Multibody Interactions Research Articles

Analytical modelling of electrical impedance based adulterant sensor for aqueous sucrose solutions

An analytical model is developed to describe the dielectric behaviour of pure DI water-sucrose solution in which sodium carbonate (Na2CO3) is added as an adulterant. Relative impact of constituent dipoles has been emphasized and multi-body dipolar interactions have been explicitly considered for a comprehensive analysis of such a system in thermal equilibrium. The theoretical model is verified with experimental data obtained from the impedance and capacitance based spectroscopic measurements. The impedance and capacitance of DI water-sucrose solution are observed to vary in a quasi-oscillatory nature with different sucrose content in it. However, such variation shows a decreasing trend and linear nature for a minimum of 1% adulterant content. The system impedance decreases and capacitance increases with increasing adulterant wt% for a given sucrose concentration. For the 0% of adulterant in the solution with varying sucrose content, the impedance and capacitance have varied from 140.12kΩ to 236.17kΩ and 40.7pF to 44.2pF, respectively. However, such values change from 111Ω to 157kΩ and 42.5pF to 72μF for the adulterant content up to 5%.

A new partitioned staggered scheme for flexible multibody interactions with strong inertial effects

In generic flexible multibody interaction problems, the differences in the mass, damping and stiffness of the bodies can be very large. Of particular interest is a small change in the higher mass structure which triggers relatively large inertial effects on the lower mass structure. In this work, a new partitioned staggered time integration scheme is developed and its applicability is extended to the problems involving low mass ratios in coupled multibody problems. The equation of motion of body with larger inertia is integrated by implicit Newmark method, whereas the smaller inertia is solved using a robust self-starting explicit integration procedure. The coupled formulation includes explicit correction terms that adjusts the amount of interfacial velocity, which plays a key role in the stability and accuracy of the simulations. A wide range of mass (10−6–10−1), damping and stiffness (10−3–103) ratios are chosen to assess the stability and accuracy characteristics of the proposed scheme. The closed-form expressions for the coupling parameter have been constructed for both matching and non-matching time stepping through the Godunov–Ryabenkii normal mode analysis. The stability of the proposed method is observed as a function of the relative properties and temporal discretisation of the coupled system. The time step of the heavier body significantly influences the stability more than the lighter body. To maintain the staggering error minimal, an optimal range of the coupling parameter is identified. The error computed with uniform variation in the time step revealed that the present method is more accurate than the existing methods. The partitioned method is an energy preserving integration method for the dynamic analysis of multibody systems. As a potential application of this scheme, flexible multibody problems in the field of offshore engineering, viz., wave energy converter and floater–mooring systems are presented and validated with experimental measurements.

Mesoscopic formulas of linear and angular momentum fluxes.

Many approaches of coarse graining have been developed under the names of Cosserat theory or polar-fluid theory for those materials in which some component elements undergo nonaffine deformations, such as elastic materials with inclusions or granular matters. For the complex elements such as living cells, however, the microscopic variables and their dynamics are often unknown, and there has been no systematic theory of coarse graining from the microscales nor the formulas like the Irving-Kirkwood formula that constitutes the macroscopic stress or couple stress in terms of some microscale quantities. We show that, for the quasi-steady states, the coarse-graining procedure must generally provide us with the Cosserat-type balance equations as long as the procedure keeps track of the conservation of linear and angular momenta, and that the fluxes of these conserved quantities should generally be expressed in the Irving-Kirkwood-type formulas, where the interparticle distance or forces and torques should be replaced by those associated to the pair of neighboring coarse-graining volumes. This framework, which refers to no particular microvariables or dynamics, is valid for active complex matters out of equilibrium and with any multibody interactions.

