Configuration Space Research Articles

Exploiting Equivariance in the Design of Tracking Controllers for Euler-Poincare Systems on Matrix Lie Groups

The trajectory tracking problem is a fundamental control task in the study of mechanical systems. Hamiltonian systems are posed on the cotangent bundle of configuration space of a mechanical system, however, symmetries for the full cotangent bundle are not commonly used in geometric control theory. In this paper, we propose a group structure on the cotangent bundle of a Lie group and leverage this to define momentum and configuration errors for trajectory tracking, drawing on recent work on equivariant observer design. We show that this error definition leads to error dynamics that are themselves “Euler-Poincare like” and use these to derive simple, almost global trajectory tracking control for fully-actuated Euler-Poincare systems on a Lie group state space.

Importance sampling within configuration space integration for adsorbate thermophysical properties: a case study for CH3/Ni(111).

A new strategy is presented for computing anharmonic partition functions for the motion of adsorbates relative to a catalytic surface. Importance sampling is compared with conventional Monte Carlo. The importance sampling is significantly more efficient. This new approach is applied to CH3* on Ni(111) as a test case. The motion of methyl relative to the nickel surface is found to be anharmonic, with significantly higher entropy compared to the standard harmonic oscillator model. The new method is freely available as part of the Minima-Preserving Neural Network within the ADTHERM package.

Exploration of beamline configuration space for identifying robust quadrupole configurations

Experimental beamlines often are regularly reconfigured to meet changing requirements of the experiments and to minimize beam losses. The configuration is usually done with the help of beam optics tools like MADX. These tools offer matching capabilities which allow to find solutions in terms of quadrupole strengths. However, such solutions are found by satisfying the given constraints only and do not take into account limited precision of actual quadrupole devices. Under the influence of quadrupole errors due to magnetic hysteresis, power converter trips etc, the original beamline optics often degrades. This results in beam losses or loss of focus at the experimental target. Readjustment of the optics costs valuable experiment time. Hence, it is desirable to operate a beamline configuration which not only meets the requirements but is also robust against quadrupole errors. Such a configuration will deviate from its nominal properties only by a small margin even when the quadrupole strengths deviate within specified intervals. We present the systematic exploration of beamline configuration space to identify robust configurations. The results are discussed for the BIGKARL beamline at Forschungszentrum Jülich and the findings are supported by experimental data.

The trials and triumphs of modelling X-ray absorption spectra of transition metal phthalocyanines.

This study explores the electronic structure of Co, Fe and Mn phthalocyanines (TMPcs) as well as their perfluorinated counterparts through a series of electronic structure calculations utilizing multireference methods and by simulating their metal L-edge and ligand (nitrogen and fluorine) K-edge X-ray absorption spectra (XAS) in an angle-resolved manner. Simulations targeting different ground-state symmetries, where relevant, have been conducted to observe changes in the N K-edge lineshape. The applicability of the quasi-degenerate formulation of n-electron valence state perturbation theory (QD-NEVPT2) for L-edge X-ray absorption spectroscopy (XAS) is evaluated, alongside the use of a restricted active space (RAS) formalism to describe the final-state multiplets generated by L-shell X-ray processes. Our findings provide valuable insights into the electronic properties of TMPcs, in particular with respect to the effect of fluorination, and demonstrate the broad applicability of various formulations of NEVPT2 in spectral simulations. Moreover, this study highlights the utility of manual truncation of the configuration spaces in order to allow for large active orbital spaces in aforementioned calculations.

Vibrational circular dichroism spectra of proline in water at different pH values.

Recording VCD spectra of aqueous solution poses a particular challenge as water is a strong infrared absorber. Likewise, the computational analysis of VCD spectra by means of DFT-based spectral calculations requires the consideration of explicit solvent molecules, thus posing an even greater challenge. Several studies suggested that by modeling the solvent environment with a few water molecules in a micro-solvation approach would be sufficient to describe experimental spectra. For example, using proline at different pH values, we herein show that a change in the relative spatial orientation of a single water molecule in five-fold solvated structures strongly affects the computed VCD spectral signatures and that Boltzmann-weighted spectra do not correctly reproduce the experiment. We thus explored an approach based on molecular dynamics and subsequent DFT-calculations, in which we considered 30 water molecules (about 1.5 solvation shells). Once again, it was found that the Boltzmann-weighted spectra obtained on the basis of several hundred structures did not correctly reproduce experimental signatures, and a simple averaging scheme resulted in well-matching spectra with comparable bandwidths. The rationale behind the procedure was that sampling the configurational space of the solvent molecules is as equally important as the conformational sampling of the solute. For conformationally more flexible molecules, it is assumed that a much larger set of structures will have to be computed in order to properly sample the conformational space of both solute and solvent.

