Multibody Interactions Research Articles

Thermodynamics and many body chaos for generalized large q SYK models

This paper considers a type of generalized large q SYK models which include multi-body interactions between Majorana fermions. We derive an effective action in the limit of large N and large q (with frac{q^2}{N} small), and find a universal expression for thermody-namical quantities. We also consider the chaos exponent using the retarded kernel method and find an efficient way to calculate the Lyapunov exponent for generalized large q SYK models numerically.

Extending Esh3D Code to Solve Interacting Eshelby's Inhomogeneity Problems

I present a new development of an open source code Esh3D in solving interacting Eshelby's inhomogeneity problems in whole, half, and finite spaces. The code resolves the interaction between multiple inhomogeneity bodies by assembling and solving a global linear system. For half or finite space problems, the code imposes Neumann and Dirichlet boundary conditions and resolves the surface‐body interaction by hybridizing Eshelby's analytical solutions with a numerical part. I demonstrate the impact of multibody interaction and surface‐body interaction by comparing the results of different problems in whole and finite spaces. This analytical‐numerical hybrid approach, compared to conventional finite element method, is inexpensive and flexible in modeling multiple and evolving inhomogeneity bodies.

Phase reduction beyond the first order: The case of the mean-field complex Ginzburg-Landau equation.

Phase reduction is a powerful technique that makes possible to describe the dynamics of a weakly perturbed limit-cycle oscillator in terms of its phase. For ensembles of oscillators, a classical example of phase reduction is the derivation of the Kuramoto model from the mean-field complex Ginzburg-Landau equation (MF-CGLE). Still, the Kuramoto model is a first-order phase approximation that displays either full synchronization or incoherence, but none of the nontrivial dynamics of the MF-CGLE. This fact calls for an expansion beyond the first order in the coupling constant. We develop an isochron-based scheme to obtain the second-order phase approximation, which reproduces the weak-coupling dynamics of the MF-CGLE. The practicality of our method is evidenced by extending the calculation up to third order. Each new term of the power-series expansion contributes with additional higher-order multibody (i.e., nonpairwise) interactions. This points to intricate multibody phase interactions as the source of pure collective chaos in the MF-CGLE at moderate coupling.

Dynamic gangway responses between TLP and semi-submersible platform during tender-assisted drilling

Numerous tender assisted drilling (TAD) platforms are built to offer comfortable accommodation for crews, on-site construction, and maintenance for production platforms. Two platforms are usually connected via a telescopic gangway, the safety and feasibility of which are crucial during personnel transfer operations. In this paper, the dynamic gangway responses of a TLP-TAD coupled system are investigated numerically and experimentally. The numerical model is established in the frequency domain by using 3D multi-body diffraction/radiation wave theory; this is followed by time domain simulation to consider the second-order drift loads and the non-linear characteristics of the mooring systems. Experiments are performed to verify the numerical model. The connection point between the gangway and platform is simplified as a joint, from which gangway responses can be derived by the global motions of the platforms. Both single-body and multi-body cases are studied under different headings for comparison. The multi-body hydrodynamic interaction is not significant in this paper, while the sway-surge and sway-heave coupling in addition to the wave shielding effect are induced. The results of gangway extension and rotation show that the dominant degree of freedom (DOF) of global motion for gangway responses is identical under different headings. The extreme value predictions of gangway responses are also performed based on Weibull distribution, and extreme sea conditions are obtained.

Extension of the [formula omitted]-[formula omitted]-SPH model for simulating Vortex-Induced-Vibration problems

In this paper, the Lagrangian particle method δ-Plus-SPH model is used to solve a series of benchmark test-cases of vortex induced vibrations (VIV). An Adaptive Particle Refinement (APR) technique is adopted to resolve correctly the boundary layer regions of the moving bodies, and to de-refine the particles that are transported far away. Furthermore, a switch correction on the pressure forces term is adopted in the momentum equation to completely remove the occurrence of the so-called Tensile Instability that leads to the development of numerical cavitation in negative pressure regions. Because of the Lagrangian nature of the method, difficulties arise when intense vortex wakes, typically developed in VIV problems, cross the outflow boundary. To this purpose, a damping zone is also implemented close to the outlet to improve the numerical stability of the scheme. The fluid–structure coupling technique is based on ghost particles properly generated inside the solid bodies. The validation is performed against test-cases for which reference solutions are available in the literature. Within those test-cases challenging benchmarks involving small mass ratios, large-amplitude body motions and multi-body interactions have been selected. For all the benchmark test-cases the δ-Plus-SPH results are in good agreement with the reference solutions, demonstrating the ability of this particle method in solving complex VIV problems.

