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At least 19 records

Statistical mechanics models for motion and force planning

The models of statistical mechanics provide an alternative to the methods of classical mechanics more traditionally used in robotics. They have a potential to: improve analysis of object collisions; handle kinematic and dynamic contact interactions within the same frmework; and reduce the need for perfect deterministic world model information. The statistical mechanics models characterize the state of the system as a probability density function (p.d.f.) whose time evolution is governed by a partial differential equation subject to boundary and initial conditions. The boundary conditions when rigid objects collide reflect the conservation of momentum. The models are being developed to embedd in remote semi-autonomous systems with a need to reason and interact with a multiobject environment.

Rodriguez, G.

A Scale-Invariant Model of Statistical Mechanics and Modified Forms of the First and the Second Laws of Thermodynamics

A scale-invariant statistical theory of fields is presented that leads to invariant definition of density, velocity, temperature, and pressure, The definition of Boltzmann constant is introduced as k(sub k) = m(sub k)v(sub k)c = 1.381 x 10(exp -23) J x K(exp -1), suggesting that the Kelvin absolute temperature scale is equivalent to a length scale. Two new state variables called the reversible heat Q(sub rev) = TS and the reversible work W(sub rev) = PV are introduced. The modified forms of the first and second law of thermodynamics are presented. The microscopic definition of heat (work) is presented as the kinetic energy due to the random (peculiar) translational, rotational, and pulsational motions. The Gibbs free energy of an element at scale Beta is identified as the total system energy at scale (Beta-1), thus leading to an invariant form of the first law of thermodynamics U(sub Beta) = Q(sub Beta) - W(sub Beta) +N(e3)U(sub Beta-1).

Sohrab, Siavash H.

Quantum Ornstein-Zernike theory for two-temperature two-component plasmas

Laboratory plasma production almost always preferentially heats either the ions or electrons, leading to a two-temperature state. In this state, density functional theory molecular dynamic simulation is the state of the art for modeling bulk material properties. We construct a statistical mechanics model for the two temperature limit that is theoretically consistent with the molecular dynamics method. We proceed to derive the electron-ion multi-temperature quantum Ornstein-Zernike equations for the first time. This allows the construction of a two-temperature two-component plasma model using the average atom from which we can compute bulk material properties at a fraction of the computation time of the two-temperature density functional theory simulation. The accuracy of the model is benchmarked against ion pair correlation and self-diffusion results from ab initio simulation. Here, we proceed to compute the viscosity and ion thermal conductivity as a function of both ion and electron temperature.

Ab initio molecular dynamics

The Safe Removal of Frozen Air from the Annulus of an LH2 Storage Tank

Large Liquid Hydrogen (LH2) storage tanks are vital infrastructure for NASA. Eventually, air may leak into the evacuated and perlite filled annular region of these tanks. Although the vacuum level is monitored in this region, the extremely cold temperature causes all but the helium and neon constituents of air to freeze. A small, often unnoticeable pressure rise is the result. As the leak persists, the quantity of frozen air increases, as does the thermal conductivity of the insulation system. Consequently, a notable increase in commodity boil-off is often the first indicator of an air leak. Severe damage can result from normal draining of the tank. The warming air will sublimate which will cause a pressure rise in the annulus. When the pressure increases above the triple point, the frozen air will begin to melt and migrate downward. Collection of liquid air on the carbon steel outer shell may chill it below its ductility range, resulting in fracture. In order to avoid a structural failure, as described above, a method for the safe removal of frozen air is needed. A thermal model of the storage tank has been created using SINDA/FLUINT modeling software. Experimental work is progressing in an attempt to characterize the thermal conductivity of a perlite/frozen nitrogen mixture. A statistical mechanics model is being developed in parallel for comparison to experimental work. The thermal model will be updated using the experimental/statistical mechanical data, and used to simulate potential removal scenarios. This paper will address methodologies and analysis techniques for evaluation of two proposed air removal methods.

cryogenic insulation

Development of a Computational Chemical Vapor Deposition Model: Applications to Indium Nitride and Dicyanovinylaniline

A computational chemical vapor deposition (CVD) model is presented, that couples chemical reaction mechanisms with fluid dynamic simulations for vapor deposition experiments. The chemical properties of the systems under investigation are evaluated using quantum, molecular and statistical mechanics models. The fluid dynamic computations are performed using the CFD-ACE program, which can simulate multispecies transport, heat and mass transfer, gas phase chemistry, chemistry of adsorbed species, pulsed reactant flow and variable gravity conditions. Two experimental setups are being studied, in order to fabricate films of: (a) indium nitride (InN) from the gas or surface phase reaction of trimethylindium and ammonia; and (b) 4-(1,1)dicyanovinyl-dimethylaminoaniline (DCVA) by vapor deposition. Modeling of these setups requires knowledge of three groups of properties: thermodynamic properties (heat capacity), transport properties (diffusion, viscosity, and thermal conductivity), and kinetic properties (rate constants for all possible elementary chemical reactions). These properties are evaluated using computational methods whenever experimental data is not available for the species or for the elementary reactions. The chemical vapor deposition model is applied to InN and DCVA. Several possible InN mechanisms are proposed and analyzed. The CVD model simulations of InN show that the deposition rate of InN is more efficient when pulsing chemistry is used under conditions of high pressure and microgravity. An analysis of the chemical properties of DCVA show that DCVA dimers may form under certain conditions of physical vapor transport. CVD simulations of the DCVA system suggest that deposition of the DCVA dimer may play a small role in the film and crystal growth processes.

