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Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.
I examine the role of entropy in the transition from incoherence to phase synchronisation in the Kuramoto model of N coupled phase oscillators on a general undirected network. In a Hamiltonian ‘action-angle’ formulation, auxiliary variables J{sub i} combine with the phases θ{sub i} to determine a conserved system with a 2N dimensional phase space. In the vicinity of the fixed point for phase synchronisation, θ{sub i}≈θ{sub j}, which is known to be stable, the auxiliary variables J{sub i} exhibit instability. This manifests Liouville’s Theorem in the phase synchronised regime in that contraction in the θ{sub i} parts of phase space are compensated for by expansion in the auxiliary dimensions. I formulate an entropy rate based on the projection of the J{sub i} onto eigenvectors of the graph Laplacian that satisfies Pesin’s Theorem. This leads to the insight that the evolution to phase synchronisation of the Kuramoto model is equivalent to the approach to a state of monotonically increasing entropy. Indeed, for unequal intrinsic frequencies on the nodes, the networks that achieve the closest to exact phase synchronisation are those which enjoy the highest entropy production. I compare numerical results for a range of networks.
Deterministic transport simulations for national-security and energy applications often operate in high-dimensional phase-space, where accuracy and cost both become major challenges. A common numerical artifact in such problems is the “ray-effect,” which appears as unphysical streaks. Beyond misinterpretation, these artifacts can contaminate tightly coupled physics, such as fluid dynamics, radiation-hydrodynamics, and laser-plasma interactions, eroding the predictive capability of entire multiphysics workflows. Our objective was to make high-dimension studies practical on modern hardware while mitigating the ray-effect without relying on prohibitively expensive sampling approaches such as Monte Carlo methods. We developed the Generic Discretization Library (GenDiL), a Graphics Processing Unit (GPU)-first framework that uses high-order Discontinuous Galerkin (DG) methods and matrix-free algorithms to reduce memory usage and improve computational efficiency, critical for phase-space simulations. GenDiL supports phase-space adaptivity in both mesh size and polynomial order (hp-adaptivity) to place resolution only where it is needed. A central capability is Local Dimensional Refinement (LDR), which couples lower-dimension continuum models to higher-dimension kinetic models through stable and conservative interfaces, so that high-fidelity physics is applied only in regions where it is essential. Building on the GenDiL framework, we developed the General SN (GSN) family of algorithms as a true generalization of the polar SN approach (discrete ordinates, often denoted SN). Rather than tying discrete ordinates to a specific polar change of coordinates, GSN formulates transport on an arbitrary change of coordinates chosen to reduce ray-effect. We studied two complementary variants: an analytic variant, where the coordinate map is prescribed in advance by a closed-form function; and a data-driven variant, where a quantity of interest, such as the net flux, guides the coordinate system. GenDiL provides the library infrastructure for efficient GPU execution, but the GSN concept is algorithmic and independent of any one library. Across representative high-dimension tests, including non-symmetric solutions, both variants delivered strong ray-effect mitigation at practical cost, moving four- to six-dimensional analysis toward repeatable, routine studies.
We systematically investigate the assembly of binary multi-flavored colloidal mixtures in two dimensions. In these mixtures all pairwise interactions between species may be tuned independently. This introduces an additional degree of freedom over more traditional binary mixtures with fixed mixing rules, which is anticipated to open new avenues for directed self-assembly. At present, colloidal self-assembly into non-trivial lattices tends to require either high pressures for isotropically interacting particles, or the introduction of directionally anisotropic interactions. Here we demonstrate tunable assembly into a plethora of structures which requires neither of these conditions. We develop a minimal model that defines a three-dimensional phase space containing one dimension for each pairwise interaction, then employ various computational techniques to map out regions of this phase space in which the system self-assembles into these different morphologies. We then present a mean-field model that is capable of reproducing these results for size-symmetric mixtures, which reveals how to target different structures by tuning pairwise interactions, solution stoichiometry, or both. Concerning particle size asymmetry, we find that domains in this model's phase space, corresponding to different morphologies, tend to undergo a continuous “rotation” whose magnitude is proportional to the size asymmetry. Such continuity enables one to estimate the relative stability of different lattices for arbitrary size asymmetries. Owing to its simplicity and accuracy, we expect this model to serve as a valuable design tool for engineering binary colloidal crystals from multi-flavored components.
