Space Distribution Research Articles

High-dimensional maximum-entropy phase space tomography using normalizing flows

Particle accelerators generate charged-particle beams with tailored distributions in six-dimensional position-momentum space (phase space). Knowledge of the phase space distribution enables model-based beam optimization and control. In the absence of direct measurements, the distribution must be tomographically reconstructed from its projections. In this paper, we highlight that such problems can be severely underdetermined and that entropy maximization is the most conservative solution strategy. We leverage —invertible generative models—to extend maximum-entropy tomography to six-dimensional phase space and perform numerical experiments to validate the model's performance. Our numerical experiments demonstrate consistency with exact two-dimensional maximum-entropy solutions and the ability to fit complicated six-dimensional distributions to large measurement sets in reasonable time. Published by the American Physical Society 2024

Universal vortex statistics and stochastic geometry of Bose-Einstein condensation

The cooling of a Bose gas in finite time results in the formation of a Bose-Einstein condensate that is spontaneously proliferated with vortices. We propose that the vortex spatial statistics is described by a homogeneous Poisson point process (PPP) with a density dictated by the Kibble-Zurek mechanism (KZM). We validate this model using numerical simulations of the two-dimensional stochastic Gross-Pitaevskii equation (SGPE) for both a homogeneous and a hard-wall trapped condensate. The KZM scaling of the average vortex number with the cooling rate is established along with the universal character of the vortex number distribution. The spatial statistics between vortices is characterized by analyzing the two-point defect-defect correlation function, the corresponding spacing distributions, and the random tessellation of the vortex pattern using the Voronoi cell area statistics. Combining the PPP description with the KZM, we derive universal theoretical predictions for each of these quantities and find them in agreement with the SGPE simulations. Our results establish the universal character of the spatial statistics of point-like topological defects generated during a continuous phase transition and the associated stochastic geometry. Published by the American Physical Society 2024

Climate disasters and the difficult human/nature relationship

Environmental disasters are concrete examples of the difficult coexistence between man and nature and expose the fragility of ecosystems and the urgent need to rethink the development model of contemporary society. With a socio-political approach, the text analyses the relationship between man and nature and the environmental tragedies caused by global warming, denouncing the development process of industrialised societies and questioning the environment destroyed by the diversity of human actions. It discusses extreme weather events that have resulted in major environmental disasters, both in Brazil and in other countries, and provides quantitative data on the victims of these disasters. It reveals the unequal distribution of income and space that exposes the most vulnerable populations to the rigours of climate change and argues that man's predatory relationship with nature is the driving force behind environmental degradation and is based on the unethical interests of the market. He concludes on the importance of urban planning, the projection of more humane spaces and obedience to environmental protection laws.

Distributions of Consecutive Level Spacings of Gaussian Unitary Ensemble and Their Ratio: ab initio Derivation

Abstract In recent studies of many-body localization in nonintegrable quantum systems, the distribution of the ratio of two consecutive energy level spacings, $r_n=(E_{n+1}-E_n)/(E_{n}-E_{n-1})$ or $\tilde{r}_n=\min (r_n,r_n^{-1})$, has been used as a measure to quantify the chaoticity, alternative to the more conventional distribution of the level spacings, $s_n=\bar{\rho }(E_n)(E_{n+1}-E_n)$, as the former makes unnecessary the unfolding required for the latter. Based on our previous work on the Tracy–Widom approach to the Jánossy densities, we present analytic expressions for the joint probability distribution of two consecutive eigenvalue spacings and the distribution of their ratio for the Gaussian unitary ensemble (GUE) of random Hermitian $N\times N$ matrices at $N\rightarrow \infty$, in terms of a system of differential equations. As a showcase of the efficacy of our results for characterizing an approach to quantum chaoticity, we contrast them to arguably the most ideal of all quantum-chaotic spectra: the zeroes of the Riemann $\zeta$ function on the critical line at increasing heights.