Kinematics and dynamics of non-developable origami

Non-developable origami is a unique type of origami structures that cannot be unfolded into a flat sheet without stretching. In this work, we study the kinematics and dynamics of such origami, theoretically, numerically and experimentally, considering rigid panels and stretchable creases. Unlike developable origami, we find that non-developable origami exhibits distinct folding angle relationships, leading to several separate branches in its kinematic configuration space with snap-through and locking behaviours. By modelling the creases as stretchable torsional springs, we derive a dynamic model to analyse the deployment of non-developable origami structures, from single-vertex origami to origami chains. Our dynamic model unveils the snap-through behaviour between the two kinematics branches of the single-vertex non-developable origami structure, which is further validated by experiments with excellent agreement. We believe that our kinematic and dynamic framework of non-developable origami will greatly expand the current design space of origami structures and guide the design of novel origami actuators.

Hyperparameters optimization for the machine learning

There is no single best Hyperparameter Optimization algorithm. Different optimization algorithms meet different Hyperparameter Optimization tasks with different constraints. To accelerate the Hyperparameter Optimization, it is necessary to parallelize training executions of various tests, introduce distributed training and prematurely stop unpromising tests. It is recommended to use a library approach to support the hyperparameter optimization service. Ray Tune is the best by far among the open source Hyperparameter Optimization. Hyperparameter optimisation (HPO) is the process of identifying a set of hyperparameters that yields an optimal model. By optimal, we mean the model that minimises a predefined loss function on a given data set. This is a repeated model training process, except that the neural network is trained with a different set of hyperparameters each time. In this process, the optimal set of hyperparameters will be identified. During the grid search, users specify a limited set of values for each hyperparameter and then select trial hyperparameters from the Cartesian product of these values. Once the grid is constructed, the GPGs are tested with the grid values. The grid search suffers when the number of hyperparameters becomes larger or the parameter search space becomes larger, as in this case the required number of estimates will grow exponentially. Another problem with grid search is its inefficiency. Since grid search treats each set of hyperparameter candidates equally, it will spend a lot of computational resources in the suboptimal configuration space without spending enough computational power on the optimal space.

Event-Triggered Attitude Consensus of Multiple Rigid Body Systems With Prescribed Performance.

The event-triggered almost global attitude consensus problem is considered in this article for multiple rigid body systems with prescribed performance. Two kinds of attitude consensus protocols using axis-angle vectors are proposed at the kinematic level with different prescribed performance constraints. The first protocol aims to achieve the event-triggered attitude consensus almost globally under jointly connected graphs. Based on a prescribed performance function with local states, the configuration space of parameterized attitude representations is shown to be positively invariant which almost globally covers [Formula: see text] . The second protocol is designed to reach attitude consensus with the prescribed transient behavior guaranteed in the event-triggered setting. By defining a prescribed performance function using the metric on axis-angle spaces, a dynamic event-triggered framework is designed to ensure both the attitude geometric topology constraint and prescribed convergence performance. Finally, numerical results are given to show the validness of the two control protocols.

