Internal Degrees Of Freedom Research Articles

Gold(i) sulfide: unusual bonding and an unexpected computational challenge in a simple solid.

We report the experimental high-pressure crystal structure and equation of state of gold(i) sulfide (Au2S) determined using diamond-anvil cell synchrotron X-ray diffraction. Our data shows that Au2S has a simple cubic structure with six atoms in the unit cell (four Au in linear, and two S in tetrahedral, coordination), no internal degrees of freedom, and relatively low bulk modulus. Despite its structural simplicity, Au2S displays very unusual chemical bonding. The very similar and relatively high electronegativities of Au and S rule out any significant metallic or ionic character. Using a simple valence bond (Lewis) model, we argue that the Au2S crystal possesses two different types of covalent bonds: dative and shared. These bonds are distributed in such a way that each Au atom engages in one bond of each kind. The multiple arrangements in space of dative and shared bonds are degenerate, and the multiplicity of configurations imparts the system with multireference character, which is highly unusual for an extended solid. The other striking feature of this system is that common computational (DFT) methods fail quite spectacularly to describe it, with 20% and 400% errors in the equilibrium volume and bulk modulus, respectively. We explain this by the poor treatment of static correlation in common density-functional approximations. The fact that the solid is structurally very simple, yet presents unique chemical bonding and is unmodelable using current DFT methods, makes it an interesting case study and a computational challenge.

Strain-effected physical properties of ferromagnetic insulating La0.88Sr0.12MnO3 thin films.

The functional perovskite La1−xSrxMnO3 (LSMO) possesses various exotic phases owing to competing physical parameters and internal degrees of freedom. In particular, the nature of the ferromagnetic insulating phase (FMI) has not been adequately explored, resulting in a limited understanding of the relationship between crystal structure and magnetism. To investigate this structure–property relationship, epitaxial La0.88Sr0.12MnO3 thin films were grown on two different substrates, (001) SrTiO3 and (001) (LaAlO3)0.3(Sr2AlTaO6)0.7, by pulsed laser deposition. Element-specific and surface-sensitive techniques were applied in conjunction with bulk magnetometry to investigate the inextricable link between the structures and magnetic properties of the films and the effects of tuning the strain. The results unambiguously demonstrate that structure–property relationship of a FMI LSMO tuned by strain has a crucial role for manipulating the properties in the FMI regime.

Molecular-Level "Observations" of the Behavior of Gold Nanoparticles in Aqueous Solution and Interacting with a Lipid Bilayer Membrane.

We use coarse-grained molecular dynamics simulations to "observe" details of interactions between ligand-covered gold nanoparticles and a lipid bilayer model membrane. In molecular dynamics simulations, one puts the individual atoms and groups of atoms of the physical system to be "observed" into a simulation box, specifies the forms of the potential energies of interactions between them (ultimately quantum based), and lets them individually move classically according to Newton's equations of motion, based on the forces arising from the assumed potential energy forms. The atoms that are chemically bonded to each other stay chemically bonded, following known potentials (force fields) that permit internal degrees of freedom (internal rotation, torsion, vibrations), and the interactions between nonbonded atoms are simplified to Lennard-Jones forms (in our case) and coulombic (where electrical charges are present) in which the parameters are previously optimized to reproduce thermodynamic properties or are based on quantum electronic calculations. The system is started out at a reasonable set of coordinates for all atoms or groups of atoms, and then permitted to develop according to the equations of motion, one small step (usually 10 fs time step) at a time, for millions of steps until the system is at a quasi-equilibrium (usually reached after hundreds of nanoseconds). We then let the system play out its motions further for many nanoseconds to observe the behavior, periodically taking snapshots (saving all positions and energies), and post-processing the snapshots to obtain various average descriptions of the system. Alkanethiols of various lengths serve as examples of hydrophobic ligands and methyl-terminated PEG with various numbers of monomer units serve as examples of hydrophilic ligands. Spherical gold particles of various diameters as well as gold nanorods form the core to which ligands are attached. The nanoparticles are characterized at the molecular level, especially the distributions of ligand configurations and their dependence on ligand length, and surface coverage. Self-assembly of the bilayer from an isotropic solution and observation of membrane properties that correspond well to experimental values validate the simulations. The mechanism of permeation of a gold NP coated with either a hydrophobic or a hydrophilic ligand, and its dependence on surface coverage, ligand length, core diameter, and core shape, is investigated. Lipid response such as lipid flip-flops, lipid extraction, and changes in order parameter of the lipid tails are examined in detail. The mechanism of permeation of a PEGylated nanorod is shown to occur by tilting, lying down, rotating, and straightening up. The nature of the information provided by molecular dynamics simulations permits understanding of the detailed behavior of gold nanoparticles interacting with lipid membranes which in turn helps to understand why some known systems work better than others and aids the design of new particles and improvement of methods for preparing existing ones.