Taylor Dispersion Analysis as a promising tool for assessment of peptide-peptide interactions

Protein-protein and peptide-peptide (self-)interactions are of key importance in understanding the physiochemical behavior of proteins and peptides in solution. However, due to the small size of peptide molecules, characterization of these interactions is more challenging than for proteins. In this work, we show that protein-protein and peptide-peptide interactions can advantageously be investigated by measurement of the diffusion coefficient using Taylor Dispersion Analysis. Through comparison to Dynamic Light Scattering it was shown that Taylor Dispersion Analysis is well suited for the characterization of protein-protein interactions of solutions of α-lactalbumin and human serum albumin. The peptide-peptide interactions of three selected peptides were then investigated in a concentration range spanning from 0.5mg/ml up to 80mg/ml using Taylor Dispersion Analysis. The peptide-peptide interactions determination indicated that multibody interactions significantly affect the PPIs at concentration levels above 25mg/ml for the two charged peptides. Relative viscosity measurements, performed using the capillary based setup applied for Taylor Dispersion Analysis, showed that the viscosity of the peptide solutions increased with concentration. Our results indicate that a viscosity difference between run buffer and sample in Taylor Dispersion Analysis may result in overestimation of the measured diffusion coefficient. Thus, Taylor Dispersion Analysis provides a practical, but as yet primarily qualitative, approach to assessment of the colloidal stability of both peptide and protein formulations.

Interpretation of Association Behavior and Molecular Interactions in Binary Mixtures from Thermoacoustics and Molecular Compression Data

Density and acoustic velocity were measured for binary liquid mixtures of formamide, N-methylacetamide (NMA), dimethylformamide (DMF), and dimethylacetamide (DMA) with acetonitrile at atmospheric pressure and 293.15 K, 298.15 K, 303.15 K, 308.15 K, or 313.15 K over the concentration range 0.12 to 0.97. Models assuming association and nonassociation of the components of the mixtures were used to predict the behavior of the studied liquids, which would typically show weak interactions. The measured properties were fitted to the Redlich–Kister polynomial to estimate the binary coefficients and standard errors. The data were used to study the molecular interactions in the binary mixtures. Furthermore, the McAllister multibody interaction model was used to correlate the properties of the binary liquid mixtures. Testing of the nonassociation and association models for the different systems showed that, compared with the nonassociation model theoretical results, the association model theoretical results were more consistent with the experimental results.

Linear diffraction analysis for optimisation of the three-float multi-mode wave energy converter M4 in regular waves including small arrays

A general frequency domain dynamic model based on the DIFFRACT code has been developed to predict the motion and power generation of the three-float multi-mode wave energy converter M4, modelled as a two-body problem. The machine has previously been shown experimentally and numerically to have broad-band high capture widths for the range of wave periods typical of offshore sites. The float sizes increase from bow to stern; the bow and mid float are rigidly connected by a beam and the stern float is connected by a beam to a hinge above the mid float where the rotational relative motion is damped to absorb power. The floats are approximately half a wavelength apart so the float forces and motion in antiphase generate relative rotation. Here regular waves representative of swell are investigated and the model is shown to give accurate predictions of experimental results for motion and power for small wave heights and motion which are representative of operational conditions. A linear damper is used to model the power take-off. Without changing the float geometry or the hinge position, adjusting the linear damping factor for each frequency is shown to increase the power by up to three times the experimental value, with a maximum close to the theoretical value for a single float. Increasing the height of the hinge point above the mid float increases the power for the higher periods but can reduce power at lower periods. Since float motion can be quite large, this result can only be indicative of qualitative trends. The effect of small rows has been investigated, up to five machines, and it is shown in particular how the performance of wave energy devices in a row was affected by the multi-body interactions and wave directions. These results are important since the optimum damping factor is shown to be frequency dependent, and increase power generation by up to three times. Furthermore, hydrodynamic interference between M4 machines in a row may significantly increase the power generation when appropriate spacings are chosen.

