Minimum Energy State Research Articles

Global minimum search via annealing: Nanoscale gold clusters

Global minimum potential energy state can be very challenging to locate in a relatively large atomistic system. Our present work investigates this problem using an example of gold nanoclusters, Au10, Au20, Au30, Au50. Nanoscale gold particles (NGPs) contribute heavily in life sciences through their applications in diagnostics and therapeutics. NGPs feature manifold atomistic configurations depending on the conditions of synthesis. We apply annealing molecular dynamics (AMD) as an alternative and supplement to the well-established eigenfollowing (EF) geometry optimization. We conclude that the combination of AMD and EF systematically works more efficiently than EF alone.

Adapting the Chemical Reaction Optimization Algorithm to the Printed Circuit Board Drilling Problem

Chemical Reaction Optimization (CRO) is an optimization metaheuristic inspired by the nature of chemical reactions as a natural process of transforming the substances from unstable to stable states. Starting with some unstable molecules with excessive energy, a sequence of interactions takes the set to a state of minimum energy. Researchers reported successful application of the algorithm in solving some engineering problems, like the quadratic assignment problem, with superior performance when compared with other optimization algorithms. We adapted this optimization algorithm to the Printed Circuit Board Drilling Problem (PCBDP) towards reducing the drilling time and hence improving the PCB manufacturing throughput. Although the PCBDP can be viewed as instance of the popular Traveling Salesman Problem (TSP), it has some characteristics that would require special attention to the transactions that explore the solution landscape. Experimental test results using the standard CROToolBox are not promising for practically sized problems, while it could find optimal solutions for artificial problems and small benchmarks as a proof of concept.

Electronic Properties and Magnetic Moment Distribution on Perovskite Type Slabs: Sr2FeMoO6, SrFeO3 and SrMoO3

Perovskite type slabs were excised from the Sr2FeMoO6, SrFeO3 and SrMoO3 bulk double perovskites, respectively, leaving (001) free surfaces. Supercells were built up for each slab, keeping a 10Å initial free space, to optimize the geometry. Once the minimum energy state was identified, the electronic and magnetic properties of the [001] oriented slabs have been calculated within the Density Functional Theory (DFT) scheme, with the Hubbard-corrected Local Density Approximation (LDA+U) and the CA−PZ functional. Magnetic moment for each atom in the systems was calculated; spin values for the Mo atoms are –0.02ħ, − 0.13ħ and 0.56ħ for the SrMoO3 slab system case and they are aligned antiferromagnetically. Contrarily, Mo magnetic moments in the Sr2FeMoO3 slab system align antiferromagnetically to the corresponding Fe atoms, being around 10% in magnitude; meanwhile, Fe moments increase and align ferromagnetically in SrFeO3. The Densities of States (DOS) and band structures were calculated also to study the electronic behaviors. The vacuum region changes from the initial 10Å, as geometry stabilizes for all the slab cases; however, slab images separation evolves notoriously different for each model.

Finding the Minimum Potential Energy State by Adiabatic Parcel Rearrangements with a Nonlinear Equation of State: An Exact Solution in Polynomial Time

AbstractThe problem of finding the state of minimum potential energy through the rearrangement of water parcels with a nonlinear equation of state is discussed in the context of a combinatorial optimization problem. It is found that the problem is identical to a classical optimization problem called the linear assignment problem. This problem belongs to a problem class known as P, a class of problems that have known efficient solutions. This is very fortunate since this study’s problem has been suggested to be an asymmetric traveling salesman problem. A problem that belongs to a class called NP-hard, for which no efficient solutions are known. The difference between the linear assignment problem and the traveling salesman problem is discussed and made clear by looking at the different constraints used for the two problems. It is also shown how the rearrangement of water parcels that minimizes the potential energy can be found in polynomial time using the so-called Hungarian algorithm. The Hungarian algorithm is then applied to a simplified ocean stratification, and the result is compared to a few different approximate solutions to the minimization problem. It is found that the improved accuracy over the approximate methods comes at a high computational cost. Last, the algorithm is applied to a realistic ocean stratification using a technique that splits the minimization problem into smaller bits.