Motion planning strategies in human control of non-rigid objects with internal degrees of freedom

The paper deals with modeling of human-like reaching movements in dynamic environments. A simple but not trivial example of reaching in a dynamic environment is the rest-to-rest manipulation of a multi-mass flexible object with the elimination of residual vibrations. Two approaches to the prediction of reaching movements are formulated in position and force actuation settings. In the first approach, either the position of the hand or the hand force is specified by the lowest order polynomial satisfying the boundary conditions of the reaching task. The second approach is based on the minimization of either the hand jerk or the hand force-change, with taking into account the dynamics of the flexible object. To verify the resulting four mathematical models, an experiment on the manipulation of a ten-masses flexible object of low stiffness is conducted. The experimental results show that the second approach gives a significantly better prediction of human movements, with the minimum hand force-change model having a slight but consistent edge over the minimum hand jerk one.

Phase-space-density limitation in laser cooling without spontaneous emission

We study the possibility to enhance the phase space density of non-interacting particles submitted to a classical laser field without spontaneous emission. We clearly state that, when no spontaneous emission is present, a quantum description of the atomic motion is more reliable than semi-classical description which can lead to large errors especially if no care is taken to smooth structures smaller than the Heisenberg uncertainty principle. Whatever the definition of position - momentum phase space density, its gain is severely bounded especially when started from a thermal sample. More precisely, the maximum phase space density, can only be improved by a factor M for M-level atoms. This bound comes from a transfer between the external and internal degrees of freedom. To circumvent this limit, one can use non-coherent light fields, informational feedback cooling schemes, involve collectives states between fields and atoms, or allow a single spontaneous emission even

High-Frequency Regime of the Acoustical Freédericksz Transition in Nematic Liquid Crystals

A novel approach to the acoustical Freedericksz transition in the high-frequency regime is developed. The prominent role played by bulk viscosities is highlighted. Using experimental data, it is shown that α/α4 = 2.7 × 103, where the combination α ≡ ρ1 + ρ2 + ρ3 + α1 + α4 + α5 + α6 consists of shear and bulk viscosities of a nematic. The magnitude of this ratio is in agreement with what is found in fluids composed by molecules possessing several internal degrees of freedom.

Modal approach to dynamic analysis of structures with attachments at uncertain locations

This paper presents an approach to calculate the natural frequency and frequency response function (FRF) statistics of structures connected to attachments at uncertain locations. The main structure is divided into two regions to which the attachment can, or cannot, be connected. The approach is based on component mode synthesis analysis of finite element models of these regions. Multi-point constraints are used to connect the attachment to the main structure to avoid the need to re-mesh the structure. The use of characteristic constraint modes is used to reduce the number of interface degrees of freedom (DOFs) and hence reduce the computational cost further. One or more baseline systems, for which the attachment is connected at a given position, are analysed and the eigensolution found. A perturbation is then applied to the baseline solution to estimate the solution for other attachment locations. The method can be applied to any problem requiring multiple re-analysis. Here, emphasis is placed on probabilistic approaches using Monte Carlo Simulation (MCS), and the natural frequency and FRF statistics are then estimated through MCS. To illustrate the approach, numerical results are presented for a beam and a plate with a randomly attached mass and a plate with an attachment with a number of internal and attachment DOFs. Numerical results are compared with experimental measurements for the cases of a beam and a plate with an attached mass. The results indicate that the method provides accurate predictions at a significantly reduced computation cost when compared to multiple direct solutions.