DYNAMICAL FORMATION SIGNATURES OF BLACK HOLE BINARIES IN THE FIRST DETECTED MERGERS BY LIGO

ABSTRACT The dynamical formation of stellar-mass black hole–black hole binaries has long been a promising source of gravitational waves for the Laser Interferometer Gravitational-Wave Observatory (LIGO). Mass segregation, gravitational focusing, and multibody dynamical interactions naturally increase the interaction rate between the most massive black holes in dense stellar systems, eventually leading them to merge. We find that dynamical interactions, particularly three-body binary formation, enhance the merger rate of black hole binaries with total mass M tot roughly as ∝ M tot β , with β ≳ 4. We find that this relation holds mostly independently of the initial mass function, but the exact value depends on the degree of mass segregation. The detection rate of such massive black hole binaries is only further enhanced by LIGO’s greater sensitivity to massive black hole binaries with M tot ≲ 80 M ⊙ . We find that for power-law BH mass functions dN/dM ∝ M −α with α ≤ 2, LIGO is most likely to detect black hole binaries with a mass twice that of the maximum initial black hole mass and a mass ratio near one. Repeated mergers of black holes inside the cluster result in about ∼5% of mergers being observed between two and three times the maximum initial black hole mass. Using these relations, one may be able to invert the observed distribution to the initial mass function with multiple detections of merging black hole binaries.

Efficient implementation of the many-body Reactive Bond Order (REBO) potential on GPU

The second generation Reactive Bond Order (REBO) empirical potential is commonly used to accurately model a wide range hydrocarbon materials. It is also extensible to other atom types and interactions. REBO potential assumes complex multi-body interaction model, that is difficult to represent efficiently in the SIMD or SIMT programming model. Hence, despite its importance, no efficient GPGPU implementation has been developed for this potential. Here we present a detailed description of a highly efficient GPGPU implementation of molecular dynamics algorithm using REBO potential. The presented algorithm takes advantage of rarely used properties of the SIMT architecture of a modern GPU to solve difficult synchronizations issues that arise in computations of multi-body potential. Techniques developed for this problem may be also used to achieve efficient solutions of different problems. The performance of proposed algorithm is assessed using a range of model systems. It is compared to highly optimized CPU implementation (both single core and OpenMP) available in LAMMPS package. These experiments show up to 6x improvement in forces computation time using single processor of the NVIDIA Tesla K80 compared to high end 16-core Intel Xeon processor.

Motility-driven glass and jamming transitions in biological tissues.

Cell motion inside dense tissues governs many biological processes, including embryonic development and cancer metastasis, and recent experiments suggest that these tissues exhibit collective glassy behavior. To make quantitative predictions about glass transitions in tissues, we study a self-propelled Voronoi (SPV) model that simultaneously captures polarized cell motility and multi-body cell-cell interactions in a confluent tissue, where there are no gaps between cells. We demonstrate that the model exhibits a jamming transition from a solid-like state to a fluid-like state that is controlled by three parameters: the single-cell motile speed, the persistence time of single-cell tracks, and a target shape index that characterizes the competition between cell-cell adhesion and cortical tension. In contrast to traditional particulate glasses, we are able to identify an experimentally accessible structural order parameter that specifies the entire jamming surface as a function of model parameters. We demonstrate that a continuum Soft Glassy Rheology model precisely captures this transition in the limit of small persistence times, and explain how it fails in the limit of large persistence times. These results provide a framework for understanding the collective solid-to-liquid transitions that have been observed in embryonic development and cancer progression, which may be associated with Epithelial-to-Mesenchymal transition in these tissues.

What is the nature of glassy state?