Photonic cellular automaton simulation of relativistic quantum fields: Observation of Zitterbewegung

Quantum cellular automaton (QCA) is a model for universal quantum computation and a natural candidate for digital quantum simulation of relativistic quantum fields. Here we introduce the first photonic platform for implementing QCA simulation of a free relativistic Dirac quantum field in 1+1 dimension, through a Dirac quantum cellular automaton (DQCA). Encoding the field position degree of freedom in the orbital angular momentum (OAM) of single photons, our state-of-the-art setup experimentally realizes eight steps of a DQCA, with the possibility of having complete control over the input OAM state preparation and the output measurement making use of two spatial light modulators. Therefore, studying the distribution in the OAM space at each step, we were able to reproduce the time evolution of the free Dirac field observing the , an oscillatory movement extremely difficult to see in a real-case experimental scenario that is a signature of the interference of particle and antiparticle states. The accordance between the expected and measured oscillations certifies the simulator performances, paving the way towards the application of photonic platforms to the simulation of more complex relativistic effects. Published by the American Physical Society 2024

Spatiotemporal Evolution and Driving Forces of Production-Living-Ecological Space in Arid Ecological Transition Zone Based on Functional and Structural Perspectives: A Case Study of the Hexi Corridor

The rational allocation of land resources is crucial to ensuring human well-being, livelihood, and survival. The study of Production-Living-Ecological Space (PLES) provides new perspectives on land resource allocation. However, few studies have assessed the feasibility of PLES optimization in ecological transition zones. For this study, using the composite functional space classification method, a classification and functional utility scoring system were constructed. Various methods, including dynamic attitude, transfer matrix, and spatial autocorrelation, were employed to characterize the evolution of the quantity and quality of PLES in the Hexi Corridor. Moreover, the mechanisms driving these changes were explored using a geodetector. Our findings revealed that: (1) The distribution of Production-Ecological Space (PES) is higher in the west and south and lower in the east and north. Production-Living Space (PLS) is scattered. Ecological-Production Space (EPS) is mostly distributed in the south or west, whereas Ecological Space (ES) is mainly located in the north and west of the Hexi Corridor. (2) From 1980 to 2020, the area of PES and PLS increased by 2037.84 km2 and 673 km2, respectively; the area of EPS was relatively stable, and the area of ES decreased by 2523.06 km2. (3) The evolution of PLES quality indicated that the high functional utility area of PES and PLS was roughly the same as the expanded functional utility area, whereas the expanded functional utility area of EPS and ES is similar to the median functional utility area. (4) The spatiotemporal evolution of PLES is closely linked to natural, economic, and social factors.

Laser-Tracing Multi-Station Measurements in a Non-Uniform-Temperature Field

Due to the increasing requirements for the improvement of the accuracy of large coordinate-measuring machines (CMMs), the laser-tracing multi-station measurement technology, as one of the advanced precision measurement technologies, is worth studying in depth in terms of its practical application for the compensation of errors in large CMMs. Since it is difficult to maintain a constant temperature of about 20 °C in the actual workshop under the influence of solar radiation and convective heat transfer, there is a gradient in the spatial temperature distribution, and the overall temperature changes with the influence of external factors with synchronous hysteresis, it is difficult for the actual calibration environment to meet the standard environmental requirements. Therefore, the influence of temperature and other environmental factors on the accuracy of laser ranging and large-scale CMM calibration should not be ignored. In this paper, on the basis of analyzing the temperature distribution and change rule of large CMM measurement space under different working conditions, the radial basis function (RBF) neural network algorithm was used to build a non-uniform-temperature field model, and based on this model and the measurement principle of the laser-tracking instrument, the method of laser tracking and interferometric ranging accuracy enhancement was put forward under a non-uniform-temperature field. Finally, based on the multi-station technique of laser tracing, an accurate solution for the volumetric error of large CMMs under the condition of non −20 °C ambient temperature was realized. Simulation results proved that compared with the traditional temperature-compensation method, the proposed method improved the measurement accuracy of the volumetric error of a large-scale CMM using laser-tracing multi-station technology in a non-uniform-temperature field by 33.5%. This study provides a new approach for improving the accuracy of laser-tracer multi-station measurement systems.

