Different Degrees Of Freedom Research Articles

Experimental realization of SWAP operation on hyper-encoded qubits.

Hyper-encoding enables storing several qubits in a single photon using its different degrees of freedom like polarization and spatial ones. This approach enables feasible implementation of multi-qubit operations. One of the basic manipulations of two or more qubits is to swap their quantum state. Here we report on feasible and stable experimental implementation of a deterministic single photon two-qubit SWAP gate that interchanges path and polarization qubits. We discuss the principle of its operation and give detailed information about experimental demonstration employing two Mach-Zehnder interferometers with one common arm. The gate characterization is done by full quantum process tomography using photons produced by heralded single-photon source. The achieved quantum process fidelity reached more than 0.94 with an effective phase uncertainty of the whole setup, evaluated by means of Allan deviation, below 2.5 deg for 2.5 h without any active stabilization. Our design provides a contribution to the hyper-encoded linear quantum optics toolbox.

Giant thermal hysteresis in Verwey transition of single domain Fe3O4 nanoparticles

Most interesting phenomena of condensed matter physics originate from interactions among different degrees of freedom, making it a very intriguing yet challenging question how certain ground states emerge from only a limited number of atoms in assembly. This is especially the case for strongly correlated electron systems with overwhelming complexity. The Verwey transition of Fe3O4 is a classic example of this category, of which the origin is still elusive 80 years after the first report. Here we report, for the first time, that the Verwey transition of Fe3O4 nanoparticles exhibits size-dependent thermal hysteresis in magnetization, 57Fe NMR, and XRD measurements. The hysteresis width passes a maximum of 11 K when the size is 120 nm while dropping to only 1 K for the bulk sample. This behavior is very similar to that of magnetic coercivity and the critical sizes of the hysteresis and the magnetic single domain are identical. We interpret it as a manifestation of charge ordering and spin ordering correlation in a single domain. This work paves a new way of undertaking researches in the vibrant field of strongly correlated electron physics combined with nanoscience.

Analysis of a tripod flexure mechanism (TFM) for mirror sub-assemblies

This paper presents the analytical compliance analysis and type synthesis for a tripod flexure mechanism (TFM) which is used in the design of the mirror sub-assembly (MSA) of future inertia-confinement-fusion (ICF) facilities. To reveal the compliance characteristics of the TFM, the static compliance analysis is conducted. The analytical compliance matrix of the TFM is obtained by using the coordinate transformation method (CT-method) of compliance matrices. The parameterized compliance matrix of the TFM is derived, and it is significantly influenced by its legs’ mounting angle θ. Different θ values generate different degree-of-freedom (DOF) characteristic of types. The finite element analysis (FEA) results are compared with analytical compliance elements results for different θ values. As to the linear linear-elastic deformations, the maximum compliance error of analytical model is less than 1% compared to the FE model. Enlightened by the compliance analysis of the TFM, a compliance-based type synthesis of the TFM is introduced in detailed processes, illustrating how θ affects the DOF characteristics. According to the results of the compliance analysis and type synthesis, a TFM was designed and fabricated for the MSA prototype, and it is experimentally verified. It is demonstrated that the parameterized compliance matrix provided is beneficial to design, analysis and type synthesis tasks of TFMs.

IsRNA: An Iterative Simulated Reference State Approach to Modeling Correlated Interactions in RNA Folding.

Coarse-grained RNA folding models promise great potential for RNA structure prediction. A key component in a coarse-grained folding model is the force field. One of the challenges in the coarse-grained force field calculation is how to treat the correlation between the different degrees of freedoms. Here, we describe a new approach (IsRNA) to extract the correlated energy functions from the known structures. Through iterative molecular dynamics simulations, we build the correlation effects into the reference states, from which we extract the energy functions. The validity of IsRNA is supported by the close agreement between the simulated Boltzmann-like probability distributions for all the structure parameters and those observed from the experimentally determined structures. The correlated energy functions derived here may provide a new tool for RNA 3D structure prediction.