Numerical Methods for a Multicomponent Two-Phase Interface Model with Geometric Mean Influence Parameters

In this paper, we consider an interface model for multicomponent two-phase fluids with geometric mean influence parameters, which is popularly used to model and predict surface tension in practical applications. For this model, there are two major challenges in theoretical analysis and numerical simulation: the first one is that the influence parameter matrix is not positive definite; the second one is the complicated structure of the energy function, which requires us to find out a physically consistent treatment. To overcome these two challenging problems, we reduce the formulation of the energy function by employing a linear transformation and a weighted molar density, and furthermore, we propose a local minimum grand potential energy condition to establish the relation between the weighted molar density and mixture compositions. From this, we prove the existence of the solution under proper conditions and prove the maximum principle of the weighted molar density. For numerical simulation, we propose a...

Study and Simulation of Deformation Mechanics Modeling of Flexible Workpiece Processing by Rayleigh-Ritz Method

This paper discusses the calculation problems of bending deformation of FWP processing. Take three axis CNC machining as an example, to establish mechanics model of flexible workpiece processing process. The flexible workpiece balance equation is a two-dimensional partial differential equation, to solve the problem of flexible workpiece bending deformation using Rayleigh-Ritz method and designing the test function of bending deformation of flexible workpiece. By satisfying the minimum potential energy condition of FWP processing to work out the approximate solution of bending deformation of flexible workpiece, find out the relationship between material properties of flexible piece, acting forceFz, and deformation value. Finally, the rectangle flexible workpiece which is made up of polyurethane sponge is selected as an experiment subject. The results show that the average relative deviation between theoretical value and observed value is only 5.51%. It is proved that the bending deformation test function satisfies the actual deformation calculation requirements.

Quantum origin of suppression for vacuum fluctuations of energy

By example of a model with a spatially global scalar field, we show that the energy density of zero-point modes is exponentially suppressed by an average number of field quanta in a finite volume with respect to the energy density in the stationary state of minimal energy. We describe cosmological implications of mechanism.

Ab initio molecular dynamics with noisy forces: validating the quantum Monte Carlo approach with benchmark calculations of molecular vibrational properties.

We present a systematic study of a recently developed ab initio simulation scheme based on molecular dynamics and quantum Monte Carlo. In this approach, a damped Langevin molecular dynamics is employed by using a statistical evaluation of the forces acting on each atom by means of quantum Monte Carlo. This allows the use of an highly correlated wave function parametrized by several variational parameters and describing quite accurately the Born-Oppenheimer energy surface, as long as these parameters are determined at the minimum energy condition. However, in a statistical method both the minimization method and the evaluation of the atomic forces are affected by the statistical noise. In this work, we study systematically the accuracy and reliability of this scheme by targeting the vibrational frequencies of simple molecules such as the water monomer, hydrogen sulfide, sulfur dioxide, ammonia, and phosphine. We show that all sources of systematic errors can be controlled and reliable frequencies can be obtained with a reasonable computational effort. This work provides convincing evidence that this molecular dynamics scheme can be safely applied also to realistic systems containing several atoms.

Dynamic versus static fission paths with realistic interactions

The properties of dynamic (least action) fission paths are analyzed and compared to the ones of the more traditional static (least energy) paths. Both the BCPM and Gogny D1M energy density functionals are used in the calculation of the HFB constrained configurations providing the potential energy and collective inertias. The action is computed as in the WKB method. A full variational search of the least-action path over the complete variational space of HFB wave functions is cumbersome and probably unnecessary if the relevant degrees of freedom are identified. In this paper, we consider the particle number fluctuation degree of freedom that explores the amount of pairing correlations in the wave function. For a given shape, the minimum action can be up a factor of three smaller than the action computed for the minimum energy state with the same shape. The impact of this reduction on the lifetimes is enormous and dramatically improves the agreement with experimental data in the few examples considered.