Sharpening up Galactic all-sky maps with complementary data

Context. Galactic all-sky maps at very disparate frequencies, such as in the radio and γ-ray regime, show similar morphological structures. This mutual information reflects the imprint of the various physical components of the interstellar medium. Aims. We want to use multifrequency all-sky observations to test resolution improvement and restoration of unobserved areas for maps in certain frequency ranges. For this we aim to reconstruct or predict from sets of other maps all-sky maps that, in their original form, lack a high resolution compared to other available all-sky surveys or are incomplete in their spatial coverage. Additionally, we want to investigate the commonalities and differences that the interstellar medium components exhibit over the electromagnetic spectrum. Methods. We built an n-dimensional representation of the joint pixel-brightness distribution of n maps using a Gaussian mixture model and investigate how predictive it is. We study the extend to which one map of the training set can be reproduced based on subsets of other maps? Results. Tests with mock data show that reconstructing the map of a certain frequency from other frequency regimes works astonishingly well, predicting reliably small-scale details well below the spatial resolution of the initially learned map. Applied to the observed multifrequency data sets of the Milky Way this technique is able to improve the resolution of, for example, the low-resolution Fermi-LAT maps as well as to recover the sky from artifact-contaminated data such as the ROSAT 0.855 keV map. The predicted maps generally show less imaging artifacts compared to the original ones. A comparison of predicted and original maps highlights surprising structures, imaging artifacts (fortunately not reproduced in the prediction), and features genuine to the respective frequency range that are not present at other frequency bands. We discuss limitations of this machine learning approach and ideas how to overcome them. In particular, with increasing sophistication of the method, such as introducing more internal degrees of freedom, it starts to internalize imaging artifacts. Conclusions. The approach is useful to identify particularities in astronomical maps and to provide detailed educated guesses of the sky morphology at not yet observed resolutions and locations.

The Origin of the Color Charge into Quarks

Showing the origin of the mass in an additional coupling between field quantum oscillators, we formulate a hypothesis of a geometrical structure of the oscillators of “fields-particles”. In this way, we define the possible structure of quarks and hadrons (as the proton). This hypothesis is reasonable if one admits field oscillators composed by sub-oscillators at semi-quantum (IQuO) and in which a degree of internal freedom is definable. Using the IQuO model, we find the origin of the sign of electric charge in to particles and, in quarks, the isospin, the strangeness and colour charge. Finally, we formulate the structure of the gluons and the variation modality of the colour charge in quarks.

On the dynamics of a rolling ball actuated by internal point masses

The motion of a rolling ball actuated by internal point masses that move inside the ball’s frame of reference is considered. The equations of motion are derived by applying Euler–Poincaré’s symmetry reduction method in concert with Lagrange–d’Alembert’s principle, which accounts for the presence of the nonholonomic rolling constraint. As a particular example, we consider the case when the masses move along internal rails, or trajectories, of arbitrary shape and fixed within the ball’s frame of reference. Our system of equations can treat most possible methods of actuating the rolling ball with internal moving masses encountered in the literature, such as circular motion of the masses mimicking swinging pendula or straight line motion of the masses mimicking magnets sliding inside linear tubes embedded within a solenoid. Moreover, our method can model arbitrary rail shapes and an arbitrary number of rails such as several ellipses and/or figure eights, which may be important for future designs of rolling ball robots. For further analytical study, we also reduce the system to a single differential equation when the motion is planar, that is, considering the motion of the rolling disk actuated by internal point masses, in which case we show that the results obtained from the variational derivation coincide with those obtained from Newton’s second law. Finally, the equations of motion are solved numerically, illustrating a wealth of complex behaviors exhibited by the system’s dynamics. Our results are relevant to the dynamics of nonholonomic systems containing internal degrees of freedom and to further studies of control of such systems actuated by internal masses.

Local martingales associated with Schramm-Loewner evolutions with internal symmetry

We consider Schramm-Loewner evolutions (SLEs) with internal degrees of freedom that are associated with representations of affine Lie algebras, following group theoretical formulation of SLEs. We reconstruct the SLEs considered by Bettelheim et al. [Phys. Rev. Lett. 95, 251601 (2005)] and Alekseev et al. [Lett. Math. Phys. 97, 243–261 (2011)] in correlation function formulation. We also explicitly formulate stochastic differential equations on internal degrees of freedom for Heisenberg algebras and the affine sl2. Our formulation enables us to find several local martingales associated with SLEs with internal degrees of freedom from computation on a representation of an affine Lie algebra. Indeed, we formulate local martingales associated with SLEs with internal degrees of freedom described by Heisenberg algebras and the affine sl2. We also find an affine sl2 symmetry of a space of SLE local martingales for the affine sl2.