Mean-field approximations for short-range four-body interactions at ν=35

Trial wavefunctions like the Moore-Read and Read-Rezayi states which minimize short range multibody interactions are candidate states for describing the fractional quantum Hall effects at filling factors $\nu = 1/2$ and $\nu = 2/5$ in the second Landau level. These trial wavefunctions are unique zero energy states of three body and four body interaction Hamiltonians respectively but are not close to the ground states of the Coulomb interaction. Previous studies using extensive parameter scans have found optimal two body interactions that produce states close to these. Here we focus on short ranged four body interaction and study two mean field approximations that reduce the four body interactions to two body interactions by replacing composite operators with their incompressible ground state expectation values. We present the results for pseudopotentials of these approximate interactions. Comparison of finite system spectra of the four body and the approximate interactions at filling fraction $\nu=3/5$ show that these approximations produce good effective descriptions of the low energy structure of the four body ineraction Hamiltonian. The approach also independently reproduces the optimal two body interaction inferred from parameter scans. We also show that for $n=3$, but not for $n=4$, the mean field approximations of the $n$-body interaction is equivalent to particle hole symmetrization of the interaction.

Molecular polarizability in open ensemble simulations of aqueous nanoconfinements under electric field.

Molecular polarization at aqueous interfaces involves fast degrees of freedom that are often averaged-out in atomistic-modeling approaches. The resulting effective interactions depend on a specific environment, making explicit account of molecular polarizability particularly important in solutions with pronounced anisotropic perturbations, including solid/liquid interfaces and external fields. Our work concerns polarizability effects in nanoscale confinements under electric field, open to an unperturbed bulk environment. We model aqueous molecules and ions in hydrophobic pores using the Gaussian-charge-on-spring BK3-AH representation. This involves nontrivial methodology developments in expanded ensemble Monte Carlo simulations for open systems with long-ranged multibody interactions and necessitates further improvements for efficient modeling of polarizable ions. Structural differences between fixed-charge and polarizable models were captured in molecular dynamics simulations for a set of closed systems. Our open ensemble results with the BK3 model in neat-aqueous systems capture the ∼10% reduction of molecular dipoles within the surface layer near the hydrophobic pore walls in analogy to reported quantum mechanical calculations at water/vapor interfaces. The polarizability affects the interfacial dielectric behavior and weakens the electric-field dependence of water absorption at pragmatically relevant porosities. We observe moderate changes in thermodynamic properties and atom and charged-site spatial distributions; the Gaussian distribution of mobile charges on water and ions in the polarizable model shifts the density amplitudes and blurs the charge-layering effects associated with increased ion absorption. The use of polarizable force field indicates an enhanced response of interfacial ion distributions to applied electric field, a feature potentially important for in silico modeling of electric double layer capacitors.

New Perspective of Mitigating the Coffee-Ring Effect: Interfacial Assembly

The evaporation of particle-laden droplets on a substrate usually results in ring-like deposits due to particle migration to the contact lines. This ubiquitous phenomenon, known as the coffee-ring effect (CRE), was initially observed in drying coffee droplets and later in many colloidal systems. The CRE has been intensively investigated during the past two decades to unveil the complexity related to its flow patterns, evaporation physics, and deposition structures after solvent evaporation. However, the contribution of colloidal particle assembly and interactions at the air–liquid interface of sessile droplets to the particle deposition requires more attention. The objective of this Review Article is to highlight the recent advances in mitigating or totally suppressing the CRE by means of interfacial assembly via manipulating the multibody interactions, for example, particle–particle, particle–substrate, particle–flow, and particle–interface interactions. Well-ordered monolayer deposition of the colloidal particles, driven by interfacial assembly, has been demonstrated by several research groups. This unique perspective of suppressing the CRE and creating well-ordered monolayer structures by assembling colloidal particles at the air–liquid interface creates a new paradigm in generating coatings and functional devices through liquid processing. General rules and guidelines are established to provide broader prospects of engineering desirable structures of colloidal particle deposition and assembly.