Computational hardness of enumerating groundstates of the antiferromagnetic Ising model in triangulations

Satisfying spin-assignments of triangulations of a surface are states of minimum energy of the antiferromagnetic Ising model on triangulations which correspond (via geometric duality) to perfect matchings in cubic bridgeless graphs. In this work we show that it is NP-complete to decide whether or not a triangulation of a surface admits a satisfying spin-assignment, and that it is #P-complete to determine the number of such assignments. Our results imply that the determination of even the entropy of the Ising model on triangulations at the thermodynamical limit is already #P-hard.The aforementioned claims are derived via elaborate (and atypical) reductions that map a Boolean formula in conjunctive normal form into triangulations of orientable closed surfaces. Moreover, the novel reduction technique enables us to prove that even very constrained versions of #MaxCut are already #P-hard.

Understanding ethylammonium nitrate stabilized cytochrome c – Molecular dynamics and experimental approach

For a conceptual understanding of how an ionic liquid stabilizes a solvated protein, in this study, using new force field parameters, a molecular dynamics simulation (MDS) of the loop and helical regions of hydrated Cytochrome c (cyt c) and its interaction with the ionic liquid ethylammonium nitrate (EAN) have been studied. For a simulation trajectory of 100ns, the changes in network of water around the protein due to EAN and subsequent reorganization of the protein have been analyzed. The radii of gyration of solvated cyt c (13.7Å) and cyt c+EAN (13.4Å) at the end of the trajectory are higher than the protein in its crystalline state (12.64Å) suggesting enhanced stability of the protein due to tightly organized assembly of EAN near the solvated cyt c. This increase in stability of the protein has been verified experimentally using fluorescence, circular dichroic spectroscopy and differential scanning calorimetry. With increasing EAN in cyt c+EAN, protein conformation shows unusually high β strand population. To check whether the beta strand is an intermediate or a local minimum state, denaturation of cyt c with urea in the presence of EAN has been undertaken. Results show that EAN helps in renaturation of the protein by forming a tightly organized assembly around the protein with the beta strand state appearing as a local minimum energy state. Thus the feasibility of using ionic liquids to form networks around the protein and their possible applications in stabilization of the proteins has been demonstrated.

GPU-accelerated replica exchange molecular simulation on solid–liquid phase transition study of Lennard-Jones fluids

Determining the solid–liquid phase transition point by conventional molecular dynamics (MD) simulations is difficult because of the tendency of the system to get trapped in local minimum energy states at low temperatures and hysteresis during cooling and heating cycles. The replica exchange method, used in performing many MD simulations of the system at different temperature conditions simultaneously and performs exchanges of these temperatures at certain intervals, has been introduced as a tool to overcome this local-minimum problem. However, around the phase transition temperature, a greater number of different temperatures are required to adequately find the phase transition point. In addition, the number of different temperature values increases when treating larger systems resulting in huge computation times. We propose a computational acceleration of the replica exchange MD simulation on graphics processing units (GPUs) in studying first-order solid–liquid phase transitions of Lennard-Jones (LJ) fluids. The phase transition temperature for a 108-atom LJ fluid has been calculated to validate our new code. The result corresponds with that of a previous study using multicanonical ensemble. The computational speed is measured for various GPU-cluster sizes. A peak performance of 196.3 GFlops with one GPU and 8.13 TFlops with 64 GPUs is achieved.

The electrostatic profile of consecutive Cβ atoms applied to protein structure quality assessment

The structure of a protein provides insight into its physiological interactions with other components of the cellular soup. Methods that predict putative structures from sequences typically yield multiple, closely-ranked possibilities. A critical component in the process is the model quality assessing program (MQAP), which selects the best candidate from this pool of structures. Here, we present a novel MQAP based on the physical properties of sidechain atoms. We propose a method for assessing the quality of protein structures based on the electrostatic potential difference (EPD) of Cβ atoms in consecutive residues. We demonstrate that the EPDs of Cβ atoms on consecutive residues provide unique signatures of the amino acid types. The EPD of Cβ atoms are learnt from a set of 1000 non-homologous protein structures with a resolution cuto of 1.6 Å obtained from the PISCES database. Based on the Boltzmann hypothesis that lower energy conformations are proportionately sampled more, and on Annsen's thermodynamic hypothesis that the native structure of a protein is the minimum free energy state, we hypothesize that the deviation of observed EPD values from the mean values obtained in the learning phase is minimized in the native structure. We achieved an average specificity of 0.91, 0.94 and 0.93 on hg_structal, 4state_reduced and ig_structal decoy sets, respectively, taken from the Decoys `R' Us database. The source code and manual is made available at https://github.com/sanchak/mqap and permanently available on 10.5281/zenodo.7134.