Numerical study on shell-side flow and heat transfer of spiral-wound heat exchanger under sloshing working conditions

Spiral-wound heat exchanger (SWHE) is under sloshing working conditions when it is used on floating liquefied natural gas (FLNG), which can remarkably influence the efficiency of liquefaction and the stability of operation. In this paper, a numerical method for realizing the sloshing of SWHE shell side with different degrees of freedom (DOFs) was successfully proposed based on ANSYS software. The sloshing simulations were carried out, and the effects of sloshing motions on the shell-side flow and heat transfer characteristics were analyzed. By comparing, the uncertainty of simulation result was within ±10%. As a result, the shell-side flow and heat transfer characteristics were obviously influenced by sloshing motions and showed periodicity. The effects of pitching and heaving were more significant than that of rolling, and the effect of sloshing period was smaller than that of sloshing amplitude. At the same time, the fluctuations’ regularity of two-phase flow and heat transfer characteristics decreased with the increasing vapor quality.

Numerical analysis for the stick-slip vibration of a transversely moving beam in contact with a frictional wall

This paper presents a numerical analysis for the stick-slip vibration of a transversely moving beam, considering both stick-slip transition and friction force discontinuity. The dynamic state of the beam was separated into the stick state and the slip state, and boundary conditions were defined for both. By applying the finite element method, two matrix-vector equations were derived: one for stick state and the other for slip state. However, the equations have different degrees of freedom depending on whether the end of a beam sticks or slips, so we encountered difficulties in time integration. To overcome the difficulties, we proposed a new numerical technique to alternatively use the matrix-vector equations with different matrix sizes. In addition, to eliminate spurious high-frequency responses, we applied the generalized-α time integration method with appropriate value of high-frequency numerical dissipation. Finally, the dynamic responses of stick-slip vibration were analyzed in time and frequency domains: the dynamic behavior of the beam was explained to facilitate understanding of the stick-slip motion, and frequency characteristics of the stick-slip vibration were investigated in relation to the natural frequencies of the beam. The effects of the axial load and the moving speed upon the dynamic response were also examined.

Articulating Parametric Nonlinearities in Computationally Efficient Hydrodynamic Models

Wave energy devices are designed, and controlled, in order to be extremely responsive to incoming wave excitation, hence maximising power absorption. Due to the consequent large motion excursions, highly nonlinear behaviour is likely to occur, especially in relation to variations in wetted surface. Moreover, nonlinearities may induce parametric instability, or activate internal mechanisms for exchanging energy between different degrees of freedom (DoFs), usually affecting the overall efficiency of the device. Consequently, single-DoF linear models may produce overly optimistic power production predictions, and neglect important dynamics of the system. One highly nonlinear phenomenon, particularly detrimental to power absorption for several wave energy converters, is parametric roll, which internally diverts part of the energy flow, from the axis where the power take-off is installed, to a secondary axis, generating parasitic motion. This paper proposes a computationally efficient multi-DoFs nonlinear model, which can effectively describe nonlinear behaviour, such as parametric pitch and roll, and their impact on motion prediction, power production assessment, and optimal control parameters.

Nonperturbative Series Expansion of Green's Functions: The Anatomy of Resonant Inelastic X-Ray Scattering in the Doped Hubbard Model.

We present a nonperturbative, divergence-free series expansion of Green's functions using effective operators. The method is especially suited for computing correlators of complex operators as a series of correlation functions of simpler forms. We apply the method to study low-energy excitations in resonant inelastic x-ray scattering (RIXS) in doped one- and two-dimensional single-band Hubbard models. The RIXS operator is expanded into polynomials of spin, density, and current operators weighted by fundamental x-ray spectral functions. These operators couple to different polarization channels resulting in simple selection rules. The incident photon energy dependent coefficients help to pinpoint main RIXS contributions from different degrees of freedom. We show in particular that, with parameters pertaining to cuprate superconductors, local spin excitation dominates the RIXS spectral weight over a wide doping range in the cross-polarization channel.

Perturbed path integrals in imaginary time: Efficiently modeling nuclear quantum effects in molecules and materials.

