Internal Degrees Of Freedom Research Articles

A Force Field for Poly(oxymethylene) Dimethyl Ethers (OMEn).

A united atom force field for the homologous series of the poly(oxymethylene) dimethyl ethers (OMEn), H3C-O-(CH2O)n-CH3, is presented. OMEn are oxygenates and promising new synthetic fuels and solvents. The molecular geometry of the OMEn, the internal degrees of freedom, and their electrostatic properties were obtained from quantum mechanical calculations. To model repulsion and dispersion, Lennard-Jones parameters were fitted to the experimental liquid densities and vapor pressures of pure OMEn (n = 1-4). The critical properties of OMEn (n = 1-4) were determined from the simulation data. Additionally, the shear viscosity of pure liquid OMEn is evaluated and compared with literature data. Finally, the solubility of CO2 in OME2, OME3, and OME4 is predicted using a literature model for CO2 and the Lorentz-Berthelot combining rules. The results agree well with experimental data from the literature.

Stability and coupling dynamic characteristics of a vibrating system with one internal degree of freedom and two vibrators

In present work the stability and coupling dynamic characteristics for a vibrating system with one internal degree of freedom, driven by two vibrators, are investigated, which is a further extension and innovation of a previous literature. In theory, the responses of the relative and absolute motion of the system are given; the synchronization criterion of the system is obtained based on the average method, and the stability criterion of the synchronous states is derived by Hamilton principle. According to the above theory results, the frequency-amplitude characteristics of the system are discussed qualitatively by numeric, as well as the stable states, phase relationships and corresponding motion types of the system in different resonant regions. The Runge-Kutta routine is employed to verify the feasibility of the used theory method. Finally, an experimental vibrating mill corresponding to the present dynamical model is designed and manufactured, and the experiments are carried out to further examine the validity of the present investigations. It is known that, in order to obtain the reasonable relative circular motion of two rigid frames, in engineering, not only the working point of the system, should be set in the sub-resonant region with respect to the natural frequency of the main vibrating system in x- and y- directions, but also the distance between the rotational center of each vibrator and the centroid of the system, must be adjusted to be larger to meet the above requirements. Only in this way, can the greater relative vibration amplitude of the system characterized by the circular motion be realized, the energy be saved, and the ideal isolation effect be satisfied.

Infinitesimal asphericity changes the universality of the jamming transition

The jamming transition of non-spherical particles is fundamentally different from the spherical case. Non-spherical particles are hypostatic at their jamming points, while isostaticity is ensured in the case of the jamming of spherical particles. This structural difference implies that the presence of asphericity affects the critical exponents related to the contact number and the vibrational density of states. Moreover, while the force and gap distributions of isostatic jamming present power-law behaviors, even an infinitesimal asphericity is enough to smooth out these singularities. In a recent work (Brito et al 2018 Proc. Natl Acad. Sci. 115 11736–41), we have used a combination of marginal stability arguments and the replica method to explain these observations. We argued that systems with internal degrees of freedom, like the rotations in ellipsoids, or the variation of the radii in the case of the breathing particles fall in the same universality class. In this paper, we review comprehensively the results about the jamming with internal degrees of freedom in addition to the translational degrees of freedom. We use a variational argument to derive the critical exponents of the contact number, shear modulus, and the characteristic frequencies of the density of states. Moreover, we present additional numerical data supporting the theoretical results, which were not shown in the previous work.

Robustness of unconventional s -wave superconducting states against disorder

We investigate the robustness against disorder of superconductivity in multiband systems where the fermions have four internal degrees of freedom. This permits unconventional $s$-wave pairing states, which may transform nontrivially under crystal symmetries. Using the self-consistent Born approximation, we develop a general theory for the effect of impurities on the critical temperature, and find that the presence of these novel $s$-wave channels significantly modifies the conclusions of single-band theories. We apply our theory to two candidate topological superconductors, YPtBi and Cu$_x$Bi$_2$Se$_3$, and show that the novel $s$-wave states display an enhanced resilience against disorder, which extends to momentum-dependent pairing states with the same crystal symmetry. The robustness of the $s$-wave states can be quantified in terms of their superconducting fitness, which can be readily evaluated for model systems.