Pilot‐scale parametric evaluation of concentrated piperazine for CO2 capture at an Australian coal‐fired power station

AbstractConcentrated piperazine (PZ) is a promising new solvent under consideration for post‐combustion capture (PCC) of CO2. A solution of 8 molal PZ was recently evaluated at the Tarong CO2 capture pilot plant in Australia. Initial operation involved evaluation of different operating conditions at the plant to determine the minimum energy conditions for this solvent. Comparison was made to results achieved previously at the same pilot plant with 30 wt% monoethanolamine (MEA). Regeneration energy requirements achieved with concentrated PZ were consistently lower than those achieved with MEA. The lowest regeneration energy for PZ at the pilot plant (2.9 MJ/kgCO2) was roughly 15% lower than the best result predicted for MEA. Inter‐cooling located at the center of the absorber column was also evaluated for the concentrated PZ solvent. The benefit of inter‐cooling was found to depend on the operating conditions of the plant, with operation at higher liquid‐to‐gas (L/G) ratios showing a more pronounced effect. For an L/G ratio of 3.3 kg/kg, inter‐cooling was found to lower the regeneration energy required for PZ by approximately 10%.

Insight derived from molecular dynamics simulations into molecular motions, thermodynamics and kinetics of HIV-1 gp120.

Although the crystal structures of the HIV-1 gp120 core bound and pre-bound by CD4 are known, the details of dynamics involved in conformational equilibrium and transition in relation to gp120 function have remained elusive. The homology models of gp120 comprising the N- and C-termini and loops V3 and V4 in the CD4-bound and CD4-unbound states were built and subjected to molecular dynamics (MD) simulations to investigate the differences in dynamic properties and molecular motions between them. The results indicate that the CD4-bound gp120 adopted a more compact and stable conformation than the unbound form during simulations. For both the unbound and bound gp120, the large concerted motions derived from essential dynamics (ED) analyses can influence the size/shape of the ligand-binding channel/cavity of gp120 and, therefore, were related to its functional properties. The differences in motion direction between certain structural components of these two forms of gp120 were related to the conformational interconversion between them. The free energy calculations based on the metadynamics simulations reveal a more rugged and complex free energy landscape (FEL) for the unbound than for the bound gp120, implying that gp120 has a richer conformational diversity in the unbound form. The estimated free energy difference of ∼−6.0 kJ/mol between the global minimum free energy states of the unbound and bound gp120 indicates that gp120 can transform spontaneously from the unbound to bound states, revealing that the bound state represents a high-probability “ground state” for gp120 and explaining why the unbound state resists crystallization. Our results provide insight into the dynamics-and-function relationship of gp120, and facilitate understandings of the thermodynamics, kinetics and conformational control mechanism of HIV-1 gp120.

Competing structures in two-dimensional trapped dipolar gases

We study a system of dipolar molecules confined in a two-dimensional trap and subject to an optical square lattice. The repulsive long-range dipolar interaction D/r(3) favors an equilateral triangular arrangement of the molecules, which competes against the square symmetry of the underlying optical lattice with lattice constant b and amplitude V. We find the minimal-energy states at the commensurate density n = 1/b(2) and establish the complete square-to-triangular transformation pathway of the lattice with decreasing V involving period-doubled, solitonic, and distorted-triangular configurations.

Magnetic reconnection in the interior of interplanetary coronal mass ejections.

