Nonrigid Systems Research Articles

A numerical-tensorial "hybrid" nuclear motion Hamiltonian and dipole moment operator for spectra calculation of polyatomic nonrigid molecules.

The analysis and modeling of high-resolution spectra of nonrigid molecules require a specific Hamiltonian and group-theoretical formulation that differs significantly from that of more familiar rigid systems. Within the framework of Hougen-Bunker-Johns (HBJ) theory, this paper is devoted to the construction of a nonrigid Hamiltonian based on a suitable combination of numerical calculations for the nonrigid part in conjunction with the irreducible tensor operator method for the rigid part. For the first time, a variational calculation from abinitio potential energy surfaces is performed using the HBJ kinetic energy operator built from vibrational, large-amplitude motion, and rotational tensor operators expressed in terms of curvilinear and normal coordinates. Group theory for nonrigid molecules plays a central role in the characterization of the overall tunneling splittings and is discussed in the present approach. The construction of the dipole moment operator is also examined. Validation tests consisting of a careful convergence study of the energy levels as well as a comparison of results obtained from independent computer codes are given for the nonrigid molecules CH2, CH3, NH3, and H2O2. This work paves the way for the modeling of high-resolution spectra of larger nonrigid systems.

Embedding Nonrigid Solutes in an Averaged Environment: A Case Study on Rhodopsins.

Many simulation methods concerning solvated molecules are based on the assumption that the solvated species and the solvent can be characterized by some representative structures of the solute and some embedding potential corresponding to this structure. While the averaging of the solvent configurations to obtain an embedding potential has been studied in great detail, this hinges on a single solute structure representation. This assumption is re-examined and generalized for conformationally flexible solutes and tested on 4 nonrigid systems. In this generalized approach, the solute is characterized by a set of representative structures and the corresponding embedding potentials. The representative structures are identified by means of subdividing the statistical ensemble, which in this work is generated by a constant-temperature molecular dynamics simulation. The embedding potential defined in the Frozen-Density Embedding Theory is used to characterize the average effect of the solvent in each subensemble. The numerical examples concern the vertical excitation energies of protonated retinal Schiff bases in protein environments. It is comprehensively shown that subensemble averaging leads to huge computational savings compared with explicit averaging of the excitation energies in the whole ensemble while introducing only minor errors in the case of the systems examined.

Inducing transient enantiomeric excess in a molecular quantum racemic mixture with microwave fields

Chiral molecules with low enantiomer interconversion barriers racemize even at cryogenic temperatures due to quantum tunneling, forming a racemic mixture that is impossible to separate using conventional chemical methods. Here we both experimentally and theoretically demonstrate a method to create and probe a state-specific enantiomeric enrichment for such molecular systems. The coherent, non-linear, and resonant approach is based on a microwave six-wave mixing scheme and consists of five phase-controlled microwave pulses. The first three pulses induce a chiral wavepacket in a chosen rotational state, while the consecutive two pulses induce a polarization for a particular rotational transition (listen transition) with a magnitude proportional to the enantiomeric excess created. The experiments are performed with the transiently chiral molecule benzyl alcohol, where a chiral molecular response was successfully obtained. This signal demonstrates that enantiomeric excess can be induced in a quantum racemic mixture of a transiently chiral molecule using the developed microwave six-wave mixing scheme, which is an important step towards controlling non-rigid chiral molecular systems.

CFD modelling of a wave-mixed bioreactor with complex geometry and two degrees of freedom motion

Optimizing bioprocesses requires an in-depth understanding, from a bioengineering perspective, of the cultivation systems used. A bioengineering characterization is typically performedviaexperimental or numerical methods, which are particularly well-established for stirred bioreactors. For unstirred, non-rigid systems such as wave-mixed bioreactors, numerical methods prove to be problematic, as often only simplified geometries and motions can be assumed. In this work, a general approach for the numerical characterization of non-stirred cultivation systems is demonstrated using the CELL-tainer bioreactor with two degree of freedom motion as an example. In a first step, the motion is recordedviamotion capturing, and a 3D model of the culture bag geometry is generatedvia3D-scanning. Subsequently, the bioreactor is characterized with respect to mixing time, and oxygen transfer rate, as well as specific power input and temporal Kolmogorov length scale distribution. The results demonstrate that the CELL-tainer with two degrees of freedom outperforms classic wave-mixed bioreactors in terms of oxygen transport. In addition, it was shown that in the cell culture version of the CELL-tainer, the critical Kolmogorov length is not surpassed in any simulation.