Stability and predictability in human control of complex objects.

Previous research on movement control suggested that humans exploit stability to reduce vulnerability to internal noise and external perturbations. For interactions with complex objects, predictive control based on an internal model of body and environment is needed to preempt perturbations and instabilities due to delays. We hypothesize that stability can serve as means to render the complex dynamics of the body and the task more predictable and thereby simplify control. However, the assessment of stability in complex interactions with nonlinear and underactuated objects is challenging, as for existent stability analyses the system needs to be close to a (known) attractor. After reviewing existing methods for stability analysis of human movement, we argue that contraction theory provides a suitable approach to quantify stability or convergence in complex transient behaviors. To test its usefulness, we examined the task of carrying a cup of coffee, an object with internal degrees of freedom. A simplified model of the task, a cart with a suspended pendulum, was implemented in a virtual environment to study human control strategies. The experimental task was to transport this cart-and-pendulum on a horizontal line from rest to a target position as fast as possible. Each block of trials presented a visible perturbation, which either could be in the direction of motion or opposite to it. To test the hypothesis that humans exploit stability to overcome perturbations, the dynamic model of the free, unforced system was analyzed using contraction theory. A contraction metric was obtained by numerically solving a partial differential equation, and the contraction regions with respect to that metric were computed. Experimental results showed that subjects indeed moved through the contraction regions of the free, unforced system. This strategy attenuated the perturbations, obviated error corrections, and made the dynamics more predictable. The advantages and shortcomings of contraction analysis are discussed in the context of other stability analyses.

A Microscopy Approach to Investigating the Energetics of Small Supported Metal Clusters

Metal clusters are partway between molecular and bulk systems and thus exhibit special physical and chemical properties. Atoms can rearrange within a cluster to form different structural isomers. Internal degrees of freedom and the interaction with the support - which both are dependent on cluster size - can promote diffusion across a support. Here, we show how fast scanning tunneling microscopy (FastSTM) can be used to investigate such dynamical behavior of individual clusters on the example of Pdn (1<=n<=19) on a hexagonal boron nitride nanomesh on Rh(111), in particular pertaining to minority species and rare events. By tuning the cluster size and varying the temperature to match the dynamics to the FastSTM frame rate, we followed steady state diffusion of clusters and atoms inside the nanomesh pore and reversible cluster isomerization in situ. While atoms diffuse along the rim of a pore, a small cluster experiences a corrugation in the potential energy landscape and jumps between six sites around the center of the pore. The atom and cluster diffusion between pores is strongly influenced by defects.

Control and Stability Evaluation of the Bipedal Walking Robot AnyWalker

In the laboratory of robotics and mechatronics of the Kuban State University, a walking non-anthropomorphic robot has been developed, capable of overcoming obstacles exceeding the size of the robot. The robot has additional internal degrees of freedom, responsible for the compensation of deflections (the dynamic stabilization system). The article presents the results of the calculation of the stability zones in the frontal plane of the robot with and without a stabilization system.

Optimizing Native Ion Mobility Q-TOF in Helium and Nitrogen for Very Fragile Noncovalent Structures

The amount of internal energy imparted to the ions prior to the ion mobility cell influences the ion structure and thus the collision cross section. Non-covalent complexes with few internal degrees of freedom and/or high charge densities are particularly sensitive to collisional activation. Here, we investigated the effects of virtually all tuning parameters of the Agilent 6560 IM-Q-TOF on the arrival time distributions of ubiquitin7+ and found conditions in which the native state prevails. We discuss the effects of solvent evaporation conditions in the source, of the entire pre-IM DC voltage gradient, of the funnel RF amplitudes. We also report on ubiquitin7+ conformations in different solvents, including native supercharging conditions. Collision-induced unfolding (CIU) can be conveniently provoked either behind the source capillary or in the trapping funnel. The softness of the instrumental conditions behind the mobility cell was further optimized with the DNA G-quadruplex [(dG4T4G4)2·(NH4+)3-8H]5-, for which ion activation results in ammonia loss. To reduce the ion internal energy and obtain the intact 3-NH4+ complex, we reduce the post-IM voltage gradient, but this results in a lower IM resolving power due to increased diffusion behind the drift tube. The article describes the various trade-offs between ion activation, ion transmission, and ion mobility performance for native MS of very fragile structures. Graphical Abstract ᅟ.