Glasses, non-crystalline solids, and amorphous materials are presently playing increasingly important roles in modern technology. In addition to conventional glass, which is an indispensable material in the current economy in architecture, transport, lighting, and environmental control, a wide variety of glasses and amorphous materials are used in increasingly sophisticated applications in optics, electronics, optoelectronics, energy science and biotechnologies. Glass is considered a vitreous supercooled liquid that is in a thermodynamically metastable state between the molten liquid state and the crystalline state. This unique property of glass is different from the solid, liquid, and gaseous states observed for other elements. The vitrification of a liquid to form a glass is often related to glass transition. This process is a complex dynamic system with multi-body interactions, and hence glass transition is still an unsolved problem in condensed matter physics up to the present time. The formation of glasses is an extremely interesting phenomenon. In terms of thermodynamic phase equilibrium, no substance should persist in the glassy state because glass is a metastable state. However, in terms of kinetics, any material can form a glassy state as long as the cooling rate and the melting viscosity are sufficiently high to prevent crystallization. A comprehensive understanding of the nature of glass formation and the factors that predominantly dominate the glass-forming ability and glass-forming regions of materials is of fundamental importance for advancing the technological applications of glasses. Glass structure is another essential question in glass science. Great efforts have been invested to develop a universal model to represent all glass structures. However, the concept of a universal structure model is incompatible with the fact that the vitreous state is in a thermodynamically metastable state because a specific structure can only arise in a thermodynamically stable state. To date, theories proposed on glass structures are based on various models rather than on the variability and diversity of glass structures in thermodynamically metastable states. The controversy surrounding the glass structure hypotheses lies in the estimation of the degree of order or disorder. While whether or not glass is an ordered state has long been a topic of debate, the structure-properties relationships are not much addressed. Understanding the nature of the glassy state is the key to the development of new glasses with improved properties and manufacturability for various engineering applications. In 2005, the question of “What is the nature of glassy state” was suggested one of the greatest scientific conundrum for science’s 125th anniversary. Herein, the present review strives to provide a comprehensive review of the recent progress made in understanding glassy state and describes the technological developments driven by this new information, especially on the basic scientific problems of glass transition, physical mechanism and theoretical prediction of glass formation, and glass structure hypotheses and technological developments. Finally, we discussed the current progress and the challenges on the nature of glassy state, and suggested possible research directions.

Phase diagrams for the adsorption of monomers with non-additive interactions

In several experimental systems phase diagrams coverage-temperature show a strong asymmetry. This behavior can be reproduced by including non-additive lateral interactions. In this work a Monte Carlo study on the canonical assembly of the criticality of monomer adsorption with non-additive interactions is presented. Traditional pairwise energies were replaced by other more general ones where the lateral interaction between two ad-atoms depends on the coverage at first sphere of coordination. This kind of energies includes multibody interactions like three-body interactions and four-body interactions, etc. These energies induce the formation of several non-additive ordered structures. Finite size scaling method was used to classify the order of phase transition of each non-additive phase. On the other hand, the corresponding phase diagrams are formed naturally, in which case the diagrams show strong asymmetries.

Geometric derivation of the microscopic stress: A covariant central force decomposition

We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle–Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving–Kirkwood–Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.

Consistency of likelihood estimation for Gibbs point processes

Strong consistency of the maximum likelihood estimator (MLE) for parametric Gibbs point process models is established. The setting is very general. It includes pairwise pair potentials, finite and infinite multibody interactions and geometrical interactions, where the range can be finite or infinite. The Gibbs interaction may depend linearly or non-linearly on the parameters, a particular case being hardcore parameters and interaction range parameters. As important examples, we deduce the consistency of the MLE for all parameters of the Strauss model, the hardcore Strauss model, the Lennard-Jones model and the area-interaction model.

Physical implementation of a Majorana fermion surface code for fault-tolerant quantum computation

We propose a physical realization of a commuting Hamiltonian of interacting Majorana fermions realizing Z2 topological order, using an array of Josephson-coupled topological superconductor islands. The required multi-body interaction Hamiltonian is naturally generated by a combination of charging energy induced quantum phase-slips on the superconducting islands and electron tunneling between islands. Our setup improves on a recent proposal for implementing a Majorana fermion surface code (Vijay et al 2015 Phys. Rev. X 5 041038), a ‘hybrid’ approach to fault-tolerant quantum computation that combines (1) the engineering of a stabilizer Hamiltonian with a topologically ordered ground state with (2) projective stabilizer measurements to implement error correction and a universal set of logical gates. Our hybrid strategy has advantages over the traditional surface code architecture in error suppression and single-step stabilizer measurements, and is widely applicable to implementing stabilizer codes for quantum computation.