R-MATRIX CALCULATIONS OF THE DEUTERIUM-TRITIUM FUSION CROSS SECTION BASED ON PRECISE COULOMB FUNCTIONS

Due to the availability of fuel, favorable kinetics, and high output energy, the deuterium-tritium (D-T) fusion reaction is dominantly used in thermonuclear fusion. This paper presents a detailed, step-by-step theoretical calculation of the D-T fusion cross-section within the framework of the phenomenological R-matrix method.The fundamental principles of the phenomenological R-matrix method are outlined.Nuclear and Coulomb interactions are addressed by the R-matrix formalism, which classifies the configuration space into internal and external regions, respectively.Precise Coulomb functions are utilized in the calculations, essential for the accurate determination of the penetration and shift factors.Precise Coulomb functions for the D+T,4He+12C systems have been calculated. The penetration and shift factors for the D+T system for a given angular momentum have been obtained.Two different R-matrix models with parameters from recent scientific papers are employed to calculate D-T fusion cross-sections and reaction rates, which are then compared with those obtained from the ENDF/B-VIII.0 library data. Within a crucial low-energy range (from 0 to 0.1 MeV), important for fusion technology, our results show quite good agreement with experimental data, while in a high-energy range, the obtained results are slightly underestimated due to non-resonant 5He levels not being taken into account. These findings indicate that the models can be used for future thermonuclear fusion applications.

An Upper Limb Exoskeleton Motion Generation Algorithm Based on Separating Shoulder and Arm Motion.

Many rehabilitation exoskeletons have been used in the field of stroke rehabilitation. Generating human-like motion is necessary for exoskeletons to help patients perform activities of daily living (ADL) while maintaining interaction quality and ergonomics. However, most of the current motion generation algorithms utilize inverse kinematics (IK) to solve the final configuration before generation, and do not consider the movement of shoulder girdle. Separately considering the shoulder girdle motion and arm motion, this paper proposes an algorithm integrated IK to generate human-like motion. The arm moves towards the target with a bell-shaped velocity in the absence of the final configuration, and the shoulder girdle maintain natural passive motion. Moreover, the generated motion can be mapped to the configuration space of exoskeletons. Compared with the experimental data collected using a motion capture system, the values of RMSE and HPDI of the generated wrist trajectory in the task space are within 0.2 and 0.17, respectively, while those of RMSE in the joint space are within 15 deg, which demonstrates the human-like nature of the generated motion.

Variational Estimation for Mechanical Systems on Lie Groups based on Geometric Mechanics

Geometric mechanics analyzes mechanical systems in the framework of variational mechanics, while accounting for the geometry of the configuration space. From the late 1970s, developments in this area produced several schemes for geometric control of mechanical systems in continuous time and discrete time. In the mid to late 2000s, geometric mechanics was first applied to state estimation of mechanical systems, particularly systems evolving on Lie groups as configuration manifolds, like rigid body systems. Much of the existing work on geometric mechanics-based estimation has been in continuous time, using deterministic, semi-stochastic and stochastic approaches. While the body of existing literature on discrete-time estimation schemes on Lie groups is not as extensive, the literature on this topic is contemporaneous with continuous-time schemes. This work describes some recent and ongoing research on geometric mechanics-based estimation schemes in continuous and discrete time from the mid-2010s, which were developed using the Lagrange-d’Alembert principle applied to rigid body systems. This approach gives (deterministic) observer designs with strong stability and robustness properties. This work concludes with potential extensions of this approach to mechanical systems with principal fiber bundles as configuration manifolds.

Configuration spaces of clusters as $E_d$-algebras

Configuration spaces of clusters as $E_d$-algebras

Six-dimensional quantum dynamics of an Eley-Rideal reaction between gaseous and adsorbed hydrogen atoms on Cu(111).

In the form of direct abstraction of a surface adsorbate by a gaseous projectile, the Eley-Rideal (ER) reaction at the gas-surface interface manifests interesting dynamics. Unfortunately, high-dimensional quantum dynamical (QD) studies for ER reactions remain very challenging, which demands a large configuration space and the coordinate transformation of wavefunctions. Here, we report the first six-dimensional (6D) fully coupled quantum scattering method for studying the ER reaction between gas phase H(D) atoms and adsorbed D(H) atoms on a rigid Cu(111) surface. Reaction probabilities and product rovibrational state distributions obtained by this 6D model are found to be quite different from those obtained by reduced-dimensional QD models, demonstrating the high-dimensional nature of the ER reaction. Using two distinct potential energy surfaces (PESs), we further discuss the influence of the PES on the calculated product vibrational and rotational state distributions, in comparison with experimental results. The lateral corrugation and the exothermicity of the PES are found to play a critical role in controlling the energy disposal in the ER reaction.