Investigating the complex interaction between polymer brush grafted surface in the approach-sliding using atomic modeling method

Polymer brush has already been widely used to modify the surface property while there is little research about the interaction between polymer-bearing surfaces at atomic scale. The complex multibody interaction among atoms makes it difficult to characterize the microscopic dynamic process using continuum mechanics. Molecular dynamics method has already been justified to be an efficient theoretical toolkit for investigating the complex dynamic behavior at atomic scale. Friction interface modified by polymer brush in confined space and the corresponding effect are investigated using parallel molecular dynamics simulation method. It is shown that some chains stretch along the direction of flow while others shrink inside the brush resulted by the normal compression. The normal force quickly increases when two end-grafted surfaces are brought into contact while the shear force keeps smaller under the same circumstances. The friction coefficient between polymer brush grafted surfaces is gradually decreased with the increasing of sliding speed which means polymer brush can dramatically improve working conditions. The components of the chains prefer to repel each other as much as possible and weaken interactions among them by stretching away and thus reducing the entropy of the chain.

Robust solid-state qubits based on nuclear quadrupole resonance technique

Advances in quantum information processing can open a way for their numerous applications in various fields of science and technology: communication, precision measurement, computing, nano-scale detectors, and sensors. Solid state with nucleus spins-1/2 is one of the natural bases for creation of a system of the interacting qubits. It was theoretically predicted and experimentally confirmed that logical gates can be realized using quantum states of a single nucleus with a spin I > 1/2. In the present paper we consider representation of a quadrupole spin-3/2 and 7/2 as well as a diatomic molecule as systems of interacting fictitious spins-1/2. It is shown that the Hamiltonians of these systems contain terms describing multi-body interactions and constants of these interactions depend on the applied magnetic field. Considering the fictitious spins as qubits influence of the unique properties of the systems on concurrence is analyzed. The representation of the molecule as a fictitious spin-1/2 system allows us to consider the bipartite concurrences between qubits formatted by the molecule states. The dependence of the concurrences on the magnetic field and its frequency can be used at development of methods to control qubit states and to realize computing protocols. Representation of spins I > 1/2 and their systems as systems of interacting fictitious spins-1/2 can be used at the investigation of properties of complex systems and realization of quantum computation.

Electron-Induced Chemistry in the Condensed Phase

Electron–molecule interactions have been studied for a long time. Most of these studies have in the past been limited to the gas phase. In the condensed-phase processes that have recently attracted attention from academia as well as industry, a theoretical understanding is mostly based on electron–molecule interaction data from these gas phase experiments. When transferring this knowledge to condensed-phase problems, where number densities are much higher and multi-body interactions are common, care must be taken to critically interpret data, in the light of this chemical environment. The paper presented here highlights three typical challenges, namely the shift of ionization energies, the difference in absolute cross-sections and branching ratios, and the occurrence of multi-body processes that can stabilize otherwise unstable intermediates. Examples from recent research in astrochemistry, where radiation driven chemistry is imminently important are used to illustrate these challenges.

A protein interaction free energy model based on amino acid residue contributions: Assessment of point mutation stability of T4 lysozyme.

Here we present a model to estimate the interaction free energy contribution of each amino acid residue of a given protein. Protein interaction energy is described in terms of per-residue interaction factors, μ. Multibody interactions are implicitly captured in μ through the combination of amino acid terms (γ) guided by local conformation indices (σ). The model enables construction of an interaction factor heat map for a protein in a given fold, allows prima facie assessment of the degree of residue-residue interaction, and facilitates a qualitative and quantitative evaluation of protein association properties. The model was used to compute thermal stability of T4 bacteriophage lysozyme mutants across seven sites. Qualitative assessment of mutational effects provides a straightforward rationale regarding whether a particular site primarily perturbs native or non-native states, or both. The presented model was found to be in good agreement with experimental mutational data (R 2 = 0.73) and suggests an approach by which to convert structure space into energy space.