Nuclear quantum effects (NQE), which include both zero-point motion and tunneling, exhibit quite an impressive range of influence over the equilibrium and dynamical properties of molecules and materials. In this work, we extend our recently proposed perturbed path-integral (PPI) approach for modeling NQE in molecular systems [I. Poltavsky and A. Tkatchenko, Chem. Sci. 7, 1368 (2016)], which successfully combines the advantages of thermodynamic perturbation theory with path-integral molecular dynamics (PIMD), in a number of important directions. First, we demonstrate the accuracy, performance, and general applicability of the PPI approach to both molecules and extended (condensed-phase) materials. Second, we derive a series of estimators within the PPI approach to enable calculations of structural properties such as radial distribution functions (RDFs) that exhibit rapid convergence with respect to the number of beads in the PIMD simulation. Finally, we introduce an effective nuclear temperature formalism within the framework of the PPI approach and demonstrate that such effective temperatures can be an extremely useful tool in quantitatively estimating the "quantumness" associated with different degrees of freedom in the system as well as providing a reliable quantitative assessment of the convergence of PIMD simulations. Since the PPI approach only requires the use of standard second-order imaginary-time PIMD simulations, these developments enable one to include a treatment of NQE in equilibrium thermodynamic properties (such as energies, heat capacities, and RDFs) with the accuracy of higher-order methods but at a fraction of the computational cost, thereby enabling first-principles modeling that simultaneously accounts for the quantum mechanical nature of both electrons and nuclei in large-scale molecules and materials.

Análisis sísmico de gradas con tres modelos mediante los métodos: espectral y del espectro de capacidad, que sirven de acceso a una estructura con aisladores sísmicos

At the Universidad de las Fuerzas Armadas - ESPE, in Ecuador, different structural blocks with and without seismic isolators of triple friction pendulum are being built. In one of them, the access stairs to the floors is located in a Structural Block with no seismic isolators; therefore, it has special construction details to allow a free displacement of the Isolators’ Building without impacting the Stairs’ Building at all. This paper addresses these details. On the other hand, three models (each with different degrees of freedom) for seismic analyses of a longitudinal frame and a transversal frame are shown. The results were obtained and compared using the Spectral Method and the Capacity Spectrum Method. Moreover, these results highlight the importance of appropriately selecting the numerical calculation model. Later on, the seismic analysis of the Structural Block of the Access Stairs is shown, using a three-phase constitutive model.

Photonic quantum simulator for unbiased phase covariant cloning

We present the results of a linear optics photonic implementation of a quantum circuit that simulates a phase covariant cloner, using two different degrees of freedom of a single photon. We experimentally simulate the action of two mirrored $$1\rightarrow 2$$ cloners, each of them biasing the cloned states into opposite regions of the Bloch sphere. We show that by applying a random sequence of these two cloners, an eavesdropper can mitigate the amount of noise added to the original input state and therefore, prepare clones with no bias, but with the same individual fidelity, masking its presence in a quantum key distribution protocol. Input polarization qubit states are cloned into path qubit states of the same photon, which is identified as a potential eavesdropper in a quantum key distribution protocol. The device has the flexibility to produce mirrored versions that optimally clone states on either the northern or southern hemispheres of the Bloch sphere, as well as to simulate optimal and non-optimal cloning machines by tuning the asymmetry on each of the cloning machines.

Sliding Modes for a Manipulator Arm of 4 Degrees of Freedom

The first step in designing a controller for a manipulating arm is to determine its configuration, which means, analyzing the main components that make up the mechanism. A manipulating arm is composed of joints, motors, sensors and other elements, which are linked to conform the different degrees of freedom (generalized coordinates: prismatic, rotational or a combination of both, which is presented as the most unusual), which allow the calculation of the dynamic model implemented to obtain the control specifications [1]. In this paper, the calculation of a controller by sliding modes for a manipulator arm with 4 rotational degrees of freedom will be done, showing the respective results and conclusions at the end.

Aeroelastic stability of a 3DOF system based on quasi-steady theory with reference to inertial coupling

This paper investigates the galloping stability of a two-dimensional three-degree-of-freedom (3DOF) system with an eccentric shape, such as an iced cable or power transmission line, incorporating inertial coupling along with the aerodynamic damping. The inertial coupling is a result of the offset of the centre of mass with respect to the elastic centre. A theoretical model is firstly constructed for the derivation of the aerodynamic damping matrix, based on quasi-steady theory, as well as the inertial coupling components in the mass matrix. The model is then employed to investigate the effects on the aeroelastic stability of the system of incorporating the inertial coupling and the results are compared with both dynamic test results and predictions from previous models. The comparisons indicate that even small eccentricity can lead to significant change of the stability of the system, for both detuned and perfectly tuned natural frequencies of the different degrees of freedom. For a system with perfectly tuned natural frequencies, and neglecting structural damping, analytical solutions of the eigenfrequencies and eigenvectors allowing for the inertial coupling, are derived for the case of no wind. Subsequently, an approximate solution is found for the prediction of the galloping stability of a system coupled by the aerodynamic damping as well as the inertial coupling. Finally, the approximate solution is verified against numerical results using examples with two cross-section shapes, showing excellent agreement.