Cardelino, Carlos

Impact resistance of fiber composites: Energy absorbing mechanisms and environmental effects

Energy absorbing mechanisms were identified by several approaches. The energy absorbing mechanisms considered are those in unidirectional composite beams subjected to impact. The approaches used include: mechanic models, statistical models, transient finite element analysis, and simple beam theory. Predicted results are correlated with experimental data from Charpy impact tests. The environmental effects on impact resistance are evaluated. Working definitions for energy absorbing and energy releasing mechanisms are proposed and a dynamic fracture progression is outlined. Possible generalizations to angle-plied laminates are described.

Chamis, C. C.

Impact resistance of fiber composites - Energy-absorbing mechanisms and environmental effects

Energy absorbing mechanisms were identified by several approaches. The energy absorbing mechanisms considered are those in unidirectional composite beams subjected to impact. The approaches used include: mechanic models, statistical models, transient finite element analysis, and simple beam theory. Predicted results are correlated with experimental data from Charpy impact tests. The environmental effects on impact resistance are evaluated. Working definitions for energy absorbing and energy releasing mechanisms are proposed and a dynamic fracture progression is outlined. Possible generalizations to angle-plied laminates are described.

Chamis, C. C.

Rare events and Griffiths phases in topological quantum error correction

The performance of quantum error correcting (QEC) codes is often studied under the assumption of spatiotemporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. Here, in this work, we study the effects of nonuniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatiotemporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code.

classical statistical mechanics

Theory of Alike Selectivity in Biological Channels

We introduce a statistical mechanical model of the selectivity filter that accounts for the interaction between ions within the channel and derive Eisenman equation of the filter selectivity directly from the condition of barrier-less conduction.

alike selectivity

A comparison of probabilistic generative frameworks for molecular simulations

Generative artificial intelligence is now a widely used tool in molecular science. Despite the popularity of probabilistic generative models, numerical experiments benchmarking their performance on molecular data are lacking. Here, in this work, we introduce and explain several classes of generative models, broadly sorted into two categories: flow-based models and diffusion models. We select three representative models: neural spline flows, conditional flow matching, and denoising diffusion probabilistic models, and examine their accuracy, computational cost, and generation speed across datasets with tunable dimensionality, complexity, and modal asymmetry. Our findings are varied, with no one framework being the best for all purposes. In a nutshell, (i) neural spline flows do best at capturing mode asymmetry present in low-dimensional data, (ii) conditional flow matching outperforms other models for high-dimensional data with low complexity, and (iii) denoising diffusion probabilistic models appear the best for low-dimensional data with high complexity. Our datasets include a Gaussian mixture model and the dihedral torsion angle distribution of the Aib9 peptide, generated via a molecular dynamics simulation. We hope our taxonomy of probabilistic generative frameworks and numerical results may guide model selection for a wide range of molecular tasks.

Artificial intelligence

Sign Problem in Tensor-Network Contraction

We investigate how the computational difficulty of contracting tensor networks depends on the sign structure of the tensor entries. Using results from computational complexity, we observe that the approximate contraction of tensor networks with only positive entries has lower computational complexity as compared to tensor networks with general real or complex entries. This raises the question of how this transition in computational complexity manifests itself in the hardness of different tensor-network-contraction schemes. We pursue this question by studying random tensor networks with varying bias toward positive entries. First, we consider contraction via Monte Carlo sampling and find that the transition from hard to easy occurs when the tensor entries become predominantly positive; this can be understood as a tensor-network manifestation of the well-known negative-sign problem in quantum Monte Carlo. Second, we analyze the commonly used contraction based on boundary tensor networks. The performance of this scheme is governed by the number of correlations in contiguous parts of the tensor network (which by analogy can be thought of as entanglement). Remarkably, we find that the transition from hard to easy—i.e., from a volume-law to a boundary-law scaling of entanglement—already occurs for a slight bias of the tensor entries toward a positive mean, scaling inversely with the bond dimension D , and thus the problem becomes easy the earlier the larger D occurs. This is in contrast both to expectations and to the behavior found in Monte Carlo contraction, where the hardness at fixed bias increases with the bond dimension. To provide insight into this early breakdown of computational hardness and the accompanying entanglement transition, we construct an effective classical statistical-mechanical model that predicts a transition at a bias of the tensor entries of 1 / D , confirming our observations. We conclude by investigating the computational difficulty of computing expectation values of tensor-network wave functions (projected entangled-pair states, PEPSs) and find that in this setting, the complexity of entanglement-based contraction always remains low. We explain this by providing a local transformation that maps PEPS expectation values to a positive-valued tensor network. This not only provides insight into the origin of the observed boundary-law entanglement scaling but also suggests new approaches toward PEPS contraction based on positive decompositions. Published by the American Physical Society 2025

