout optimization for wave energy converters.

Engineering NonBinary Rydberg Interactions via Phonons in an Optical Lattice.

Coupling electronic and vibrational degrees of freedom of Rydberg atoms held in optical tweezer arrays offers a flexible mechanism for creating and controlling atom-atom interactions. We find that the state-dependent coupling between Rydberg atoms and local oscillator modes gives rise to two- and three-body interactions which are controllable through the strength of the local confinement. This approach even permits the cancellation of two-body terms such that three-body interactions become dominant. We analyze the structure of these interactions on two-dimensional bipartite lattice geometries and explore the impact of three-body interactions on system ground state on a square lattice. Focusing specifically on a system of ^{87}Rb atoms, we show that the effects of the multibody interactions can be maximized via a tailored dressed potential within a trapping frequency range of the order of a few hundred kilohertz and for temperatures corresponding to a >90% occupation of the atomic vibrational ground state. These parameters, as well as the multibody induced timescales, are compatible with state-of-the-art arrays of optical tweezers. Our work shows a highly versatile handle for engineering multibody interactions of quantum many-body systems in most recent manifestations on Rydberg lattice quantum simulators.

Self-assembly of finite-sized colloidal aggregates

One of the challenges of self-assembling finite-sized colloidal aggregates with a sought morphology is the necessity of precisely sorting the position of the colloids at the microscopic scale to avoid the formation of off-target structures. Microfluidic platforms address this problem by loading into single droplets the exact amount of colloids entering the targeted aggregate. Using theory and simulations, in this paper, we validate a more versatile design allowing us to fabricate different types of finite-sized aggregates, including colloidal molecules or core-shell clusters, starting from finite density suspensions of isotropic colloids in bulk. In our model, interactions between particles are mediated by DNA linkers with mobile tethering points, as found in experiments using DNA oligomers tagged with hydrophobic complexes immersed into supported bilayers. By fine-tuning the strength and number of the different types of linkers, we prove the possibility of controlling the morphology of the aggregates, in particular, the valency of the molecules and the size of the core-shell clusters. In general, our design shows how multivalent interactions can lead to microphase separation under equilibrium conditions.

Modeling chemo-hydrodynamic interactions of phoretic particles: A unified framework

A theoretical framework based on the method of reflections for Laplace's and Stokes' equations is developed to systematically determine multibody chemohydrodynamic interactions of autophoretic colloids. This approach is an efficient alternative to full numerical simulations of suspension dynamics.

A simple lattice Monte Carlo simulation to model interfacial and crowded water rearrangements

A finite, two-dimensional lattice model of liquid water captures the essential nearly four-coordinate hydrogen bonding network, while permitting a simple Metropolis Monte Carlo simulation in conditions ranging from crowded to dilute. This model examines excluded volume perturbations of hydrogen bond switching, avoiding complex topological and chemical heterogeneity of realistic interfaces. Retardation factors (relative to bulk) for switching agree with previous statistical models and atomistic molecular dynamics simulations of hydrated proteins. The model enables straightforward spatial mapping of retardation factors that are difficult to measure in atomistic simulations. The spatially-dependent retardation factors decrease exponentially from the interface. Simulating varying degrees of crowding, we do not find any cooperative, collective contributions anticipated from some recent spectroscopic observations suggesting correlated hydrogen bonding rearrangements of confined water. Longer-range cooperative interfacial influences may arise from complex chemical patterning of the surface, or to non-entropic influences such as multi-body interactions or altered hydrogen bond strengths.