Collective Abstraction

This paper develops a novel theory of abstraction—what we call collective abstraction. The theory solves a notorious problem for noneliminative structuralism. The noneliminative structuralist holds that in addition to various isomorphic systems there is a pure structure that can be abstracted from each of these systems; but existing accounts of abstraction fail for nonrigid systems like the complex numbers. The problem with the existing accounts is that they attempt to define a unique abstraction operation. The theory of collective abstraction instead simultaneously defines a collection of distinct abstraction operations, each of which maps a system to its corresponding pure structure. The theory is precisely formulated in an essentialist language. This allows us to throw new light on the question to what extent structuralists are committed to symmetric dependence. Finally, we apply the theory of collective abstraction to solve a problem about converse relations.

Improvement of the performance of a multi-blade tool based on selective equipment with cutting ceramics

The increasing pace of industrial production for the production of products and the widespread complexity of the designs of manufactured products, justified by scientific and technological progress, pose a permanent task to the metalworking industry to improve technological processes in order to reduce the time of manufacturing parts and material costs. These requirements lead to the desire of manufacturers to reduce traditional technological processes and significantly increase the processing speed. In such conditions, traditional tool materials are often not applicable, while some materials that were previously not in demand due to the lack of necessary technological conditions are becoming increasingly relevant. One of such materials is cutting ceramics – a material that has the highest efficiency at high cutting speeds, but due to the brittle nature of the fracture provides low stability when used in non-rigid technological systems, under high loads and insufficient attention to the equipment of the tool with ceramic cutting plates. The article is devoted to improving the performance of a multi-blade tool based on selective equipment with ceramic cutting plates during the finishing of the working surfaces of high-precision cast-iron body parts. In the course of this study, the problems of using a multi-blade tool for milling high-precision planes were identified, a way to solve the identified problems was determined, a device was created to determine the microstructural parameters of cutting ceramics based on the known dependence of microstructural characteristics on the electrical resistivity of oxidecarbide cutting plates, a method was developed for selectively equipping a multi-blade cutting tool with oxide-carbide ceramic cutting plates. The effectiveness of the proposed solutions is confirmed by experimental studies.

Evolution of posts-from rigid to flexible

Once endodontic treatment is completed, the tooth must be provided with adequate protection. The endodontically treated teeth are considerably more brittle due to structural changes in the tooth structure, which is more prone to fracture if they are not properly crowned. Not every root treated needs a post space. Predominantly when the roof of the pulp chamber is removed, it weakens the tooth thus resulting in the need for strong interior and exterior support like a post system. It is critical that the implications (remaining tooth structure, number of teeth, periodontal support, active caries, and good oral hygiene as well as tooth biomechanics) largely influence the restorative approach. Several alterations of the natural shape of the canal become necessary to accommodate a circular post inside the root. Non-rigid post systems such as glass, quartz, and silicon fiber posts have become hugely popular since their introduction in the 1990s. Requirements include an optimal combination of resilience, stiffness, flexibility, and strength. These posts have modulus similar to dentin and provide a more uniform distribution of stress on the remaining tooth structure. Sometimes an anatomic post becomes necessary where fiber posts are contraindicated. Here, it requires more than one visit. Thus, we need to have a thorough knowledge of what type of post to be used.

Determination of Nanosized Adsorbate Mass in Solution Using Mechanical Resonators: Elimination of the So Far Inseparable Liquid Contribution

Assumption-free mass quantification of nanofilms, nanoparticles, and (supra)molecular adsorbates in a liquid environment remains a key challenge in many branches of science. Mechanical resonators can uniquely determine the mass of essentially any adsorbate; yet, when operating in a liquid environment, the liquid dynamically coupled to the adsorbate contributes significantly to the measured response, which complicates data interpretation and impairs quantitative adsorbate mass determination. Employing the Navier–Stokes equation for liquid velocity in contact with an oscillating surface, we show that the liquid contribution for rigid systems can be eliminated by measuring the response in solutions with identical kinematic viscosity but different densities. Guided by this insight, we used the quartz crystal microbalance (QCM), one of the most widely employed mechanical resonators, to experimentally demonstrate that the kinematic-viscosity matching can be utilized to quantify the dry mass of rigid and in many cases also nonrigid adsorbate systems, including, e.g., rigid nanoparticles, tethered biological nanoparticles (lipid vesicles), as well as highly hydrated polymeric films. For all the adsorbates, the dry mass determined using the kinematic-viscosity matching was within the uncertainty limits of the corresponding mass determined using complementary methods, i.e., QCM in air, scanning electron microscopy, surface plasmon resonance, and theoretical estimations. The same approach applied to the simultaneously measured energy dissipation made it possible to quantify the mechanical properties of the adsorbate and its attachment to the surface, as demonstrated by, for example, probing the hydrodynamic stabilization induced by nanoparticle crowding. In addition to a unique means to quantify the liquid contribution to the measured response of mechanical resonators, we also envision that the kinematic-viscosity-matching approach will open up applications beyond mass determination, including a new means to investigate orientation, spatial distribution, and binding strength of adsorbates without the need for complementary techniques.

