Particular Degrees Of Freedom Research Articles

Partial Learning Using Partially Explicit Discretization for Multicontinuum/Multiscale Problems with Limited Observation: Dual Continuum Heterogeneous Poroelastic Media Simulation

In this paper, we consider the poroelasticity problem in heterogeneous media. The mathematical model is described by a coupled system of equations for displacement and pressure in the coupled dual continuum porous media. We propose a new method based on hybrid explicit–implicit (HEI) learning to solve the poroelasticity problem in dual continuum heterogeneous media. We use a finite element method with standard linear basis functions for spatial approximation. We apply the explicit–implicit time scheme, where the explicit scheme is used for the low-conductive continuum and the implicit scheme for the high-conductive. The fixed-strain splitting scheme is used to accelerate the computation and decouple the flow and mechanics problems. The main idea of the proposed method is partial learning of particular degrees of freedom of the high-conductive continuum’s pressure (implicit part of the flow). First, we train a deep neural network (DNN) to obtain values of the implicit part of the flow at some spatial points at some time moments. Then, we apply the Discrete Empirical Interpolation Method (DEIM) combined with Proper Orthogonal Decomposition (POD) to restore the complete implicit parts and perform linear interpolation over time. Consequently, we treat the high-conductive continuum’s pressure as a known function and use it to find the other continuum’s pressure and displacements. Numerical results for the two-dimensional model problem are presented. The results demonstrate that the proposed method provides fast and accurate predictions.

Superconductivity from repulsion in the doped 2D electronic Hubbard model: an entanglement perspective

We employ the momentum space entanglement renormalization group (MERG) scheme developed in references (Mukherjee et al 2021 J. High Energy Phys. JHEP04(2021)148; Patra and Lal 2021 Phys. Rev. B 104 144514) for the study of various insulating, superconducting and normal phases of the doped and the undoped 2D Hubbard model on a square lattice found recently by us (Mukherjee and Lal 2020 New J. Phys. 22 063007; Mukherjee and Lal 2020 New J. Phys. 22 063008). At each MERG step, disentanglement of particular degrees of freedom, transforms the tensor network representation of the many-particle states. The MERG reveals distinct holographic entanglement features for the normal metallic, topologically ordered insulating quantum liquid and Neél antiferromagnetic symmetry-broken ground states of the 2D Hubbard model at half-filling, clarifying the essence of the entanglement phase transitions that separates the three phases. An MERG analysis of the quantum critical point of the hole-doped 2D Hubbard model reveals the evolution of the many-particle entanglement of the quantum liquid ground state with hole-doping, as well as how the collapse of Mottness is concomitant with the emergence of d-wave superconductivity.

On the use of intra-molecular distance and angle constraints to lengthen the time step in molecular and stochastic dynamics simulations of proteins.

Computer simulation of proteins in aqueous solution at the atomic level of resolution is still limited in time span and system size due to limited computing power available and thus employs a variety of time‐saving techniques that trade some accuracy against computational effort. An example of such a time‐saving technique is the application of constraints to particular degrees of freedom when integrating Newton's or Langevin's equations of motion in molecular dynamics (MD) or stochastic dynamics (SD) simulations, respectively. The application of bond‐length constraints is standard practice in protein simulations and allows for a lengthening of the time step by a factor of three. Applying recently proposed algorithms to constrain bond angles or dihedral angles, it is investigated, using the protein trypsin inhibitor as test molecule, whether bond angles and dihedral angles involving hydrogen atoms or even stiff proper (torsional) dihedral angles as well as improper ones (maintaining particular tetrahedral or planar geometries) may be constrained without generating too many artificial side effects. Constraining the relative positions of the hydrogen atoms in the protein allows for a lengthening of the time step by a factor of two. Additionally constraining the improper dihedral angles and the stiff proper (torsional) dihedral angles in the protein does not allow for an increase of the MD or SD time step.

On the use of multiple-time-step algorithms to save computing effort in molecular dynamics simulations of proteins.