Free-Surface Effects on Interaction of Multiple Ships Moving at Different Speeds

Ships often have to pass each other in proximity in harbor areas and waterways in dense shipping-traffic environment. Hydrodynamic interaction occurs when a ship is overtaking (or being overtaken) or encountering other ships. Such an interactive effect could be magnified in confined waterways, e.g., shallow and narrow rivers. Since Yeung published his initial work on ship interaction in shallow water, progress on unsteady interaction among multiple ships has been slow, though steady, over the following decades. With some exceptions, nearly all the published studies on ship-to-ship problem neglected free-surface effects, and a rigid-wall condition has often been applied on the water surface as the boundary condition. When the speed of the ships is low, this assumption is reasonably accurate as the hydrodynamic interaction is mainly induced by near-field disturbances. However, in many maneuvering operations, the encountering or overtaking speeds are actually moderately high (Froude number Fn > 0.2, where (equation) U is ship speed, g is the gravitational acceleration, and L is the ship length), especially when the lateral separation between ships is the order of ship length. Here, the far-field effects arising from ship waves can be important. The hydrodynamic interaction model must take into account the surface-wave effects. Classical potential-flow formulation is only able to deal with the boundary value problem when there is only one speed involved in the free-surface boundary condition. For multiple ships traveling with different speeds, it is not possible to express the free surface boundary condition by a single velocity potential. Instead, a superposition method can be applied to account for the velocity field induced by each vessel with its own and unique speed. The main objective of the present article is to propose a rational superposition method to handle the unsteady free-surface boundary condition containing two or more speed terms, and validate its feasibility in predicting the hydrodynamic behavior in ship encountering. The methodology used in the present article is a three-dimensional boundary-element method based on a Rankine-type (infinite-space) source function, initially introduced by Bai and Yeung. The numerical simulations are conducted by using an in-house-developed multibody hydrodynamic interaction program "MHydro." Waves generated and forces (or moments) are calculated when ships are encountering or passing each other. Published model-test results are used to validate our calculations, and very good agreement has been observed. The numerical results show that free-surface effects need to be taken into account for Fn > 0.2.

Influence of Polymer Bidispersity on the Effective Particle–Particle Interactions in Polymer Nanocomposites

We investigate the role played by the bidispersity of polymer chains on the local structure and the potential of mean force (PMF) between silica nanoparticles (NPs) in a polystyrene melt. We use the hybrid particle-field molecular dynamics technique which allows to efficiently relax polymer nanocomposites even with high molecular weights.The NPs we investigate are either bare or grafted with polystyrene chains immersed in a melt of free polystyrene chains, whereas the grafted and the free polystyrene chains are either monodisperse or bidisperse. The two-body PMF shows that a bidisperse distribution of free polymer chains increases the strength of attraction between a pair of ungrafted NPs. If the NPs are grafted by polymer chains, the effective interaction crucially depends on bidispersity and grafting density of the polymer chains: for low grafting densities, the bidispersity of both free and grafted chains increases the repulsion between the NPs, whereas for high grafting densities we observe two different effects. An increase of bidispersity in free chains causes the rise of the repulsion between the NPs, while an increase of bidispersity in grafted chains promotes the rise of attraction. Additionally, a proper treatment of multi-body interactions improves the simpler two-body PMF calculations, in both unimodal and bimodal cases. We found that, by properly tuning the bidispersity of both free and grafted chains, we can control the structure of the composite materials, which can be confirmed by experimental observations. As a result, the hybrid particle-field approach is confirmed to be a valid tool for reproducing and predicting microscopic interactions, which determine the stability of the microscopic structure of the composite in a wide range of conditions.

Wave action by arrays of vertical cylinders with arbitrary smooth cross-section

This paper presents an analytical model to solve the linear wave diffraction problem by arrays of bottom-mounted cylinders with arbitrary smooth cross-section. Based on the assumption of ideal fluid and potential theory, the unknown coefficients of total velocity potential can be solved by system of linear equations, which are obtained from the boundary conditions. The accuracy of the present method is verified by comparing it with the numerical tool in terms of the wave force and wave run-up. Multiple cylinders with different configurations are tested, the cross-section of which is circular with cosine perturbation. The results show that the proposed method could obtain an accurate prediction of the wave action with multiple cylinder problems. Finally, the diffraction wave is investigated on arrays of bottom-mounted cylinders with different cross-section and layout. The near-trapping problem with effects of the multi-body interaction are also investigated.

Quantum Multibody Interactions in Halide-Assisted Vapor-Synthesized Monolayer WSe2 and Its Integration in a High Responsivity Photodetector with Low-Interface Trap Density

Among the two-dimensional (2D) transitional-metal dichalcogenides, monolayer (1L) tungsten diselenide (WSe2) has recently attracted a great deal of interest because of its direct band gap and tunab...

Shape-controlled crystallisation pathways in dense fluids of ccp-forming hard polyhedra

Emergent directional entropic forces that favour facet-to-facet alignment of neighbouring colloidal particles – arising from multi-body interactions upon crowding – should cause the process by which colloidal crystals form from fluids of hard polyhedra to be different than that from fluids of hard spheres. We compute nucleation-free energy barriers for a family of shapes that all self-assemble the same cubic close-packed (ccp) crystal structure formed by hard spheres and find that changing rhombicuboctahedra into rhombic dodecahedra by successively removing facets that compete with the ccp structure cause a systematic decrease in barrier heights. We show that this decrease arises from the increased prominence of facets aligned with neighbouring shapes in the target crystal, which produce local environments in the fluid that facilitate crystallisation.