Probing the microhydration of metal carbonyls: a photoelectron velocity-map imaging spectroscopic and theoretical study of Ni(CO)3(H2O)n.

A series of microhydrated nickel carbonyls, Ni(CO)3(H2O)n- (n = 0-4), are prepared via a laser vaporization supersonic cluster source in the gas phase and identified by mass-selected photoelectron velocity-map imaging spectroscopy and quantum chemical calculations. Vertical detachment energies for the n = 1-4 anions are measured from the photoelectron spectra to be 1.429 ± 0.103, 1.698 ± 0.090, 1.887 ± 0.080, and 2.023 ± 0.074 eV, respectively. The C-O stretching vibrational frequencies in the corresponding neutral clusters are determined to be 1968, 1950, 1945, and 1940 cm-1 for n = 1-4, respectively, which are characteristic of terminal CO. It is determined that the hydrogen atom of the first water molecule is bound to the nickel center. Addition of a second water molecule prefers solvation at the carbonyl terminal. Spectroscopy combined with theory suggests that the solvation of nickel tricarbonyl is dominated by a water-ring network. The present findings would have important implications for the fundamental understanding of the multifaceted mechanisms of the multibody interaction of water and carbon monoxide with transition metals.

Multibody Interactions, Phase Behavior, and Clustering in Nanoparticle-Polyelectrolyte Mixtures.

We present the results of a computational study of the interactions, phase-behavior and aggregation characteristics of charged nanoparticles (CNPs) suspended in solution of oppositely charged polyelectrolytes (PEs). We used an extension of the mean-field polymer self-consistent field theory (SCFT) model presented in our earlier work ( Macromolecules , 2014 , 47 , 6095 - 6112 ) to explicitly characterize the multibody interactions in such systems. For dilute-moderate particle volume fractions, the magnitudes of three and higher multibody interactions were seen to be weak relative to the contributions from pair interactions. On the basis of such results, we embeded the pair-interaction potentials within a thermodynamic perturbation theory approach to identify the phase behavior of such systems. The results of such a framework suggested that the gas and FCC crystal phases were thermodynamically stable, whereas the fluidlike phase was metastable in such systems. To complement the parameters studied using SCFT, we used a recently developed multibody simulation approach to study the aggregation and cluster morphologies in CNP-PE mixtures. For low particle charges, such systems mainly exhibited clusters arising from direct contact aggregation between CNPs. However, for higher particle and PE charges and low PE concentrations, large regions of PE-bridged clusters were seen to form. We present a morphological phase diagram summarizing such results.

Phase Transitions in Delaunay Potts Models

We establish phase transitions for classes of continuum Delaunay multi-type particle systems (continuum Potts models) with infinite range repulsive interaction between particles of different type. In one class of the Delaunay Potts models studied the repulsive interaction is a triangle (multi-body) interaction whereas in the second class the interaction is between pairs (edges) of the Delaunay graph. The result for the edge model is an extension of finite range results in \cite{BBD04} for the Delaunay graph and in \cite{GH96} for continuum Potts models to an infinite range repulsion decaying with the edge length. This is a proof of an old conjecture of Lebowitz and Lieb. The repulsive triangle interactions have infinite range as well and depend on the underlying geometry and thus are a first step towards studying phase transitions for geometry-dependent multi-body systems. Our approach involves a Delaunay random-cluster representation analogous to the Fortuin-Kasteleyn representation of the Potts model. The phase transitions manifest themselves in the percolation of the corresponding random-cluster model. Our proofs rely on recent studies \cite{DDG12} of Gibbs measures for geometry-dependent interactions.