Đorđe Alfirević and Sanja Simonović Alfirević: Principles of residential space configuration, Institute of Architecture and Urban and Spatial Planning of Serbia and Faculty of Architecture of the University of Belgrade, Belgrade, 2023

Đorđe Alfirević and Sanja Simonović Alfirević: Principles of residential space configuration, Institute of Architecture and Urban and Spatial Planning of Serbia and Faculty of Architecture of the University of Belgrade, Belgrade, 2023

Study of the Stability of the Mathematical Model of the Bound Pendulums Motion

The article presents a study of the dynamics of an oscillatory dissipative system of two elastically coupled pendulums in a magnetic field. Nonlinear normal modes of oscillation of a pendulum system have been studied, taking into account the resistance to the medium and the damping moment created by the elastic element. A system with two degrees of freedom is considered, in which the masses of the pendulums differ significantly, which leads to the possibility of localization of oscillations. In the following study, the mass ratio is chosen as a small parameter. For approximate calculations of magnetic forces, the Padé approximation is used, which best satisfies the experimental data. This approximation provides a very accurate description of the magnetic excitation. The presence of external influences in the form of magnetic forces and various types of loads that exist in many engineering systems significantly complicates the analysis of vibration modes of nonlinear systems. Studies have been carried out of nonlinear normal modes of oscillations in this system, one of the modes being a coupled mode, and the second being a localized mode. The oscillation modes are constructed using the multiscale method. Both regular and complex behavior when changing system parameters have been studied. The influence of these parameters was studied for small and large initial angles of inclination of the pendulum. Analytical solution based on the fourth order Runge-Kutta method compared with numerical simulation results. The initial conditions for calculating the vibration modes were determined by the analytical solution. Numerical modeling, consisting of constructing phase diagrams, trajectories in configuration space, and amplitude-frequency characteristics, allows one to evaluate the dynamics of a system, which can be either regular or complex. The stability of oscillation modes was studied using numerical analysis tests, which are implementations of the Lyapunov stability criterion. In this case, the stability of the oscillation modes is determined by assessing the orthogonal deviations of the corresponding trajectories of the oscillation modes in the configuration space.

A JUSTIFIED GRAPH ANALYSIS OF PRAYER SPACE IN FLOODED HOMES

Indonesia's risks of natural disasters force its people to live and adapt. It happens in Samarinda's urban settlements, which flood annually. Indonesia, a religious country, applied religion to most aspects of life. The religious element is persistent even in homes being inundated by floods. Devout Muslims consistently perform the five daily Shalah and sometimes Sunnah prayers in flooded conditions. This paper analyzed the spatial configuration of the Muslim prayer space in the flooded residence from different phases. The study method was based on Justified Graph analysis, and the sample was a stilt house in some periods. The research locus was in the most settlement area covering frequent floods. This research found that Integration and Mean Depth were the critical factors in prayer spaces in flooded homes due to the connection with other spaces, visual control, and interaction. Muslim home renovations should have a prayer space with high Integration value and low Mean Depth. High Integration connects the prayer space to numerous rooms, making controlling and interacting with others during a flood easier. Low Mean Depth allows easy access to the prayer space from the main entrance. A prayer space will ensure the house has a safe area during a flood.

Efficient enumeration and visualization of helix-coil ensembles

Helix-coil models are routinely used to interpret circular dichroism data of helical peptides or predict the helicity of naturally-occurring and designed polypeptides. However, a helix-coil model contains significantly more information than mean helicity alone, as it defines the entire ensemble—the equilibrium population of every possible helix-coil configuration—for a given sequence. Many desirable quantities of this ensemble are either not obtained as ensemble averages or are not available using standard helicity-averaging calculations. Enumeration of the entire ensemble can allow calculation of a wider set of ensemble properties, but the exponential size of the configuration space typically renders this intractable. We present an algorithm that efficiently approximates the helix-coil ensemble to arbitrary accuracy by sequentially generating a list of the M highest populated configurations in descending order of population. Truncating this list of (configuration, population) pairs at a desired accuracy provides an approximating sub-ensemble. We demonstrate several uses of this approach for providing insight into helix-coil ensembles and folding mechanisms, including landscape visualization.