Sailing yacht performance prediction based on coupled CFD and rigid body dynamics in 6 degrees of freedom

Traditional Velocity Prediction Programs (VPPs) for sailing yachts rely on empirical relations, while modern techniques include CFD. Normally a multi-dimensional matrix of CFD results is pre-computed and forces and moments obtained by interpolation during a VPP execution. A more exact technique is to use the CFD code itself as a VPP, i.e. to simultaneously integrate the flow and rigid body equations in time. In the present paper a technique of this coupled type is introduced.An initial guess is required for speed and attitude, and by time integration in six degrees of freedom this guess is corrected to a steady state solution. Three phases are identified. First the attitude is kept constant over a period of time to stabilize the flow. Thereafter the different degrees of freedom are released successively and the rudder activated to achieve yaw balance. Finally, in the converged phase, the net forces and moments are zero in all degrees of freedom and the results reported.The performance prediction is carried out for a dinghy and a large high-performance racing yacht. Convergence of all variables is demonstrated and the results used for finding the optimum speed to windward and downwind. Details of the numerical setup are reported.

Do event horizons exist?

Event horizons are the defining feature of classical black holes. They are the key ingredient of the information loss paradox which, as paradoxes in quantum foundations, is built on a combination of predictions of quantum theory and counterfactual classical features: neither horizon formation nor its crossing by a test body can be detected by a distant observer. Furthermore, horizons are unnecessary for the production of Hawking-like radiation. We demonstrate that when this radiation is taken into account, it can prevent horizon crossing/formation in a large class of models. We conjecture that horizon avoidance is a general feature of collapse. The nonexistence of event horizons dispels the paradox, but opens up important questions about thermodynamic properties of the resulting objects and correlations between different degrees of freedom.

Multitier self-consistent GW+EDMFT

We discuss a parameter-free and computationally efficient ab initio simulation approach for moderately and strongly correlated materials, the multitier self-consistent $GW$+EDMFT method. This scheme treats different degrees of freedom, such as high-energy and low-energy bands, or local and nonlocal interactions, within appropriate levels of approximation, and provides a fully self-consistent description of correlation and screening effects in the solid. The ab initio input is provided by a one-shot $G^0W^0$ calculation, while the strong-correlation effects originating from narrow bands near the Fermi level are captured by a combined $GW$ plus extended dynamical mean-field (EDMFT) treatment. We present the formalism and technical details of our implementation and discuss some general properties of the effective EDMFT impurity action. In particular, we show that the retarded impurity interactions can have non-causal features, while the physical observables, such as the screened interactions of the lattice system, remain causal. We then turn to stretched sodium as a model system to explore the performance of the multitier self-consistent $GW$+EDMFT method in situations with different degrees of correlation. While the results for the physical lattice spacing $a_0$ show that the scheme is not very accurate for electron-gas like systems, because nonlocal corrections beyond $GW$ are important, it does provide physically correct results in the intermediate correlation regime, and a Mott transition around a lattice spacing of $1.5a_0$. Remarkably, even though the Wannier functions in the stretched compound are less localized, and hence the bare interaction parameters are reduced, the self-consistently computed impurity interactions show the physically expected trend of an increasing interaction strength with increasing lattice spacing.