The role of phase space occupation effects for the formation of twoand three-particle bound states in a dense medium is investigated within an algebraic approach suitable for systems with short-range interactions. It is shown that for two-fermion bound states due to the account of the exchange symmetry (phase space occupation) effect (Pauli blocking) in a dense medium the binding energy is reduced and vanishes at a critical density (Mott effect). For three-fermion bound states, within a Faddeev equation approach, the intermediate formation of pair correlations leads to the representation as a suitably symmetrized fermion-boson bound state. It is shown that the Bose enhancement of fermion pairs can partially compensate the Pauli blocking between the fermions. This leads to the general result obtained by algebraic methods: three-fermion bound states in a medium with high phase space occupation appear necessarily as Borromean states beyond the Mott density of the two-fermion bound state.
We analyze the transverse momentum (p T ) and rapidity (y) spectra of top quark pairs, hadronic top quarks, and top quarks produced in proton-proton (pp) collisions at center-of-mass energy $\sqrt{s}=8$ TeV. For ${p}_{{\rm{T}}}$ spectra, we use the superposition of the inverse power-law suggested by the QCD (quantum chromodynamics) calculus and the Erlang distribution resulting from a multisource thermal model. For y spectra, we use the two-component Gaussian function resulting from the revised Landau hydrodynamic model. The modelling results are in agreement with the experimental data measured at the detector level, in the fiducial phase-space, and in the full phase-space by the ATLAS Collaboration at the Large Hadron Collider (LHC). Based on the parameter values extracted from p T and y spectra, the event patterns in three-dimensional velocity (β x -β y -β z ), momentum (p x -p y -p z ), and rapidity (y 1 -y 2 -y) spaces are obtained, and the probability distributions of these components are also obtained.
The applicability of Navier–Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman–Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. Finally, I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics.
Purpose: egs-brachy is a fast, new EGSnrc user-code for brachytherapy applications. This study characterizes egs-brachy features that enhance simulation efficiency. Methods: Calculations are performed to characterize efficiency gains from various features. Simulations include radionuclide and miniature x-ray tube sources in water phantoms and idealized prostate, breast, and eye plaque treatments. Features characterized include voxel indexing of sources to reduce boundary checks during radiation transport, scoring collision kerma via tracklength estimator, recycling photons emitted from sources, and using phase space data to initiate simulations. Bremsstrahlung cross section enhancement (BCSE), uniform bremsstrahlung splitting (UBS), and Russian Roulette (RR) are considered for electronic brachytherapy. Results: Efficiency is enhanced by a factor of up to 300 using tracklength versus interaction scoring of collision kerma and by up to 2.7 and 2.6 using phase space sources and particle recycling respectively compared to simulations in which particles are initiated within sources. On a single 2.5 GHz Intel Xeon E5-2680 processor cor, simulations approximating prostate and breast permanent implant ((2 mm){sup 3} voxels) and eye plaque ((1 mm){sup 3}) treatments take as little as 9 s (prostate, eye) and up to 31 s (breast) to achieve 2% statistical uncertainty on doses within the PTV. For electronic brachytherapy, BCSE, UBS, and RR enhance efficiency by a factor >2000 compared to a factor of >10{sup 4} using a phase space source. Conclusion: egs-brachy features provide substantial efficiency gains, resulting in calculation times sufficiently fast for full Monte Carlo simulations for routine brachytherapy treatment planning.