RUNAWAY M DWARF CANDIDATES FROM THE SLOAN DIGITAL SKY SURVEY

We present a sample of 20 runaway M dwarf candidates (RdMs) within 1 kpc of the Sun whose Galactocentric velocities exceed 400 km s$^{-1}$. The candidates were selected from the SDSS DR7 M Dwarf Catalog of West et al. (2011). Our RdMs have SDSS+USNO-B proper motions that are consistent with those recorded in the PPMXL, LSPM, and combined WISE+SDSS+2MASS catalogs. Sixteen RdMs are classified as dwarfs, while the remaining four RdMs are subdwarfs. We model the Galactic potential using a bulge-disk-halo profile (Kenyon et al. 2008; Brown et al. 2014). Our fastest RdM, with Galactocentric velocity 658.5 $\pm$ 236.9 km s$^{-1}$, is a possible hypervelocity candidate, as it is unbound in 77% of our simulations. About half of our RdMs have kinematics that are consistent with ejection from the Galactic center. Seven of our RdMs have kinematics consistent with an ejection scenario from M31 or M32 to within 2{\sigma}, although our distance-limited survey makes such a realization unlikely. No more than four of our RdMs may have originated from the Leo stream. We propose that to within measurement errors, most of our bound RdMs are likely disk runaways or halo objects, and may have been accelerated through a series of multi-body interactions within the Galactic disk or possibly supernovae explosions.

Density Functional Theory Study on the Interactions of Metal Ions with Long Chain Deprotonated Carboxylic Acids.

In this work, interactions between carboxylate ions and calcium or sodium ions are investigated via density functional theory (DFT). Despite the ubiquitous presence of these interactions in natural and industrial chemical processes, few DFT studies on these systems exist in the literature. Special focus has been placed on determining the influence of the multibody interactions (with up to 4 carboxylates and one metal ion) on an effective pair-interaction potential, such as those used in molecular mechanics (MM). Specifically, DFT calculations are employed to quantify an effective pair-potential that implicitly includes multibody interactions to construct potential energy curves for carboxylate-metal ion pairs. The DFT calculated potential curves are compared to a widely used molecular mechanics force field (OPLS-AA). The calculations indicate that multibody effects do influence the energetic behavior of these ionic pairs and the extent of this influence is determined by a balance between (a) charge transfer from the carboxylate to the metal ions which stabilizes the complex and (b) repulsion between carboxylates, which destabilizes the complex. Additionally, the potential curves of the complexes with 1 and 2 carboxylates and one counterion have been examined to higher separation distance (20 Å) by the use of relaxed scan optimization and constrained density functional theory (CDFT). The results from the relaxed scan optimization indicate that near the equilibrium distance, the charge transfer between the metal ion and the deprotonated carboxylic acid group is significant and leads to non-negligible differences between the DFT and MM potential curves, especially for calcium. However, at longer separation distances the MM calculated interaction potential functions converge to those calculated with CDFT, effectively indicating the approximate domain of the separation distance coordinate where charge transfer between the ions is occurring.

Three-dimensional simulations of dilute and concentrated suspensions using smoothed particle hydrodynamics

A three-dimensional model for a suspension of rigid spherical particles in a Newtonian fluid is presented. The solvent is modeled with smoothed particle hydrodynamics method, which takes into account exactly the long-range multi-body hydrodynamic interactions between suspended spheres. Short-range lubrication forces which are necessary to simulate concentrated suspensions, are introduced pair-wisely based on the analytical solution of Stokes equations for approaching/departing objects. Given that lubrication is singular at vanishing solid particle separations, an implicit splitting integration scheme is used to obtain accurate results and at the same time to avoid prohibitively small simulation time steps. Hydrodynamic interactions between solid particles, at both long-range and short-range limits, are verified against theory in the case of two approaching spheres in a quiescent medium and under bulk shear flow, where good agreements are obtained. Finally, numerical results for the suspension viscosity of a many-particle system are shown and compared with analytical solutions available in the dilute and semi-dilute case as well as with previous numerical results obtained in the concentrated limit.