Computer simulation of proteins in aqueous solution at the atomic level of resolution is still limited in time span and system size due to limited computing power available and thus employs a variety of time‐saving techniques that trade some accuracy against computational effort. Examples of such time‐saving techniques are the application of constraints to particular degrees of freedom or the use of a multiple‐time‐step (MTS) algorithm distinguishing between particular forces when integrating Newton's equations of motion. The application of two types of MTS algorithms to bond‐stretching forces versus the remaining forces in molecular dynamics (MD) simulations of a protein in aqueous solution or of liquid water is investigated and the results in terms of total energy conservation and the influence on various other properties are compared to those of MD simulations of the same systems using bond‐length, and for water bond‐angle, constraints. At comparable computational effort, the use of bond‐length constraints in proteins leads to better energy conservation and less distorted properties than the two MTS algorithms investigated.

Feynman-Smoluchowski ratchet in an effective one-dimensional picture

A simple two-dimensional (2D) model of the Feynman-Smoluchowski ratchet is studied. Motion of the wheel, driven by stochastic hits of the surrounding molecules, is described as diffusion along the longitudinal coordinate $x$; the stochastic motion of the pawl is represented in the transverse coordinate $y$. Different temperatures of the reservoirs connected to the particular degrees of freedom, together with asymmetry of the energetic landscape of the system, give rise to the ratchet effect. We apply mapping of the corresponding 2D Fokker-Planck equation onto the longitudinal coordinate $x$. The mapped 1D equation is of the generalized Fick-Jacobs type with an effective potential containing a part increasing or decreasing with $x$, connected with vorticity of the scaled driving force and the stationary probability current. It is responsible for the final rectified motion in the longitudinal direction.

The influence of the hexopyranose ring geometry on the conformation of glycosidic linkages investigated using molecular dynamics simulations

The conformation of the carbohydrate molecules is a subject of many theoretical and experimental studies. The different timescales associated with the particular degrees of freedom hinder the progress in both those fields. The present paper reports the results of computational studies aimed at elucidating and characterizing the potential correlations between the two main structural determinants of the carbohydrate structure, i.e. the ring conformation and the orientation of the glycosidic bonds (expressed in terms of the ϕ and ψ glycosidic dihedral angles). The free energy landscapes computed for 16 different oligomers composed of unsubstituted, 1,4-linked hexopyranose residues allowed for a detailed insight into how the ring geometry affects the glycosidic linkage conformation. The factor of main importance appeared to be the local changes of the chain length induced by the ring conformational rearrangements. This effect is important mainly for the carbohydrate chains exploiting the glycosidic bonds of uniform orientation with respect to the ring (i.e. either exclusively axially or exclusively equatorially oriented). The shape of the ring may affect the (ϕ,ψ) free energy maps but only if the population of the alternative ring conformers is relatively high and (at the same time) the presence of such conformers is associated with the significant shifts of the favorable ϕ and ψ values.

Multi‐Resolution Simulation of Biomolecular Systems: A Review of Methodological Issues

Theoretical-computational modeling with an eye to explaining experimental observations in regard to a particular chemical phenomenon or process requires choices concerning essential degrees of freedom and types of interactions and the generation of a Boltzmann ensemble or trajectories of configurations. Depending on the degrees of freedom that are essential to the process of interest, for example, electronic or nuclear versus atomic, molecular or supra-molecular, quantum- or classical-mechanical equations of motion are to be used. In multi-resolution simulation, various levels of resolution, for example, electronic, atomic, supra-atomic or supra-molecular, are combined in one model. This allows an enhancement of the computational efficiency, while maintaining sufficient detail with respect to particular degrees of freedom. The basic challenges and choices with respect to multi-resolution modeling are reviewed and as an illustration the differential catalytic properties of two enzymes with similar folds but different substrates with respect to these substrates are explored using multi-resolution simulation at the electronic, atomic and supra-molecular levels of resolution.

Multi-Resolution Simulation in Biochemistry: Methodological Issues and Exploration of Peptide Folding and the Origins of Differential Catalysis Observed between Two Structurally Similar Enzymes

Theoretical-computational modelling with an eye to explaining experimental observations in regard to a particular chemical phenomenon or process requires choices concerning essential degrees of freedom and types of interactions and the generation of a Boltzmann ensemble or trajectories of configurations. Depending on the degrees of freedom that are essential to the process of interest, e.g. electronic or nuclear versus atomic, molecular or supra-molecular, quantum or classical-mechanical equations of motion are to be used. In multi-resolution simulation, various levels of resolution, e.g. electronic, atomic, supra-atomic or supra-molecular, are combined in one model. This allows an enhancement of the computational efficiency, while maintaining sufficient detail with respect to particular degrees of freedom. The basic challenges and choices with respect to multi-resolution modelling are reviewed and as illustrations the reversible folding of polypeptides and the differential catalytic properties of two enzymes with similar folds but different substrates with respect to these substrates are explored using multi-resolution simulation at the electronic, atomic and supra-molecular level of resolution.www.igc.ethz.ch and www.gromos.net