We investigate phonon transport in dicalcium nitride (Ca 2 N), an electride with two-dimensional confined electron layers, using first-principles density functional theory and the phonon Boltzmann transport equation. The in-plane (κ[100]) and out-of-plane (κ[001]) lattice thermal conductivities at 300 K are found to be 11.72 W m -1 K -1 and 2.50 W m -1 K -1 , respectively. Spectral analysis of lattice thermal conductivity shows that ~85% of $κ_{[100]}$ and $κ_{[001]}$ is accumulated by phonons with frequencies less than 5.5 THz and 2.5 THz, respectively. Modal decomposition of lattice thermal conductivity further reveals that the optical phonons contribute to ~68% and ~55% of overall $κ_{[100]}$ and $κ_{[001]}$, respectively. Phonon dispersion suggests that the large optical phonon contribution is a result of low frequency optical phonons with high group velocities and the lack of phonon bandgap between the acoustic and optical phonon branches. We find that the optical phonons with frequencies below ~5.5 THz have similar three-phonon phase space and scattering rates as acoustic phonons. Comparison of the contributions from emission and absorption processes reveals that the three-phonon phase space and scattering rates of phonons—optical or acoustic—with frequencies below 5.5 THz are largely dominated by absorption processes. We conclude that the large contribution to lattice thermal conductivity by optical phonons is due to the presence of multiple low frequency optical phonon modes with high group velocities and similar phase space and scattering rates as the acoustic phonons. This study provides the frequency and temperature dependent lattice thermal conductivity and insights into phonon transport in Ca 2 N, both of which have important implications for the development of Ca 2 N based devices.
GaGeTe is a layered van der Waals material composed of germanene and GaTe sublayers that has been recently predicted to be a basic Z 2 topological semimetal. To date, only one polytype of GaGeTe is known with trigonal centrosymmetric structure (α phase, space group R-3m, No. 166). Here we show that as-grown samples of GaGeTe show traces of at least another polytype with hexagonal non-centrosymmetric structure (β phase, space group P6 3 mc, No. 186). Moreover, we suggest that another bulk hexagonal polytype (γ phase, space group P-3m1, No. 164) could also be found near room conditions. Both α and β polytypes have been identified and characterized by means of X-ray diffraction and Raman scattering measurements with the support of ab initio calculations. We provide the vibrational properties of both polytypes and show that the Raman spectrum reported for GaGeTe almost forty years ago and attributed to the α phase, was, in fact, that of the secondary β phase. Additionally, we show that a Fermi resonance occurs in α-GaGeTe under non-resonant excitation conditions, but not under resonant excitation conditions. Theoretical calculations show that bulk β-GaGeTe is a non-centrosymmetric weak topological semimetal with even smaller lattice thermal conductivity than centrosymmetric bulk α-GaGeTe. In perspective, our work paves the way for the control and engineering of GaGeTe polytypes to design and implement complex van der Waals heterostructures formed by a combination of centrosymmetric and non-centrosymmetric layers of up to three different polytypes in a single material, suitable for a number of fundamental studies and technological applications.
Monte Carlo simulations are an essential tool in particle physics data analysis. Events are typically generated alongside weights that redistribute the cross section of the simulated process across the phase space. These weights can be negative, and several post hoc methods have been developed to eliminate or mitigate the negative values. All of these methods share the common strategy of approximating the average weight as a function of phase space. We introduce an alternative approach, which, instead of reweighting to the average, refines the initial weights with a scaling transformation, utilizing a phase space-dependent factor. Since this new refinement method does not need to model the full weight distribution, it can be more accurate. High-dimensional and unbinned phase space is processed using neural networks for the refinement method. In addition to the refinement method, we introduce a new resampling protocol, which can be used in conjunction with any weight transformation to not only preserve the average weight but also the statistical uncertainties of the initial distribution. Using both realistic and synthetic examples, we show that the new neural refinement method is able to match or exceed the accuracy of similar weight transformations and that the new resampling protocol is simpler in implementation than previous methods while exhibiting equivalent statistical properties.