The influence of biophysical characteristics on elephant space use in an African savanna

Understanding the influence of biophysical variables on spatial distribution and seasonal locations of elephants is valuable inter alia in understanding their movement patterns, and the carrying capacity to optimise the conservation of their habitats. Furthermore, understanding elephant distribution in time and space is beneficial for predicting locations for tourist viewing and determining potential areas of human–wildlife conflicts. In this study, we examined the environmental drivers of seasonal variations in elephant ranges and movement using telemetry data. Using the elephant tracking data and biophysical characteristics, the Adaptive-Local Convex Hull (a-LoCoH) and the Maximum Entropy Modelling (MaxEnt) algorithm were adopted to determine their potential locations and distribution in a protected area. The jackknife approach was used to assess the environmental factors influencing seasonal elephant movements based on collar data from ten individual elephants tracked between December 2015 and April 2018. The performance of the elephant distribution models for the two seasons was assessed using the area under the curve from the receiver operating characteristic based on a 30% test holdout data. Results showed that the core a-LoCoH home of elephants was larger in the dry than wet season (Wilcoxon signed-rank test; W = 3, Z = 2.4973, p < 0.012). However, no noticeable differences were observed (Wilcoxon signed-rank test; W = 10, Z = 1.7838, p < 0.07) between the dry and wet season for the total (90%) a-LoCoH ranges. The MaxEnt modelling results showed that distance to the artificial water holes was the most influential variable in predicting the potential elephant spatial distribution in both wet and dry seasons, while the normalised difference vegetation index, a proxy for forage availability, was more influential in the dry season in predicting elephant distribution. The study concludes that seasonal elephant space use is mostly influenced by water availability in both seasons, while forage availability and variability influence elephant distribution more strongly in the dry than wet season. The study provides valuable insight into the biophysical characteristics of elephant home ranges. This is useful for the sustainable management of elephants and their habitats.

Anomalous quantum transport in fractal lattices

Fractal lattices are self-similar structures with repeated patterns on different scales. Quantum transport through such structures is subtle due to the possible co-existence of localized and extended states. Here, we study the dynamical properties of two fractal lattices, the Sierpiński gasket and the Sierpiński carpet. While the gasket exhibits sub-diffusive behavior, sub-ballistic transport occurs in the carpet. We show that the different dynamical behavior is in line with qualitative differences of the systems’ spectral properties. Specifically, in contrast to the Sierpiński carpet, the Sierpiński gasket exhibits an inverse power-law behavior of the level spacing distribution. As a possible technological application, we discuss a memory effect in the Sierpiński gasket which allows to read off the phase information of an initial state from the spatial distribution after long evolution times. We also show that interpolating between fractal and regular lattices allows for flexible tuning between different transport regimes.

Investigation of the humidity control in the printing space for the material extrusion of medical biodegradable hydrogel

Materials extrusion for medical biodegradable hydrogel manifests potential for the fabrication of biomimetic functionalized tissues in tissue engineering. However, the uncontrollable shape of 3D printed structures usually leads to shrinkage as well as collapse of the prepared biocompatible scaffold, which limits the potential to develop large-size tissue or organs. Uncontrollable ambient humidity during the 3D printing process is a primary cause of the moisture loss and geometric variation of prepared architectures, which means the humidity in the printing space of hydrogel materials must be controlled accurately throughout the extrusion process. This study proposed a novel configuration of humidity-controlled atmospheric enclosure, by which the humidity distribution in the printing space can be accurately regulated. Subsequently, a fluid-thermal-humidity coupling field simulation model based on the finite element method was established to numerically investigate the humidity field in the printing space. Furthermore, printing trials were conducted with the proposed atmospheric enclosure, and the moisture loss of 3D architecture was avoided. The size of the scaffold was improved evidently from 25 mm(length) × 25 mm(width) × 0.6 mm(height) to 25 mm(length) × 25 mm(width) × 3.5 mm(height).