Biomechanical analysis of lumbar interbody fusion supplemented with various posterior stabilization systems.

Biomechanical comparison between rigid and non-rigid posterior stabilization systems following lumbar interbody fusion has been conducted in several studies. However, most of these previous studies mainly focused on investigating biomechanics of adjacent spinal segments or spine stability. The objective of the present study was to compare biomechanical responses of the fusion devices when using different posterior instrumentations. Finite-element model of the intact human lumbar spine (L1-sacrum) was modified to simulate implantation of the fusion cage at L4-L5 level supplemented with different posterior stabilization systems including (i) pedicle screw-based fixation using rigid connecting rods (titanium rods), (ii) pedicle screw-based fixation using flexible connecting rods (PEEK rods) and (iii) dynamic interspinous spacer (DIAM). Stress responses were compared among these various models under bending moments. The highest and lowest stresses in endplate, fusion cage and bone graft were found at the fused L4-L5 level with DIAM and titanium rod stabilization systems, respectively. When using PEEK rod for the pedicle screw fixation, peak stress in the pedicle screw was lower but the ratio of peak stress in the rods to yield stress of the rod material was higher than using titanium rod. Compared with conventional rigid posterior stabilization system, the use of non-rigid stabilization system (i.e., the PEEK rod system and DIAM system) following lumbar interbody fusion might increase the risks of cage subsidence and cage damage, but promote bony fusion due to higher stress in the bone graft. For the pedicle screw-based rod stabilization system, using PEEK rod might reduce the risk of screw breakage but increased breakage risk of the rod itself.

Experimental modeling of deforming osteoarthrosis of the knee in small rodents

The results of experimental work on modeling deforming osteoarthrosis of the knee joint in small rodents are presented. The pathogenetic basis of this process is a violation of the blood supply and the distribution of physiological load in the joint. Variants of rigid and non-rigid limb immobilization systems are proposed. The results of morphofunctional assessment are given, indicating a violation of the anatomical and histological structure of the metaphysis, pineal gland and metaepiphysis of the femur and tibia. The leading role in the development of deforming osteoarthritis of the knee belongs to the violation of the physiological distribution of the dynamic load on the joint, and the most vulnerable to the progression of this process are subchondral structures. Violation of regional blood circulation of the lower limb of the animal was achieved by crossing the femoral artery. Limb immobilization was carried out for 4 weeks. The results were evaluated by the severity of changes in the morphological structure of the operated joints and radiographic examination. The high mitotic activity of cellular elements, revealed as a result of histological examination in all groups of animals, indicates the rapid formation of vascular collaterals in rats. It was noted that with non-rigid immobilization of the joint with a plaster cast, the cartilaginous tissue of the articular surface becomes thinner, while the subchondral structures change slightly. With severe immobilization of the joint in the external fixation apparatus, significant changes are revealed precisely in the structure of subchondral structures. In animals subjected to a two-week rehabilitation period after dismantling the external fixation apparatus, a further progression of the pathological process was noted. Thus, with severe immobilization of the limb in the experiment, it was possible to obtain a stable joint deformation corresponding to the 3rd clinical and radiological stage of osteoarthritis.

Tunneling Splittings in Water Clusters from Path Integral Molecular Dynamics.

We present calculations of tunneling splittings in selected small water clusters, based on a recently developed path integral molecular dynamics (PIMD) method. The ground-rotational-state tunneling motions associated with the largest splittings in the water dimer, trimer, and hexamer are considered, and we show that the PIMD predictions are in very good agreement with benchmark quantum and experimental results. As the tunneling spectra are highly sensitive to both the details of the quantum dynamics and the potential energy surface, our calculations are a validation of the MB-Pol surface as well as the accuracy of PIMD. The favorable scaling of PIMD with system size paves the way for calculations of tunneling splittings in large, nonrigid molecular systems with motions that cannot be treated accurately by other methods, such as the semiclassical instanton.

Technology of road construction and laying of pipelines in marshy and waterlogged areas using pontoon modules

The development of environmentally friendly technology for the construction of non-rigid roads and systems for laying pipelines on block elements from composite pontoon modules in swampy and waterlogged areas for the Far North and Siberia is presented.