Supersymmetry in string bit models with internal degrees of freedom

We study in a general way the construction of string bit Hamiltonians which are supersymmetric, We construct several quadratic and quartic polynomials in string bit creation and annihilation operators ${\bar\phi}^A_{a_1\cdots a_n}$, ${\phi}^A_{a_1\cdots a_n}$,which commute with the supersymmetry generators $Q^a$. Among these operators are ones with the spinor tensor structure required to provide the lightcone worldsheet vertex insertion factors needed to give the correct interactions for the IIB superstring, whenever a closed string separates into two closed strings or two closed strings join into one.

Protein Conformational Dynamics Probed Correlation Spectroscopy of Multiply Scattered Light

To assess the dynamics of proteins due to their external and internal degrees of freedom, we used a optical correlation spectroscopy method, that provides the spectrum of optical fluctuations due to protein dynamics in solution. In the case of acto-myosin forced out-of-equilibrium by its chemically driven motor activity, the difference spectrum between thermal and driven fluctuations reveals the frequency-amplitude properties of the conformational dynamics of myosin. This optical method is the so-called DWS (diffusive wave spectroscopy), first proposed by Maret and Wolf in 1987 (Z. Phys.). Practically, when illuminated by a highly monochromatic and coherent light beam in the strong scattering regime, the sample produces a diffusive light flux inside the sample. Outside of the sample, one obtains an intensity speckle field that is determined by the scattering properties and the spatial distribution of the scatterers, with fixed speckles if scatterers are immobile. By measuring the speckle intensity autocorrelation function, one obtains the fluctuation spectrum of the scaterrers. Using that method, we found that conformational changes of myosin occur at times-scales that are typically 2 to 3 orders of magnitude faster that the shortest time of the enzymatic activity cycle. To improve the sensitivity of that method, we introduce a new concept called Cavity Amplified Speckle Decorrelation Spectroscopy. The phase fluctuations of the light scattered by a given sample are amplified by placing it inside a closed Lambertian cavity with highly diffusively reflecting walls, which ergodically forces the light multiple times back into the sample. This new concept will be illustrated with a few biological and non-biological samples, showing that previously undetected fluctuations can be measured over 8-10 decades in the frequency domain, and resolved with unprecedented sensitivity.

Quantum master equations for a system interacting with a quantum gas in the low-density limit and for the semiclassical collision model

A quantum system interacting with a dilute gas experiences irreversible dynamics. The corresponding master equation can be derived within two different approaches: The fully quantum description in the low-density limit and the semiclassical collision model, where the motion of gas particles is classical whereas their internal degrees of freedom are quantum. The two approaches have been extensively studied in the literature, but their predictions have not been compared. This is mainly due to the fact that the low-density limit is extensively studied for mathematical physics purposes, whereas the collision models have been essentially developed for quantum information tasks such as a tractable description of the open quantum dynamics. Here we develop and for the first time compare both approaches for a spin system interacting with a gas of spin particles. Using some approximations, we explicitly find the corresponding master equations including the Lamb shifts and the dissipators. The low density limit in the Born approximation for fast particles is shown to be equivalent to the semiclassical collision model in the stroboscopic approximation. We reveal that both approaches give exactly the same master equation if the gas temperature is high enough. This allows to interchangeably use complicated calculations in the low density limit and rather simple calculations in the collision model.

Braiding properties of paired spin-singlet and non-Abelian hierarchy states

We study explicit model wave functions describing the fundamental quasiholes in a class of non-Abelian fractional quantum Hall states. This class is a family of paired spin-singlet states with internal degrees of freedom. We determine the braid statistics of the quasiholes by determining the monodromy of the explicit quasihole wave functions, that is how they transform under exchanges of quasihole coordinates. The statistics is shown to be the same as that of the quasiholes in the Read–Rezayi states, up to a phase. We also discuss the application of this result to a class of non-Abelian hierarchy wave functions.