Heating mode transitions in capacitively coupled CF4 plasmas at low pressure

Abstract Capacitively coupled plasmas operated in CF4 at low pressure are frequently used for dielectric plasma etching. For such applications the generation of different ion and neutral radical species by energy dependent electron impact ionization and dissociation of the neutral background gas is important. These processes are largely determined by the space and time dependent electron energy distribution function and, thus, by the electron power absorption dynamics. In this work and based on a particle-in-cell/Monte Carlo collision model, we show that the electron heating mode in such plasmas is sensitive to changes of the gap at a constant pressure of 3 Pa. At a gap of 1.5 cm, the dominant mode is found to be a hybrid combination of the Drift-Ambipolar (DA) and the α-mode. As the gap is increased to 2 cm and 2.5 cm, the bulk power absorption and ambipolar power absorption decreases, and the DA mode decays. When the gap reaches 3 cm, the α-mode becomes more prominent, and at a gap of 3.75 cm the α-mode is dominant. These mode transitions are caused by a change of the electronegativity and are found to affect the discharge characteristics. The presence of the DA-mode leads to significant positive electron power absorption inside the bulk region and negative power absorption within the sheaths on time average, as electrons are accelerated from the bulk towards the collapsed sheath. The heating mode transitions result in a change from negative to positive total electron power absorption within the sheaths as the gap increases. When accounting for secondary electron emission, the transition of the heating mode can occur at shorter gaps due to the enhanced plasma density and decreased electronegativity.

Intermediate spectral statistics of rational triangular quantum billiards.

Triangular billiards whose angles are rational multiples of π are one of the simplest examples of pseudo-integrable models with intriguing classical and quantum properties. We perform an extensive numerical study of spectral statistics of eight quantized rational triangles, six belonging to the family of right-angled Veech triangles and two obtuse rational triangles. Large spectral samples of up to one million energy levels were calculated for each triangle, which permits one to determine their spectral statistics with great accuracy. It is demonstrated that they are of the intermediate type, sharing some features with chaotic systems, like level repulsion, and some with integrable systems, like exponential tails of the level spacing distributions. Another distinctive feature of intermediate spectral statistics is a finite value of the level compressibility. The short-range statistics such as the level spacing distributions, and long-range statistics such as the number variance and spectral form factors were analyzed in detail. An excellent agreement between the numerical data and the model of gamma distributions is revealed.

Two mass-imbalanced atoms in a hard-wall trap: Deep learning integrability of many-body systems.

The study of integrable systems has led to significant advancements in our understanding of many-body physics. We design a series of numerical experiments to analyze the integrability of a mass-imbalanced two-body system through energy-level statistics and deep learning of wave functions. The level spacing distributions are fitted by a Brody distribution and the fitting parameter ω is found to separate the integrable and nonintegrable mass ratios by a critical line ω=0. The convolutional neural network built from the probability density images could identify the transition points between integrable and nonintegrable systems with high accuracy, yet in a much shorter computation time. A brilliant example of the network's ability is to identify a new integrable mass ratio 1/3 by learning from the known integrable case of equal mass, with a remarkable network confidence of 98.22%. The robustness of our neural networks is further enhanced by adversarial learning, where samples are generated by standard and quantum perturbations mixed in the probability density images and the wave functions, respectively.

Unified bi-encoder bispace-discriminator disentanglement for cross-domain echocardiography segmentation

Disentanglement-based methods effectively facilitate domain-invariant feature learning in Unsupervised Domain Adaptation (UDA) by leveraging complementary domain-specific information relating to statistical distribution differences. However, in scenarios involving cross-domain echocardiography, spectral information is important for determining distribution differences. Existing disentanglement-based methods overlook these spectral differences, resulting in insufficient learning of domain-specific features and unreliable domain-invariant feature disentanglement across different medical centers (domains). In addition, aligning the global marginal distribution in cross-domain disentanglement results in spatially misaligned semantics in domain-invariant features at the pixel level, which hinders robust UDA segmentation. We advance disentanglement learning by designing a novel unified bi-encoder bispace-discriminator disentanglement network (UB2D-Net) to disentangle reliable domain-invariant features and adapt the pixel-level aligned semantics preserved therein, thereby achieving robust cross-domain echocardiography segmentation. A space distribution constraint loss is designed to incorporate bispace (spatial and spectral) knowledge into the unified bi-encoder disentanglement path to promote the learning of sufficient domain-specific features in disentanglement. Furthermore, we leverage the confidence-aware weight, which is a novel form of the spatial attention mechanism, to transfer the pixel-level aligned semantics preserved in UDA for the spatial consistency-guided segmentation. We validated our UB2D-Net for cross-domain left ventricular segmentation on two public echocardiography datasets. Extensive comparison and ablation experiments of UDA segmentation in either CAMUS → EchoNet-Dynamic or EchoNet-Dynamic → CAMUS tasks demonstrated that our method outperformed strong state-of-the-art algorithms.