Pairing with Spin Fluctuations

Superconductivity requires a “pairing interaction”—an indirect attractive force between the conduction electrons that can overcome their direct Coulomb repulsion. To prove which particular degrees of freedom provide this pairing interaction is supremely difficult: nearly 40 years elapsed between the discovery of superconductivity in 1911 and the “smoking gun” measurement of the isotope effect that proved that lattice distortions provide the pairing interaction in conventional superconductors, and 26 years have elapsed since the discovery of high-temperature superconductivity, and still the pairing mechanism in cuprates is hotly debated. Thus it is a remarkable step forward that NMRmeasurements reported in Physical Review Letters by Taisuke Hattori of Kyoto University, Japan, and colleagues [1] have provided strong evidence that ferromagnetic fluctuations provide the pairing force that leads to superconductivity in an exotic, and comparatively recently discovered [2], class of superconductors in which ferromagnetism and superconductivity seem to happily coexist. Knowledge of the pairing mechanism will lead to a deeper understanding of the superconducting states of these, and possibly other, unconventional superconductors.

Enhanced sampling of particular degrees of freedom in molecular systems based on adiabatic decoupling and temperature or force scaling

A method to enhance sampling of a small subset of N(h) particular degrees of freedom of a system of N(h) + N(l) degrees of freedom is presented. It makes use of adiabatically decoupling these degrees of freedom by increasing their mass followed by either increasing their temperature or reducing their interaction or the force acting on them. The appropriate statistical-mechanical expressions for use of these methods in simulation studies are derived. As long as the subset of mass-increased degrees of freedom is small compared to the total number of degrees of freedom of the system, sampling of this subset of degrees of freedom can be much enhanced at the cost of a slight perturbation of the configurational distribution. This is illustrated for a test system of 1000 SPC, simple point charge, water molecules at 300 K and a density of 997 kg m(-3). Various fractions N(h)/(N(h) + N(l)) of water molecules were adiabatically decoupled to different degrees. The size of the diffusion coefficient of these decoupled water molecules was used as a measure for how much the sampling was enhanced and the average potential energy per water molecule was used as a measure of how much the configurational distribution of the system gets distorted. A variety of parameter values was investigated and it was found that for N(h)/(N(h) + N(l)) ≤ 0.1 the diffusion of the N(h) molecules could be enhanced by factors up to 35 depending on the method, the ratio N(h)/(N(h) + N(l)), the extent of adiabatic decoupling, and the temperature or force scaling factors, at the cost of a slight perturbation of the configurational distribution.

Time-resolved resonant soft x-ray diffraction with free-electron lasers: Femtosecond dynamics across the Verwey transition in magnetite

Resonant soft x-ray diffraction (RSXD) with femtosecond (fs) time resolution is a powerful tool for disentangling the interplay between different degrees of freedom in strongly correlated electron materials. It allows addressing the coupling of particular degrees of freedom upon an external selective perturbation, e.g., by an optical or infrared laser pulse. Here, we report a time-resolved RSXD experiment from the prototypical correlated electron material magnetite using soft x-ray pulses from the free-electron laser FLASH in Hamburg. We observe ultrafast melting of the charge-orbital order leading to the formation of a transient phase, which has not been observed in equilibrium.

A non-rigid cluster rewriting approach to solve systems of 3D geometric constraints

We present a new constructive solving approach for systems of 3D geometric constraints. The solver is based on the cluster rewriting approach, which can efficiently solve large systems of constraints on points, and incrementally handle changes to a system, but can so far solve only a limited class of problems. The new solving approach extends the class of problems that can be solved, while retaining the advantages of the cluster rewriting approach. Whereas previous cluster rewriting solvers only determined rigid clusters, we also determine two types of non-rigid clusters, i.e. clusters with particular degrees of freedom. This allows us to solve many additional problems that cannot be decomposed into rigid clusters, without resorting to expensive algebraic solving methods. In addition to the basic ideas of the approach, an incremental solving algorithm, two methods for solution selection, and a method for mapping constraints on 3D primitives to constraints on points are presented.