Improvement of the mathematical model of the navigation area for the optimal ship passage route

Planning the optimal route of a vessel passage is a key problem in the design of traffic planning and navigation systems. This problem consists in the need to determine the trajectory from the initial point to the final point, which ensures the absence of collisions with obstacles. When solving this problem, it is also necessary to take into account the dynamics of the vessel, the uncertainty and non-stationarity of the water environment, the time to calculate the path and the physical feasibility of the trajectory. The planning task is traditionally formulated as the task of optimizing the state of the current position of the vessel relative to the target position. Most often, this problem is solved in the configuration space, which consists of a set of obstacles, kinematic and dynamic constraints, and a set of points in the swimming areas. Planning methods are divided into global and local. Global methods build a route based on a known map, while local methods adjust the path when obstacles are detected. However, at the moment, mathematical models of the navigation area only partially take into account the uncertainties of the zones in which the vessel operates. This determines the planning of local trajectories within a specific swimming area using a simple straight-line algorithm. Since in the process of planning the transition from «berth» to «berth» in order to ensure the navigational safety of the ship, it is necessary to use all available information to compile the most detailed imaginary model of the ship's transition before the start of each voyage. In order to solve this task, this paper proves that in the process of building the optimal route, it is necessary to conduct a full analysis of all stages of the passage of the vessel, which increases the optimality of the planned passage route. The mathematical model of the navigation area for the optimal route of the ship's passage has been improved, in which the mathematical apparatus of fuzzy sets is applied

Electrophysiological characteristics and ablation of ventricular arrhythmias originating from the intramural basal inferior septum.

The electrocardiographic and electrophysiological characteristics of ventricular arrhythmia (VA) arising from the intramural basal inferior septum (BIS) have not been specifically addressed to date. The aim of the current study was to characterize intramural BIS-VA and distinguish it from those with endocardial origins besides clarifying the anatomical configurations of the pyramidal space. Fifty-five consecutive patients undergoing catheter ablation of VAs from BIS were identified and divided into three groups: the left ventricular (LV)-BIS group (n = 28), right ventricular (RV)-BIS group (n = 8), and intramural group (Intra, n = 19). Compared with the LV-BIS and RV-BIS groups, patients in the Intra group presented with no adequate earliest activation time at the two-sided BIS and epicardial coronary system [right: 7.79 ± 2.38 vs. left: 7.16 ± 2.59 vs. the middle cardiac vein (MCV): 6.26 ± 1.73 ms, P = 0.173] and poor-matched pacing-produced QRS at each site. Under the intracardiac echocardiography view, the pyramidal base was the broadest part of the septum and served as the division of the two-sided BIS. Focal ablation yielded promising acute-term and long-term procedural success in the LV-BIS and RV-BIS groups. But for the Intra group, VAs disappeared only after stepwise ablation successively targeted early preferential exit. After follow-up, three patients in the Intra group had recurrent VA, and all of them were treated well by a redo procedure or drug therapy. Intramural VAs were relatively common in the BIS region in our series. Intra-procedural mapping was important to distinguish the intramural VAs from other VAs by comparing the local activation time and pacing mapping. Procedural success could be achieved by stepwise ablation on the counterpart sides of the BIS and within the MCV.

Vibrational Analysis of Constrained Molecular Systems.

Vibrational spectroscopy, including infrared (IR), Raman spectroscopy, and vibrational circular dichroism, is instrumental in determining the structure and composition of molecules. These techniques are highly sensitive to molecular conformations. However, full molecular optimization, necessary for theoretical vibrational spectra, can lead to unintended conformational changes, especially in large biomolecules like polypeptides. To address this, dihedral angle constraints can be imposed during optimization to preserve the molecule's native conformation. Constraint-optimized molecular geometries, not being true stationary points in the full configurational space, pose challenges for traditional vibrational analysis. We address this by considering such geometries as subspace minima, reformulating vibrational analysis to incorporate constraints. Normal modes and spectra consistent with these constraints are obtained by projecting the force constant matrix onto a space orthogonal to the constrained coordinates. This method, illustrated by the example of enkephalin, yields 3N - 6 - m nonzero frequencies after constraint projection, demonstrating its applicability to biomolecules with flexible conformations. Our approach offers a comprehensive mathematical framework to compute vibrational spectra of molecules with conformationally flexible subunits under environmental constraints.