Gottesman-Kitaev-Preskill (GKP) codes encode a qubit in displaced phase-space combs of a continuous-variable (CV) quantum system and are useful for correcting a variety of high-weight photonic errors. Here we propose atomic ensemble analogs of the single-mode CV GKP code by using the quantum central limit theorem to pull back the phase-space structure of a CV system to the compact phase space of a quantum spin system. We study the optimal recovery performance of these codes under error channels described by stochastic relaxation and isotropic ballistic dephasing processes using the diversity combining approach for calculating channel fidelity. Additionally, we find that the spin GKP codes outperform other spin system codes such as cat codes or binomial codes. Our spin GKP codes based on the two-axis countertwisting interaction and superpositions of SU(2) coherent states are direct spin analogs of the finite-energy CV GKP codes, whereas our codes based on one-axis twisting do not yet have well-studied CV analogs. A state preparation scheme for the spin GKP codes is proposed which uses the linear-combination-of-unitaries method, applicable to both the CV and spin GKP settings. Finally, we discuss a fault-tolerant approximate gate set for quantum computing with spin-GKP-encoded qubits, obtained by translating gates from the CV GKP setting using the quantum central limit theorem.
The AC susceptibilities of Fe{sub 1−x}Co{sub x}Si (0.1 ≤ x ≤ 0.7) alloys were measured and compared with that of MnSi. The range of skyrmion phase in the H-T phase space was enlarged and moved to higher temperatures when approximately 1/3 of the Fe was substituted with Co. Comparing with MnSi, the skyrmion phase of Fe{sub 0.7}Co{sub 0.3}Si was found thermodynamically more stable under a much lower and narrower critical field near 280 ± 50 Oe. The stability range in the H-T phase space and the free energy reduction ΔE (as a function of the applied magnetic field) for both the Fe{sub 0.7}Co{sub 0.3}Si and MnSi were compared.
Work over the last several years has demonstrated the impressive performance gains that can be attained by using Moment-Based Acceleration (MBA), or High-Order/Low-Order (HOLO), methods in a variety of transport applications. In the field of neutronics, Nonlinear Diffusion Acceleration (NDA) has been used to accelerate the solution to the fixed-source problem and the k-eigenvalue problem. These methods efficiently move a major portion of the computational work out of the full phase-space (high-order (HO)) domain into a reduced phase-space (low-order (LO)) setting. In previous implementations, NDA has only been applied to isotropic scattering problems. In this paper, we will extend this methodology to anisotropic scattering. This initial work on anisotropic scattering will focus on the 1-D multi-group neutron transport equation. This summary focuses on a fixed-source problem, but the extension to criticality problems is straight-forward via NDA-NCA. Within this paper, we have described a method for extending Nonlinear Diffusion Acceleration to solve problems with anisotropic scattering. We demonstrated that a consistent low-order system, resembling the low-order system from, could be constructed. We demonstrated that the NDA method performed exceptionally in the presence of anisotropic scattering. NDA reduced the number of iterations required to meet the convergence tolerance by a factor of 500 over source iteration for a one fixed-source problem and by 3.5-50 x for the Henyey-Greenstein problems. This method is equally well-suited for eigenvalue problems. The NDA method allows us to transition the eigenvalue iteration to the low-order domain.
Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman–von Neumann formulation of classical mechanics. The Koopman–von Neumann formulation implies that the conservation of the probability distribution function on phase space, as expressed by the Liouville equation, can be recast as an equivalent Schrödinger equation on Hilbert space with a Hermitian Hamiltonian operator and a unitary propagator. This Schrödinger equation is linear in the momenta because it derives from a constrained Hamiltonian system with twice the classical phase-space dimension. A quantum computer with finite resources can be used to simulate a finite-dimensional approximation of this unitary evolution operator. Quantum simulation of classical dynamics is exponentially more efficient than a deterministic Eulerian discretization of the Liouville equation if the Koopman–von Neumann Hamiltonian is sparse. Utilizing quantum walk techniques for state preparation and amplitude estimation for the calculation of observables leads to a quadratic improvement over classical probabilistic Monte Carlo algorithms.