Experimental consequences of Bogoliubov Fermi surfaces

Superconductors involving electrons with internal degrees of freedom beyond spin can have internally anisotropic pairing states that are impossible in single-band superconductors. As a case in point, in even-parity multiband superconductors that break time-reversal symmetry, nodes of the superconducting gap are generically inflated into two-dimensional Bogoliubov Fermi surfaces. The detection and characterization of these quasiparticle Fermi surfaces requires the understanding of their experimental consequences. In this paper, we derive the low-energy density of states for a broad range of possible nodal structures. Based on this, we calculate the low-temperature form of observables that are commonly employed for the characterization of nodal superconductors, i.e., the single-particle tunneling rate, the electronic specific heat and Sommerfeld coefficient, the thermal conductivity, the magnetic penetration depth, and the NMR spin-lattice relaxation rate, in the clean limit. We also address the question whether the topological invariant of the Bogoliubov Fermi surfaces is associated with topologically protected surface states, with negative results. This work is meant to serve as a guide for experimental searches for Bogoliubov Fermi surfaces in time-reversal-symmetry-breaking superconductors.

Пределы "физической детонации" при течении предварительно колебательно-возбужденного водорода в ударной трубе

Physical detonation" - - - is a phenomenon when the detonation is caused not by chemical, but by physical energy focused on internal degrees of freedom, in this case on the vibrational degrees of freedom of hydrogen molecules. The Monte-Carlo method of non-stationary statistical simulation has been used to study the possibility of this phenomenon for pre-vibrationally excited hydrogen to a certain temperature in a shock tube. The boundary of this temperature above which "physical detonation" takes place in the numerical experiment is determined.

Dissociative electron attachment to MgCN

Dissociative electron attachment (DEA) to the molecule MgCN and its isomer MgNC has been proposed as a possible source of CN− in the interstellar media. We have carried out electron scattering calculations using the complex Kohn Variational Method as a function of the internal degrees of freedom of the molecule to obtain the resonance energy surfaces and autoionization widths. We use these data as input to form the Hamiltonian relevant to the nuclear dynamics. The multidimensional time-dependent Schrodinger equation is solved using the MultiConfiguration Time-Dependent Hartree (MCTDH) approach. We compute the DEA cross sections and discuss the implications for CN− formation in circumstellar envelopes.

Quantum Skyrmions in Frustrated Ferromagnets

We develop a quantum theory of magnetic skyrmions and antiskyrmions in a spin-1/2 Heisenberg magnet with frustrating next-nearest neighbor interactions. Using exact diagonalization we show numerically that a quantum skyrmion exists as a stable many-magnon bound state and investigate its quantum numbers. We then derive a phenomenological Schr\"odinger equation for the quantum skyrmion and its internal degrees of freedom. We find that quantum skyrmions have highly unusual properties. Their bandwidth is exponentially small and arises from tunneling processes between skyrmion and antiskyrmion. The bandstructure changes both qualitatively and quantitatively when a single spin is added or removed from the quantum skyrmion, reflecting a locking of angular momentum and spin quantum numbers characteristic for skyrmions. Additionally, while for weak forces the quantum skyrmion is accelerated parallel to the force, it moves in a perpendicular direction for stronger fields.