Numerical study of polymerization processes on various catalytic systems

A set of algorithms for determining the averaged molecular characteristics of the polymer and finding the optimal initial concentrations was built on the basis of the mathematical software for solving rigid and non-rigid systems of ordinary differential equations describing various polymerization processes. With the help of the developed mathematical and software computational experiments were carried out for various technological parameters and production recipes for the considered processes. The dependencies of the molecular mass characteristics of the copolymer on the time of polymerization or conversion of monomers were built, which showed agreement with the data obtained as a result of experiments in the central factory laboratory of Synthez-Kauchuk OJSC (Sterlitamak, Republic of Bashkortostan) and the laboratory of physico-chemical studies of polymers of BashSU.

Towards a priori uncertainty quantification in coarse-grained molecular dynamics: Generalized multipole potentials.

In computational materials science, coarse-graining approaches often lack a priori uncertainty quantification (UQ) tools that estimate the accuracy of a reduced-order model before it is calibrated or deployed. This is especially the case in coarse-grained (CG) molecular dynamics (MD), where "bottom-up" methods need to run expensive atomistic simulations as part of the calibration process. As a result, scientists have been slow to adopt CG techniques in many settings because they do not know in advance whether the cost of developing the CG model is justified. To address this problem, we present an analytical method of coarse-graining rigid-body systems that yields corresponding intermolecular potentials with controllable levels of accuracy relative to their atomistic counterparts. Critically, this analysis: (i) provides a mathematical foundation for assessing the quality of a CG force field without running simulations; and (ii) provides a tool for understanding how atomistic systems can be viewed as appropriate limits of reduced-order models. Simulated results confirm the validity of this approach at the trajectory level and point to issues that must be addressed in coarse-graining fully non-rigid systems.

Analytical solution and numerical study on water hammer in a pipeline closed with an elastically attached valve

The influence of dynamic fluid-structure interaction (FSI) onto the course of water hammer (WH) can be significant in non-rigid pipeline systems. The essence of this effect is the dynamic transfer of liquid energy to the pipeline structure and back, which is important for elastic structures and can be negligible for rigid ones. In the paper a special model of such behavior is analyzed. A straight pipeline with a steady flow, fixed to the floor with several rigid supports is assumed. The transient is generated by a quickly closed valve installed at the end of the pipeline. FSI effects are assumed to be present mainly at the valve which is fixed with a spring dash-pot attachment. Analysis of WH runs, especially transient pressure changes, for various stiffness and damping parameters of the spring dash-pot valve attachment is presented in the paper. The solutions are found analytically and numerically. Numerical results have been computed with the use of an own computer program developed on the basis of the four equation model of WH-FSI and the specific boundary conditions formulated at the valve. Analytical solutions have been found with the separation of variables method for slightly simplified assumptions. Damping at the dash-pot is taken into account within the numerical study. The influence of valve attachment parameters onto the WH courses was discovered and it was found the transient amplitudes can be reduced. Such a system, elastically attached shut-off valve in a pipeline or other, equivalent design can be a real solution applicable in practice.

Theoretical volume profiles for conformational changes: Application to internal rotation of benzene ring in 1,12-dimethoxy-[12]-paracyclophane.

Identification of the transition state is an important step in the study of reaction kinetics and mechanisms. However, for non-rigid chemical systems where multiple viable reaction pathways may exist, enumeration of all possible transition states quickly becomes computationally expensive, if at all feasible. As an alternative approach, we recently proposed a methodology where the volumetric properties of a flexible reaction system are used to locate its transition state ensemble through a comparison of its theoretically determined volume profile and experimental activation volumes derived from high pressure kinetic data. In this work, we apply this method to internal rotation of the benzene ring in 1,12-dimethoxy-[12]-paracyclophane. For this system, the transition state ensemble was found to be the state with the lowest volume, where the benzene ring and the flexible methylene tether are coplanar. This result was verified by comparison with a Gibbs free energy profile obtained via umbrella sampling.

Ab initio effective rotational and rovibrational Hamiltonians for non-rigid systems via curvilinear second order vibrational Møller-Plesset perturbation theory.

We present a perturbative method for ab initio calculations of rotational and rovibrational effective Hamiltonians of both rigid and non-rigid molecules. Our approach is based on a curvilinear implementation of second order vibrational Møller-Plesset perturbation theory extended to include rotational effects via a second order contact transformation. Though more expensive, this approach is significantly more accurate than standard second order vibrational perturbation theory for systems that are poorly described to zeroth order by rectilinear normal mode harmonic oscillators. We apply this method to and demonstrate its accuracy on two molecules: Si2C, a quasilinear triatomic with significant bending anharmonicity, and CH3NO2, which contains a completely unhindered methyl rotor. In addition to these two examples, we discuss several key technical aspects of the method, including an efficient implementation of Eckart and quasi-Eckart frame embedding that does not rely on numerical finite differences.