Diffraction Enhanced Imaging (DEI) or Analyzer Based Imaging (ABI) uses a perfect crystal monochromator and matching analyzer to achieve sensitivity to x-ray refraction and ultra small-angle scattering on the order of 0.01 micro-radians. As such, a thermal bump caused by heat-load in the order of 1 W is detrimental. The heat load at the HEX (High Energy Engineering X-ray) super-conducting wiggler (SCW) beamline, under construction at the NSLS-II, is on the order of 1 kW. How to reconcile the three orders of magnitude difference between the HEX source power and the DEI/ABI requirements? The solution involves using a double-crystal bent-Laue monochromator as pre-monochromator to prepare a beam with a large divergence and bandwidth that is matched to a flat crystal post-monochromator. We show through phase-space (x-ray energy vs. angle as viewed by a flat crystal) analysis and Dumond diagrams that there is indeed a unique bending radius that matches the double-crystal bent-Laue monochromator in phase space to the flat Bragg crystal. The matched system has a desirable feature that the phase space of the bent crystal’s output beam is much larger than that of the flat crystal, making the combined system stable. Based on these considerations, here we present our optical design for performing DEI/ABI at the HEX beamline
Energetic particle effects in magnetic confinement fusion devices are commonly studied by hybrid kinetic-fluid simulation codes whose underlying continuum evolution equations often lack the correct energy balance. While two different kinetic-fluid coupling options are available (current coupling and pressure coupling), this paper applies the Euler–Poincaré variational approach to formulate a new conservative hybrid model in the pressure-coupling scheme. In our case the kinetics of the energetic particles are described by guiding center theory. The interplay between the Lagrangian fluid paths and phase space particle trajectories reflects an intricate variational structure which can be approached by letting the four-dimensional guiding center trajectories evolve in the full six-dimensional phase space. Then, the redundant perpendicular velocity is integrated out to recover a four-dimensional description. A second equivalent variational approach is also reported, which involves the use of phase space Lagrangians. Not only do these variational structures confer on the new model a correct energy balance, but also they produce a cross-helicity invariant which is lost in the other pressure-coupling schemes reported in the literature.
Context. Open clusters (OCs) are fundamental benchmarks where theories of star formation and stellar evolution can be tested and validated. Coma Berenices (Coma Ber) and Latyshev 2 (Group X) are the second and third OCs closest to the Sun, making them excellent targets to search for low-mass stars and ultra-cool dwarfs. In addition, this pair will experience a flyby in 10–16 Myr, making it a benchmark to test pair interactions of OCs. Aims. We aim to analyse the membership, luminosity, mass, phase-space (i.e. positions and velocities), and energy distributions for Coma Ber and Latyshev 2 and test the hypothesis of the mixing of their populations at the encounter time. Methods. We developed a new phase-space membership methodology and applied it to Gaia data. With the recovered members, we inferred the phase-space, luminosity, and mass distributions using publicly available Bayesian inference codes. Then, with a publicly available orbit integration code and members’ positions and velocities, we integrated their orbits 20 Myr into the future. Results. In Coma Ber, we identified 302 candidate members distributed in the core and tidal tails. The tails are dynamically cold and asymmetrically populated. The stellar system called Group X is made of two structures: the disrupted OC Latyshev 2 (186 candidate members) and a loose stellar association called Mecayotl 1 (146 candidate members), and both of them will fly by Coma Ber in 11.3 ± 0.5 Myr and 14.0 ± 0.6 Myr, respectively, and each other in 8.1 ± 1.3 Myr. Conclusions. We study the dynamical properties of the core and tails of Coma Ber and also confirm the existence of the OC Latyshev 2 and its neighbour stellar association Mecayotl 1. Although these three systems will experience encounters, we find no evidence supporting the mixing of their populations.