Ground state excitation of an atom strongly coupled to a free quantum field

This paper presents a nonperturbative treatment of strong-coupling induced effects in atom-field systems which cannot be seen in traditional perturbative treatments invoking compromising assumptions such as the Born-Markov, rotating wave or Fermi Golden rule. We consider an atom whose internal degrees of freedom are modeled by a harmonic oscillator, bilinearly coupled to a scalar quantum field, representing one of the two polarizations of an electromagnetic field. Because the whole system is Gaussian we can solve this problem exactly. Using the open quantum system conceptual framework and the influence functional formalism we derive the dynamics of the reduced density matrix for the atom which enables the calculation of atomic transition probability and other relevant physical quantities. Finding an exact solution to this problem has the distinct advantage of enabling one to capture fully the strong coupling regime and discover interesting effects such as spontaneous ground state excitation which is unfathomable in perturbative treatments. The conventional description of atomic-optical activities is predicated on the assumption that the state of the total atom-field system is a product state of the atomic excitations and the photon number states, an assumption which is valid only for vanishingly weak coupling. The correct energy eigenfunctions to use should be that of the Hamiltonian of the combined atom-field system. Other features associated with finite to strong coupling effects such as resonance peak broadening and transition from a gapped to a gapless spectrum can all be understood from this perspective. Finally, to put the issues in a proper perspective we take the perturbative limit of the exact results and compare them with those from conventional TDPT. This enables one to pin-point where the deficiencies of TDPT lie as one removes the ultra-weak coupling assumption.

Observer dependence of entanglement in nonrelativistic quantum mechanics

It was recently shown that, in general, the von Neumann spin entropy of fermionic particles is not invariant under Lorentz boosts. We show that an analogous result can be recovered (at the lowest order of $v^2 /c^2$) using plain nonrelativistic quantum mechanics provided one uses that energy weighs: $E=m c^2$. This should (i) help to moderate the skepticism on the observer-dependence of the spin entropy of fermionic particles, (ii) emphasize the soft relativistic nature of this result, and (iii) show that this is a particular case of a more general class of systems, since our calculation only assumes a nonrelativistic particle endowed with an internal degree of freedom.

Coupled micro-Doppler signatures of closely located targets

The classical Doppler shift originates from the movement of a target's center of mass, but it does not hold information about the internal dynamics of the scattering object. In contrast, micro-Doppler signatures contain data about the micro-motions that arise from internal degrees of freedom within the target (such as rotation and vibration), which can be remotely detected by careful analysis of the scattered field. Here we investigate, both theoretically and experimentally, how coupling between a pair of closely situated targets affects the resulting micro-Doppler signatures. The presented model considers a pair of near-field coupled resonators with dynamically reconfigurable scattering properties. Voltage controlled varactor diodes enable modulating the scattering cross-section of each target independently, mimicking rotational degrees of freedom. As a result, coupled micro-Doppler combs are observed, containing new frequency components that arise from the near field coupling, making it possible to extract information about the internal geometry of the system from far-field measurements. From a practical point of view, micro-Doppler spectroscopy allows remote classification of distant objects, while deep understanding of the coupling effects on such signatures in the low frequency regime can provide valuable insight for radar and sonar systems, as well as optical and stellar radio-interferometry, among many others.

Equation of motion for a bound system of charged particles

We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of polarizabilities. Due to the lack of separation of the total momentum from the internal degrees of freedom, the notion of polarizability of the bound state immersed in the continuum spectrum of the global motion is nontrivial. We introduce a bound-continuum perturbation theory and obtain a complete formula for the equation of motion for a polarizable bound system, such as atom, ion, or the nucleus. This formula may find applications when high precision is sought and small effects due polarizabilities are important.

Active gel segment behaving as an active particle.

We reduce a one-dimensional model of an active segment (AS), which is used, for instance, in the description of contraction-driven cell motility, to a zero-dimensional model of an active particle (AP) characterized by two internal degrees of freedom: position and polarity. Both models give rise to hysteretic force-velocity relations showing that an active agent can support two opposite polarities under the same external force and that it can maintain the same polarity while being dragged by external forces with opposite orientations. This double bistability results in a rich dynamic repertoire which we illustrate by studying static, stalled, motile, and periodically repolarizing regimes displayed by an active agent confined in a viscoelastic environment. We show that the AS and AP models can be calibrated to generate quantitatively similar dynamic responses.