Schramm–Loewner evolution with Lie superalgebra symmetry

We propose a generalization of Schramm–Loewner evolution (SLE) that has internal degrees of freedom described by an affine Lie superalgebra. We give a general formulation of SLE corresponding to representation theory of an affine Lie superalgebra whose underlying finite-dimensional Lie superalgebra is basic classical type, and write down stochastic differential equations on internal degrees of freedom in case that the corresponding affine Lie superalgebra is [Formula: see text]. We also demonstrate computation of local martingales associated with the solution from a representation of [Formula: see text].

Entanglement-like properties in spin–orbit coupled ultra cold atom and violation of Bell-like inequality

We show that the general quantum state of synthetically spin–orbit coupled ultra cold bosonic atoms, whose condensate was experimentally created recently by Lin et al (2011 Nature 471, 83), shows entanglement between motional degrees of freedom (momentum) and internal degrees of freedom (hyperfine spin). We demonstrate the violation of Bell-like inequality (CHSH) for such states that provide a unique opportunity to verify fundamental principles like quantum contextuality for commutating observables which are not spatially separated. We analyze in detail the Rabi oscillation executed by such an atom-laser system and how this influences quantities like entanglement entropy, the violation of Bell-like inequality, etc. We also discuss the implications of our result in testing quantum contextuality and Bell’s Inequality violation by macroscopic quantum object like Bose–Einstein condensate of ultra cold atoms.

Phonon localization in an ion chain under irradiation with a Bessel laser beam

Trapped ions offer an excellent platform to investigate fascinating phenomena in quantum physics. Here we propose an experimental scheme to achieve Anderson localization of phonons using an ion chain under irradiation of a laser Bessel beam. The quasiperiodicity comes from the characteristic of the Bessel beam, which is only relevant to the positions of the individual ions with respect to the standing wave of the Bessel beam, rather than the internal degrees of freedom of the ions. We demonstrate, by the inverse participation ratio, the delocalization-localization transition, which is sensitive to the strength and the phase of the Bessel beam laser. Our model involving long-range phonon hopping could present richer phenomena than the Aubry-Andr\'e model including only nearest-neighbor coupling.

Kinematic Design of a New Four Degree-of-Freedom Parallel Robot for Knee Rehabilitation

Rehabilitation robots are increasingly being developed in order to be used by injured people to perform exercise and training. As these exercises do not need wide range movements, some parallel robots with lower mobility architecture can be an ideal solution for this purpose. This paper presents the design of a new four degree-of-freedom (DOF) parallel robot for knee rehabilitation. The required four DOFs are two translations in a vertical plane and two rotations, one of them around an axis perpendicular to the vertical plane and the other one with respect to a vector normal to the instantaneous orientation of the mobile platform. These four DOFs are reached by means of two RPRR limbs and two UPS limbs linked to an articulated mobile platform with an internal DOF. Kinematics of the new mechanism are solved and the direct Jacobian is calculated. A singularity analysis is carried out and the gained DOFs of the direct singularities are calculated. Some of the singularities can be avoided by selecting suitable values of the geometric parameters of the robot. Moreover, among the found singularities, one of them can be used in order to fold up the mechanism for its transportation. It is concluded that the proposed mechanism reaches the desired output movements in order to carry out rehabilitation maneuvers in a singularity-free portion of its workspace.

Application of Model Kinetic Equations to Calculations of Super- and Hypersonic Molecular Gas Flows

For the purpose of taking the internal degrees of freedom into account, threetemperature approximating model equations, which are a generalization of the R- and ES–BGKmodels, are proposed for a diatomic gas. The surface pressure, friction, and heat transfer coefficients are compared with the direct simulation Monte Carlo (DSMC) solution in the problem of flow past a cylinder in the super- and hypersonic flow regimes. The dependence of the surface coefficients on the rotational collision number is analyzed.