Coupled elastodynamics of piston compression ring subject to sweep excitation

The piston compression ring's primary function is to seal the combustion chamber, thus mitigating gas leakage to the crankcase and avoiding loss of pressure loading. As a result, the ring is meant to conform closely to the cylinder surface which promotes increased friction. The compression ring is subjected to combustion pressure loading, ring tension, varying inertial force and friction. It is a slender ring of low mass, thus undergoes complex elastodynamic behaviour, when subjected to a multitude of forces. These motions occur in the ring's radial in-plane and axial out-of-plane dynamics, which comprise flutter, ring axial jump, compression-extension, ring twist and rotational drag. An implication of these motions can be loss of sealing, gas blow-by, loss of power and lubricant degradation/oil loss, to name but a few. Consequently, understanding and accurately predicting ring dynamic behaviour under transient conditions is an important step in any subsequent modelling for evaluation of cylinder system efficiency. There have been a plethora of investigations for ring dynamics, often decoupling the ring behaviour in its in-plane and out-of-plane motions. This approach disregards any transfer of dynamic energy from one degree of freedom to another which is only applicable to rectangular ring cross-sections. Alternatively, there are computationally intensive approaches such as finite element analysis which are not conducive for inclusion in any subsequent system level engine modelling where ring response alters in an instantaneous manner. This would require embedded finite element analysis within a transient analysis. This paper presents a finite difference numerical analysis for coupled in-plane and out-of-plane motions of compression rings with practical cross-sectional geometries, which are mostly not rectangular. The formulated method can be integrated into a system level transient cyclic analysis of ring-bore contact. The presented approach takes into account the energy transfer between different degrees of freedom. The predictions are validated against precise non-contact measurements of ring elastodynamic behaviour under amplitude-frequency sweeps. This approach has not hitherto been reported in literature and constitutes the main contribution of the paper.

Direct transfer of classical non-separable states into hybrid entangled two photon states

Hybrid entangled states, having entanglement between different degrees-of-freedom (DoF) of a particle pair, are of great interest for quantum information science and communication protocols. Among different DoFs, the hybrid entangled states encoded with polarization and orbital angular momentum (OAM) allow the generation of qubit-qudit entangled states, macroscopic entanglement with very high quanta of OAM and improvement in angular resolution in remote sensing. Till date, such hybrid entangled states are generated by using a high-fidelity polarization entangled states and subsequent imprinting of chosen amount of OAM using suitable mode converters such as spatial light modulator in complicated experimental schemes. Given that the entangled sources have feeble number of photons, loss of photons during imprinting of OAM using diffractive optical elements limits the use of such hybrid states for practical applications. Here we report, on a simple generic experimental scheme to generate hybrid entangled states in polarization and OAM through direct transfer of classical non-separable states of the pump beam in parametric down conversion process. As a proof of principle, using local non-separable pump states of OAM mode l = 3, we have produced quantum hybrid entangled states with entanglement witness parameter of ~1.25 ± 0.03 violating by 8 standard deviation.

Car resale price forecasting: The impact of regression method, private information, and heterogeneity on forecast accuracy

The paper investigates statistical models for forecasting the resale prices of used cars. An empirical study is performed to explore the contributions of different degrees of freedom in the modeling process to the forecast accuracy. First, a comparative analysis of alternative prediction methods provides evidence that random forest regression is particularly effective for resale price forecasting. It is also shown that the use of linear regression, the prevailing method in previous work, should be avoided. Second, the empirical results demonstrate the presence of heterogeneity in resale price forecasting and identify methods that can automatically overcome its detrimental effect on the forecast accuracy. Finally, the study confirms that the sellers of used cars possess informational advantages over market research agencies, which enable them to forecast resale prices more accurately. This implies that sellers have an incentive to invest in in-house forecasting solutions, instead of basing their pricing decisions on externally generated residual value estimates.

A predictive coding model of gaze shifts and the underlying neurophysiology

ABSTRACTA comprehensive model of gaze control must account for a number of empirical observations at both the behavioural and neurophysiological levels. The computational model presented in this article can simulate the coordinated movements of the eye, head, and body required to perform horizontal gaze shifts. In doing so it reproduces the predictable relationships between the movements performed by these different degrees of freedom (DOFs) in the primate. The model also accounts for the saccadic undershoot that accompanies large gaze shifts in the biological visual system. It can also account for our perception of a stable external world despite frequent gaze shifts and the ability to perform accurate memory-guided and double-step saccades. The proposed model also simulates peri-saccadic compression: the mis-localization of a briefly presented visual stimulus towards the location that is the target for a saccade. At the neurophysiological level, the proposed model is consistent with the existence of cortical neurons tuned to the retinal, head-centred, body-centred, and world-centred locations of visual stimuli and cortical neurons that have gain-modulated responses to visual stimuli. Finally, the model also successfully accounts for peri-saccadic receptive field (RF) remapping which results in reduced responses to stimuli in the current RF location and an increased sensitivity to stimuli appearing at the location that will be occupied by the RF after the saccade. The proposed model thus offers a unified explanation for this seemingly diverse range of phenomena. Furthermore, as the proposed model is an implementation of the predictive coding theory, it offers a single computational explanation for these phenomena and relates gaze shifts to a wider framework for understanding cortical function.