The influence of pipeline supports stiffness onto the water hammer run

▪ Water hammer (WH) phenomenon may produce various undesired effects in pipelines. Dynamic interaction between the liquid and the structure is known to influence the transient pipe flow parameters in non-rigid systems. One can expect that due to basic energy conservation considerations the energy outflow from the liquid to the elastic structure would result in lowering of WH pressures. However, this effect is not unambiguous and is not clearly and uniquely explained in literature. Thus, its proper understanding is of great practical importance.In the paper the authors try to examine these effects mainly on the basis of experimental results acquired from measurements at a special test rig designed and constructed at the Institute of Fluid-Flow Machinery in Gdansk. The main part of the rig is a cooper pipeline of the length of about 59m, fixed to the floor with a number of elastic supports. WH runs were generated, measured and analyzed for supports of varying stiffness. Pipeline free vibrations induced by mechanical shock were measured as well. The conclusions have been found and they are presented in the paper. Still, a very important part of the job was to find the physical interpretation and explanation of the results, which allows for understanding of that phenomenon.

On comprehensive cascade control strategy considering a class of overactuated autonomous non-rigid space systems with model uncertainties

With a focus on a number of state-of-the-art techniques in the area of autonomous non-rigid space systems control, realization of a comprehensive strategy is worthy of investigation to handle a set of parameters of the present overactuated processes with model uncertainties. In a word, the subject behind the research is to guarantee the desirable performance of a class of the autonomous space systems, which can be considered through the moments of inertia, the central of mass, the profile of the thrust vector and the misalignments of the propellant engine to deal with mission operation plans. There is the attitude cascade strategy including the low thrust three-axis engine off mode control, the low thrust x-axis engine on mode control and finally the high thrust y,z-axis engine on mode control, respectively. The control strategy is realized in a number of loops, as long as the on and off modes of the propellant engine are focused on the Euler angles control, in finite burn time, and quaternion vector control, in non-burn time, respectively, in line with parameters variations. It is to note that the parameters variations are coherently different in each one of the engine modes. The dynamics of high-low thrusters are taken into real consideration, where the control allocations in association with the pulse-width pulse-frequency modulators are employed to cope with a set of on–off reaction thrusters. The investigated results are finally analyzed in line with some related well-known benchmarks to verify the approach performance. The main contribution and motivation of the strategy investigated here is to propose a novel three-axis comprehensive cascade robust control solution to be able to deal with the parameters of autonomous non-rigid space systems under control with model uncertainties, in a synchronous manner, once the results regarding the tracking of the three-axis referenced commands are efficient with high accuracy along with the recent potential outcomes, researched in this area.

Adaptive-passive vibration isolation between nonrigid machines and nonrigid foundations using a dual-beam periodic structure with shape memory alloy transverse connection

This paper examines the problem of broadband vibration control of nonrigid systems employing periodic structures with tunable parameters. It investigates this by using a semi-two-dimensional model that applies a dual-beam periodic structure with transverse branches as a parameter-tunable isolator. Conventional study of vibration control problems, including the problem of vibration control by periodic structures, usually reduces systems to equivalent single- or multi-mount models with only a unidirectional translation at a mounting point. This assumption of decoupling leads to the erroneous prediction of vibratory power transmission when designing an isolator for a nonrigid system. Such a periodic structure involves the coupling of vibrations between different mounting points and different directions of motion and is therefore a reasonable simulation of the real-life problem. However, its application as a periodic isolator has not been proposed previously. The configuration of shape memory alloy (SMA) branches and non-SMA dual beams is proposed in order that this structure can effectively exploit the advantages of SMA materials, namely their significantly varying Young׳s moduli which can be tuned to adjust and widen the stop bands, and can prevent the associated limitation of hysteresis. Equations are derived governing the vibration transmitted through any number of periodic mounts between nonrigid machines and foundations. Based on the derived results, two methodologies are developed to determine the proper Young׳s moduli of the SMA branches and minimize the transmitted power. The numerical results demonstrate that the adaptive SMA branches at the proper temperatures are able to attenuate broadband vibration by adjusting the locations and broadening the widths of stop bands. With the application of a semi-two-dimensional periodic structure to broadband vibration isolation, this paper provides an approach and supporting methodologies for broadband vibration control using periodic structures.