Ship Hydrodynamics in Confined Waterways

The hydrodynamic performance of a vessel is highly dependent on its maneuvering waterways. The existence of the banks and bottom, as well as the presence of the other vessels, could have a significant influence on a ship's hydrodynamic behavior. In confined waterways, many researchers suspect the applicability of the classical potential flow method because of its nonviscous and irrotational assumption. The main objective of the present article is to improve and develop the boundary value problem (BVP) of a potential flow method and validate its feasibility in predicting the hydrodynamic behavior of ships advancing in confined waterways. The methodology used in the present study is a 3D boundary element method based on a Rankine-type Green function. The numerical simulations are performed by using the in-house developed multibody hydrodynamic interaction program MHydro. The waves and forces (or moments) are calculated when ships are maneuvering in shallow and narrow channels, when ships are entering locks, or when two ships are encountering or passing each other. These calculations are compared with the benchmark test data published in MASHCON, and the published computational fluid dynamics results. It has been found that the free-surface elevation, lateral force, and roll moment can be well predicted in ship-bank and ship-bottom problems. However, the potential flow solver fails to predict the sign of the yaw moment because of the cross-flow effect. When a ship is entering a lock, the return-flow effect has to be considered. By adding a proper return-flow velocity to the BVP, the modified potential flow solver could predict the resistance and lateral forces very well. However, it fails to predict the yaw moment because of the flow separation at the lock entrance. The potential flow method is very reliable in predicting the ship-ship problem. The resistance and lateral force, as well as the yaw moment, can be predicted well by using the potential flow method.

Glassy Phase of Optimal Quantum Control.

We study the problem of preparing a quantum many-body system from an initial to a target state by optimizing the fidelity over the family of bang-bang protocols. We present compelling numerical evidence for a universal spin-glasslike transition controlled by the protocol time duration. The glassy critical point is marked by a proliferation of protocols with close-to-optimal fidelity and with a true optimum that appears exponentially difficult to locate. Using a machine learning (ML) inspired framework based on the manifold learning algorithm t-distributed stochastic neighbor embedding, we are able to visualize the geometry of the high-dimensional control landscape in an effective low-dimensional representation. Across the transition, the control landscape features an exponential number of clusters separated by extensive barriers, which bears a strong resemblance with replica symmetry breaking in spin glasses and random satisfiability problems. We further show that the quantum control landscape maps onto a disorder-free classical Ising model with frustrated nonlocal, multibody interactions. Our work highlights an intricate but unexpected connection between optimal quantum control and spin glass physics, and shows how tools from ML can be used to visualize and understand glassy optimization landscapes.

Study on photoelectric characteristics of monolayer WS2 films.

It is important to determine the time-dependent evolution of the excited monolayer WS2, which will provide a basis for the reasonable design of optoelectronic devices based on two-dimensional transition metal dichalcogenides. Here, we made a simple and large-area photodetector based on the monolayer WS2, with high light sensitivity and fast response, benefiting from the special dynamics of carrier involving the exciton, trion, and charge. Moreover, we tested the relaxation behavior of the excited monolayer WS2 by employing transient absorption (TA). It was found that the multi-body interaction among exciton would occur after the density of pump photon increases to 3.45 × 1014 photons per cm2. The exciton dissociation accompanying the generation of trion would appear in the photo-induced relaxation process, which would be a benefit for the operation of this photodetector. Increasing the energy of the exciton is good for the generation of carrier by comparing the relaxation behavior of WS2 excited to A and B exciton states. However, the bound exciton relaxation, originating from the capture process of the defect state, would exist and play an unfavorable role during the functioning of devices.

Rubidium D1 and D2 far wing line shapes induced by rare gases

The far wing absorption cross-sections for the rubidium D1 (5 2S1/2–5 2P1/2) and D2 (5 2S1/2–5 2P3/2) transitions are observed at 10,000 Torr of 4He, 3He, Ne, Ar, Kr, and Xe with alkali densities of 3.3 × 1011 to 3.7 × 1015 molecules per cm3. Blue satellites are observed for the D2 transition, with shifts ranging from 782 cm−1 for helium to 319 cm−1 for Xe. The shifts vary inversely with product polarizability and the cross-section at the peak increases linearly with polarizablity. A red satellite is observed for the Xe broadened D1 line at 796.5 nm, consistent with a difference potential with well of 83 cm−1. The scaling of the cross-section with buffer gas pressure in the far wing suggest multi-body interactions contribute to these high pressure line shapes.