Recent in situ observations of interplanetary coronal mass ejections (ICMEs) found signatures of reconnection exhausts in their interior or trailing edge. Whereas reconnection on the leading edge of an ICME would indicate an interaction with the coronal or interplanetary environment, this result suggests that the internal magnetic field reconnects with itself. In light of this data, we consider the stability properties of flux ropes first developed in the context of astrophysics, then further elaborated upon in the context of reversed field pinches (RFPs). It was shown that the lowest energy state of a flux rope corresponds to ∇ × B = λB with λ a constant, the so-called Taylor state. Variations from this state will result in the magnetic field trying to reorient itself into the Taylor state solution, subject to the constraints that the toroidal flux and magnetic helicity are invariant. In reversed field pinches, this relaxation is mediated by the reconnection of the magnetic field, resulting in a sawtooth crash. If we likewise treat the ICME as a flux rope, any deviation from the Taylor state will result in reconnection within the interior of the flux tube, in agreement with the observations by Gosling et al. Such a departure from the Taylor state takes place as the flux tube cross section expands in the latitudinal direction, as seen in magnetohydrodynamic (MHD) simulations of flux tubes propagating through the interplanetary medium. We show analytically that this elongation results in a state which is no longer in the minimum energy Taylor state. We then present magnetohydrodynamic simulations of an elongated flux tube which has evolved away from the Taylor state and show that reconnection at many surfaces produces a complex stochastic magnetic field as the system evolves back to a minimum energy state configuration.

An effective correlated mean-field theory applied in the spin-1/2 Ising ferromagnetic model

We developed a new treatment for mean-field theory applied in spins systems, denominated effective correlated mean-field (ECMF). We apply this theory to study the spin-1/2 Ising ferromagnetic model with nearest-neighbor interactions on a square lattice. We use clusters of finite sizes and study the criticality of the ferromagnetic system, where we obtain a convergence of critical temperature for the value kBTc/J≃2.27905±0.00141. Also the behavior of magnetic and thermodynamic properties, using the condition of minimum energy of the physical system is obtained.

TH-A-9A-06: Inverse Planning of Gamma Knife Radiosurgery Using Natural Physical Models

Purpose: Treatment-planning systems rely on computer intensive optimization algorithms in order to provide radiation dose localization. We are investigating a new optimization paradigm based on natural physical modeling and simulations, which tend to evolve in time and find the minimum energy state. In our research, we aim to match physical models with radiation therapy inverse planning problems, where the minimum energy state coincides with the optimal solution. As a prototype study, we have modeled the inverse planning of Gamma Knife radiosurgery using the dynamic interactions between charged particles and demonstrate the potential of the paradigm. Methods: For inverse planning of Gamma Knife radiosurgery: (1) positive charges are uniformly placed on the surface of tumors and critical structures. (2) The Gamma Knife dose kernels of 4mm, 8mm and 16mm radii are modeled as geometric objects with variable charges. (3) The number of shots per each kernel radii is obtained by solving a constrained integer-linear problem. (4) The shots are placed into the tumor volume and move under electrostatic forces. The simulation is performed until internal forces are zero or maximum iterations are reached. (5) Finally, non-negative least squares (NNLS) is used to calculate the beam-on times for each shot. Results: A 3D C-shaped tumor surrounding a spherical critical structure was used for testing the new optimization paradigm. These tests showed that charges spread out evenly covering the tumor while keeping distance from the critical structure, resulting in a high quality plan. Conclusion: We have developed a new paradigm for dose optimization based on the simulation of physical models. As prototype studies, we applied electrostatic models to Gamma Knife radiosurgery and demonstrated the potential of the new paradigm. Further research and fine-tuning of the model are underway. NSF CBET-0853157

Spontaneous generation of a crystalline ground state in a higher derivative theory

The possibility of Spontaneous Symmetry Breaking in momentum space in a generic Lifshitz scalar model–a non-relativistic scalar field theory with higher spatial derivative terms–has been studied. We show that the minimum energy state, the ground state, has a lattice structure, where the translation invariance of the continuum theory is reduced to a discrete translation symmetry. The scale of translation symmetry breaking (or induced lattice spacing) is proportional to the inverse of the momentum of the condensate particle. The crystalline ground state is stable under excitations below a certain critical velocity. The small fluctuations above the ground state can have a phonon like dispersion under suitable choice of parameters.At the beginning we have discussed the effects of next to nearest neighbor interaction terms in a model of linear triatomic molecule depicted by a linear system of three particles of same mass connected by identical springs. This model is relevant since in the continuum limit the next to nearest neighbor interaction terms generate higher (spatial) derivative wave equation, the main topic of this paper.