Reference frames, superselection rules, and quantum information

Recently, there has been much interest in a new kind of ``unspeakable'' quantum information that stands to regular quantum information in the same way that a direction in space or a moment in time stands to a classical bit string: the former can only be encoded using particular degrees of freedom while the latter are indifferent to the physical nature of the information carriers. The problem of correlating distant reference frames, of which aligning Cartesian axes and synchronizing clocks are important instances, is an example of a task that requires the exchange of unspeakable information and for which it is interesting to determine the fundamental quantum limit of efficiency. There have also been many investigations into the information theory that is appropriate for parties that lack reference frames or that lack correlation between their reference frames, restrictions that result in global and local superselection rules. In the presence of these, quantum unspeakable information becomes a new kind of resource that can be manipulated, depleted, quantified, etc. Methods have also been developed to contend with these restrictions using relational encodings, particularly in the context of computation, cryptography, communication, and the manipulation of entanglement. This paper reviews the role of reference frames and superselection rules in the theory of quantum-information processing.

Non-singlet Q-deformed N=(1,0) and N=(1,1/2) U(1) actions

Abstract In this Letter we construct N = ( 1 , 0 ) and N = ( 1 , 1 / 2 ) non-singlet Q-deformed supersymmetric U ( 1 ) actions in components. We obtain an exact expression for the enhanced supersymmetry action by turning off particular degrees of freedom of the deformation tensor. We analyze the behavior of the action upon restoring weekly some of the deformation parameters, obtaining a non-trivial interaction term between a scalar and the gauge field, breaking the supersymmetry down to N = ( 1 , 0 ) . Additionally, we present the corresponding set of unbroken supersymmetry transformations. We work in harmonic superspace in four Euclidean dimensions.

Conformational changes in glycine tri- and hexapeptide

We have investigated the potential energy surfaces for glycine chains consisting of three and six amino acids. For these molecules we have calculated potential energy surfaces as a function of the Ramachandran angles ϕ and ψ, which are widely used for the characterization of the polypeptide chains. These particular degrees of freedom are essential for the characterization of proteins folding process. Calculations have been carried out within ab initio theoretical framework based on the density functional theory and accounting for all the electrons in the system. We have determined stable conformations and calculated the energy barriers for transitions between them. Using a thermodynamic approach, we have estimated the times of the characteristic transitions between these conformations. The results of our calculations have been compared with those obtained by other theoretical methods and with the available experimental data extracted from the Protein Data Base. This comparison demonstrates a reasonable correspondence of the most prominent minima on the calculated potential energy surfaces to the experimentally measured angles ϕ and ψ for the glycine chains appearing in native proteins. We have also investigated the influence of the secondary structure of polypeptide chains on the formation of the potential energy landscape. This analysis has been performed for the sheet and the helix conformations of chains of six amino acids.

Ab initiostudy of alanine polypeptide chain twisting

We have investigated the potential energy surfaces for alanine chains consisting of three and six amino acids. For these molecules we have calculated potential energy surfaces as a function of the Ramachandran angles and , which are widely used for the characterization of the polypeptide chains. These particular degrees of freedom are essential for the characterization of the proteins folding process. Calculations have been carried out within the ab initio theoretical framework based on the density functional theory and accounting for all the electrons in the system. We have determined stable conformations and calculated the energy barriers for transitions between them. Using a thermodynamic approach, we have estimated the times of characteristic transitions between these conformations. The results of our calculations have been compared with those obtained by other theoretical methods and with the available experimental data extracted from the Protein Data Base. This comparison demonstrates a reasonable correspondence of the most prominent minima on the calculated potential energy surfaces to the experimentally measured angles and for alanine chains appearing in native proteins. We have also investigated the influence of the secondary structure of polypeptide chains on the formation of the potential energy landscape. This analysis has been performed for the sheet and the helix conformations of chains of six amino acids.

An extended Weyl-Wigner transformation for special finite spaces

Abstract We extend the Weyl-Wigner transformation to those particular degrees of freedom described by a finite number of states using a technique of constructing operator bases developed by Schwinger. Discrete transformation kernels are presented instead of continuous coordinate-momentum pair system and systems such as the one-dimensional canonical continuous coordinate-momentum pair system and the two-dimensional rotation system are described by special limits. Expressions are explicitly given for the spin one-half case.