Deriving a lattice model for neo-Hookean solids from finite element methods

Lattice models are popular methods for simulating deformation of solids by discretizing continuum structures into spring networks. Despite the simplicity and efficiency, most lattice models only rigorously converge to continuum models for lattices with regular shapes. Here, we derive a lattice model for neo-Hookean solids directly from finite element methods (FEM). The proposed lattice model can handle complicated geometries and tune the material compressibility without significantly increasing the complexity of the model. Distinct lattices are required for irregular structures, where the lattice spring stiffness can be pre-calculated with the aid of FEM shape functions. Multibody interactions are incorporated to describe the volumetric deformation. We validate the lattice model with benchmark tests using FEM. The simplicity and adaptability of the proposed lattice model open possibilities to develop novel numerical platforms for simulating multiphysics and multiscale problems via integrating it with other modeling techniques.

Numerical Study of Soft Colloidal Nanoparticles Interaction in Shear Flow.

The mechanical behavior of nanoparticle assemblies depends on complex particle interactions that are difficult to study experimentally. Depending on the nanoparticle morphology, these interactions could lead to adhesive and elastic-plastic behavior during contact deformation. The aim of this research is to study the effect of contact interactions between polymer nanoparticles and their impact on the macroscopic properties of formed aggregates. For this purpose, the discrete element method (DEM) was used to develop an interaction model combining elastic-plastic deformation and adhesion to study the behavior of spherical polymeric nanoparticles. Initially, a pair of particles interacting in the normal direction was simulated to evaluate the effect of adhesion and plastic deformation in the pull-off force of the contact. Based on these results, the simulations were extended to a dispersed system of nanoparticles, in which multibody interactions become dominant. Considering the aggregation between the nanoparticles induced by a shear flow, we performed an analysis of the number of aggregates and aggregates size in time to characterize the strength of clusters formed during the process. The simulation results showed that the interaction strength upon breakage of the clusters, correlating with the aggregates size, depends on the nanoparticle's softness. In this way, we verified that the type of contact interaction directly influences the macroscopic mechanical response of nanoparticle assemblies. Therefore, our model represents a new way of predicting the mechanical behavior of polymer nanoparticle systems and of optimizing it by adjusting primary particle properties.

Modeling strong discontinuities in the material point method using a single velocity field

We propose a new way to include strong velocity discontinuities in the material point method (MPM). We use the recent idea of damage gradient partitioning to dynamically determine whether or not deformed locations of material points are on the same side of a discontinuity as each node of a finite element discretization of the Eulerian velocity field. Velocity basis functions associated with the finite element nodes are then altered to ensure that their contributions to discontinuous components of the velocity are supported only at points assigned to the same side of the discontinuity. The partitioning of material points relative to each finite element node eliminates the need for indexing partitions, and accommodates discontinuities that do not partition material into disjoint bodies (e.g., propagating cracks). By building velocity discontinuities directly into the approximation space, sliding contact, separation, and multi-body interaction are possible within a single velocity field. The methodology avoids the need to track contact surfaces, construct and evolve explicit cracks, or use multiple velocity fields. Several numerical examples are computed to support these claims. The examples are also compared to the conventional MPM, demonstrating the method’s superiority in dealing with sliding contact and separation.

Random field Ising-like effective theory of the glass transition. II. Finite-dimensional models

As in the preceding paper we aim at identifying the effective theory that describes the fluctuations of the local overlap with an equilibrium reference configuration close to a putative thermodynamic glass transition. We focus here on the case of finite-dimensional glass-forming systems, in particular supercooled liquids. The main difficulty for going beyond the mean-field treatment comes from the presence of diverging point-to-set spatial correlations. We introduce a variational low-temperature approximation scheme that allows us to account, at least in part, for the effect of these correlations. The outcome is an effective theory for the overlap fluctuations in terms of a random-field + random-bond Ising model with additional, power-law decaying, pair and multi-body interactions generated by the point-to-set correlations. This theory is much more tractable than the original problem. We check the robustness of the approximation scheme by applying it to a fully connected model already studied in the companion paper. We discuss the physical implications of this mapping for glass-forming liquids and the possibility it offers to determine the presence or not of a finite-temperature thermodynamic glass transition.