Multiscale analysis of heterogeneous materials in boundary representation

AbstractThis paper deals with a numerical method for modeling heterogeneous materials with nonlinear behavior. Many novel high‐performance materials consist of different components. In the frame of nonlinear behavior the resulting macroscopic material properties cannot be determined without great experimental effort. In order to simulate the nonlinear material behavior, a nested finite element method (FE2) is used. An accompanying homogenization is performed for each load step. The material behavior is determined from the represented volume element (RVE) on the heterogeneous micro structure. The present approach is dealing with a discretization method of the heterogeneous structure. It based on the geometrical data of the interface boundary of the different constituents. A quad‐tree algorithm, in combination with a trimming algorithm is used for the mesh generation. Based on the geometrical data it yields an initial mesh for the analysis. Within the algorithm a staircase approximation of voids or inclusions is circumvented. However, the resulting mesh yields polygonal elements with an arbitrary number of nodes on the element boundary. To this end a novel polygonal element formulation is provided. It is based on the scaled boundary finite element method (SBFEM). The basic idea is to scale the boundary representation in relation to a scaling center. In contrast to SBFEM the present method makes us of an approximation of the displacement response in scaling direction. This enables the analysis of geometrical and material‐related nonlinear problems in solid mechanics. The interpolation at the boundary in circumferential direction is independent of the interpolation in scaling direction. This allows for novel refinement strategies, where e.g. p‐refinement is only applied for the interior element domain. The internal degrees of freedom are eliminated by static condensation. It leads to an element formulation with an arbitrary number of nodes at the element boundary. Thus, the present element is perfectly suited for a quad‐tree meshing algorithm of the RVE. Its hierarchical, tree‐like data structure makes it very useful for adaptive mesh refinements of complex geometries and regions with localized gradients. The classical hanging‐nodes problem for standard elements is omitted by the present element formulation. Some numerical examples show the capability of the formulation with respect to the numerical homogenization of heterogeneous materials.

Calculating the model of a nondiagonal rotation invariant angle for a complicated scatterer.

In the research on scattering polarimetry, a scattering mechanism is described by an internal degree of freedom called rotation invariant parameter α. Traditionally, α is calculated by the diagonal scattering matrix of the single scatterer. However, when the research object is a scatterer with complicated surface and microstructure, the traditional calculation of parameter α is biased, since the corresponding scattering matrix is a nondiagonal matrix. To address this problem, this paper proposes a scientific model based on Cameron decomposition to raise the accuracy of parameter α in the complicated scatterer. The rotation invariant parameter with higher accuracy is renamed as a nondiagonal rotation invariant angle. In the verified experiments, the experimental values of each nondiagonal rotation invariant angle are compared with the referenced values calculated by optical constant and incident angle. The results demonstrate that fewer residuals are achieved than by the traditional method. Based on the presented calculating model, the scattering mechanism difference interval between two different materials is proposed as a judging area to distinguish the differences between scattering mechanisms in application.

Breakdown of the equivalence between gravitational mass and energy due to quantum effects

We review our recent theoretical results about inequivalence between passive and active gravitational masses and energy in the semiclassical variant of general relativity, where the gravitational field is not quantized but matter is quantized. To this end, we consider the simplest quantum body with internal degrees of freedom — a hydrogen atom. We concentrate our attention on the following physical effects, related to electron mass. The first one is the inequivalence between passive gravitational mass and energy at the microscopic level. Indeed, the quantum measurement of gravitational mass can give a result which is different from the expected one, [Formula: see text], where the electron is initially in its ground state; [Formula: see text] is the bare electron mass. The second effect is that the expectation values of both the passive and active gravitational masses of stationary quantum states are equivalent to the expectation value of the energy. The most spectacular effects are the inequivalence of the passive and active gravitational masses and the energy at the macroscopic level for an ensemble of coherent superpositions of stationary quantum states. We show that, for such superpositions, the expectation values of passive and active gravitational masses are not related to the expectation value of energy by Einstein’s famous equation, [Formula: see text]. In this paper, we also improve several drawbacks of the original pioneering works.