Chen, Jielun (ORCID:0000000178411545)

Perturbative Stability and Error-Correction Thresholds of Quantum Codes

Topologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general Calderbank-Shor-Steane codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip errors, and simultaneously describes a generalized ℤ 2 lattice-gauge theory with quenched disorder. We observe that the clean limit of the latter is precisely the discretized imaginary-time path integral of the corresponding quantum code Hamiltonian when the errors are turned into a perturbative 𝑋 or 𝑍 magnetic field. Motivated by error-correction considerations, we define general order parameters for all such generalized ℤ 2 lattice-gauge theories, and show that they are generally lower bounded by success probabilities of error correction. For CSS codes satisfying the low-density parity-check condition and with a sufficiently large code distance, we prove the existence of a low-temperature ordered phase of the corresponding lattice-gauge theories, particularly for those lacking Euclidean spatial locality and/or when there is a nonzero code rate. We further argue that these results provide evidence for stable phases in the corresponding perturbed quantum Hamiltonians, obtained in the limit of continuous imaginary time. To do so, we distinguish space- and timelike defects in the lattice-gauge theory. A high free-energy cost of spacelike defects corresponds to a successful “memory experiment” and suppresses the energy splitting among the ground states, while a high free-energy cost of timelike defects corresponds to a successful “stability experiment” and points to a nonzero gap to local excitations.

quantum error correction

The 55 K specific heat anomaly in palladium hydride

A specific heat anomaly in PdH and PdD has been observed by Aston et al. (1957) close to 55 K. Its position was found to be independent of hydrogen concentration and its magnitude to be linear in hydrogen concentration. Ferguson's (1965) and Brodowsky's (1972) explanations of the anomaly are shown to be unsatisfactory. This is true also for the detailed mechanical statistical model proposed by Staford and McLellan (1974) for interstitial solid solutions of hydrogen in transition metals. It is shown that Gopal's (1966) simple Schottky model of specific heat anomaly, which considers a system of several levels with Boltzmann statistics, provides much better agreement with experiment than the more elaborate models, both in magnitude and in predicting a linear dependence on hydrogen concentration.

Jacobi, N.

Node-avoiding Levy flight - A numerical test of the epsilon expansion

A study is conducted of an extension of Levy flight to include self-repulsion in the path of the walk. The extension is called node-avoiding Levy flight and its equivalence to the n approaches 0 limit of a statistical mechanical model for a magnetic system with long-range interactions between the spins is shown. By use of this equivalence it is possible to make a detailed comparison beween the results of the epsilon expansion for the magnetic model, a Monte Carlo simulation of the Levy flight model, and the results of a Flory-type argument. This is the first comparison of the epsilon expansion for epsilon much less than 1 with a numerical simulation for any model. Some speculations are made on applications of the model of node-avoiding Levy flight.

Halley, J. W.

Intelligent control and adaptive systems; Proceedings of the Meeting, Philadelphia, PA, Nov. 7, 8, 1989

Various papers on intelligent control and adaptive systems are presented. Individual topics addressed include: control architecture for a Mars walking vehicle, representation for error detection and recovery in robot task plans, real-time operating system for robots, execution monitoring of a mobile robot system, statistical mechanics models for motion and force planning, global kinematics for manipulator planning and control, exploration of unknown mechanical assemblies through manipulation, low-level representations for robot vision, harmonic functions for robot path construction, simulation of dual behavior of an autonomous system. Also discussed are: control framework for hand-arm coordination, neural network approach to multivehicle navigation, electronic neural networks for global optimization, neural network for L1 norm linear regression, planning for assembly with robot hands, neural networks in dynamical systems, control design with iterative learning, improved fuzzy process control of spacecraft autonomous rendezvous using a genetic algorithm.

Rodriguez, Guillermo

A computer aided thermodynamic approach for predicting the formation of Z-DNA in naturally occurring sequences

The ease with which a particular DNA segment adopts the left-handed Z-conformation depends largely on the sequence and on the degree of negative supercoiling to which it is subjected. We describe a computer program (Z-hunt) that is designed to search long sequences of naturally occurring DNA and retrieve those nucleotide combinations of up to 24 bp in length which show a strong propensity for Z-DNA formation. Incorporated into Z-hunt is a statistical mechanical model based on empirically determined energetic parameters for the B to Z transition accumulated to date. The Z-forming potential of a sequence is assessed by ranking its behavior as a function of negative superhelicity relative to the behavior of similar sized randomly generated nucleotide sequences assembled from over 80,000 combinations. The program makes it possible to compare directly the Z-forming potential of sequences with different base compositions and different sequence lengths. Using Z-hunt, we have analyzed the DNA sequences of the bacteriophage phi X174, plasmid pBR322, the animal virus SV40 and the replicative form of the eukaryotic adenovirus-2. The results are compared with those previously obtained by others from experiments designed to locate Z-DNA forming regions in these sequences using probes which show specificity for the left-handed DNA conformation.

Non-NASA Center