Results of cement-augmented pedicle screw surgery in the treatment of thoracic and lumbar spine collapse in severe osteoporosis patients

Objective: This 2023 study aimed to assess pain relief, functional recovery, and kyphosis correction following pedicle screw surgery with cement augmentation in severe osteoporosis patients with vertebral collapse. Methods: Seventy-one patients underwent surgery and were evaluated for postoperative pain reduction (VAS score), functional improvement (ODI score), vertebral kyphosis angle, pre- and postoperative spinal curvature angles, and complications. Results: The study included 71 participants (13 males, 58 females; mean age 67.6±6.7 years). Trauma sources included falls (47.9%), heavy lifting (17%), and unclear mechanisms (35.2%). Mean hospital stay was 12±6.5 days. Preoperative, postoperative, and 1/6-month VAS scores were 8.7, 2.2, 1.5, 0.9 respectively (p&lt;0.001). ODI scores were 77.6, 52.8, 43.0, 37.9 respectively (p&lt;0.001). Kyphotic angle (vertebral body) decreased from preop 12.9° to postop 9.9°, 1/6 months 10.1° (p&lt;0.001); at surgical site, preop 15.4° to 1/6 months 11.9° (p&lt;0.001). Cement leakage occurred in 36.6% of cases, mostly asymptomatic, with distribution in the disc space (2.8%), blood vessels (8.5%), around vertebral body (12.7%), spinal canal (14.1%), and lungs (2.8%). Conclusion: Pedicle screw fixation with enhanced cement augmentation effectively manages severe osteoporotic vertebral compression fractures, providing significant pain relief, improved postoperative function, and spinal alignment. Symptomatic cement leakage is rare.

Beyond Linear Response: Equivalence between Thermodynamic Geometry and Optimal Transport.

A fundamental result of thermodynamic geometry is that the optimal, minimal-work protocol that drives a nonequilibrium system between two thermodynamic states in the slow-driving limit is given by a geodesic of the friction tensor, a Riemannian metric defined on control space. For overdamped dynamics in arbitrary dimensions, we demonstrate that thermodynamic geometry is equivalent to L^{2} optimal transport geometry defined on the space of equilibrium distributions corresponding to the control parameters. We show that obtaining optimal protocols past the slow-driving or linear response regime is computationally tractable as the sum of a friction tensor geodesic and a counterdiabatic term related to the Fisher information metric. These geodesic-counterdiabatic optimal protocols are exact for parametric harmonic potentials, reproduce the surprising nonmonotonic behavior recently discovered in linearly biased double well optimal protocols, and explain the ubiquitous discontinuous jumps observed at the beginning and end times.

Phase space reconstruction technique for beam optimization in the Low Energy High Intensity Proton Accelerator (LEHIPA)

The Low Energy High Intensity Proton Accelerator (LEHIPA) has been commissioned to the design energy of 20 MeV at BARC, India. The low energy beam transport (LEBT) channel of LEHIPA consists of two solenoids and drift spaces for matching the 50 keV proton beam from the ECR ion source (ECR-IS) to the RFQ. The ion beam extracted from the ECR-IS also contains molecular species like H2 + and H3 +. Proton fraction in the beam is found to degrade slowly with time due to surface contamination of the plasma chamber and this reduction in proton beam current has implications for longitudinal and transverse beam dynamics. Hence, it becomes important to characterise the beam at different proton fraction levels to understand the end-to-end beam dynamics of LEHIPA. Computed Tomography (CT) technique has been used for the beam phase-space reconstruction in LEHIPA, using a Python program, incorporating the feature of filtering secondary species from the beam profiles measured using slit scanners in the LEBT. Simultaneous Algebraic Reconstruction Technique (SART) is used in the reconstruction since it is identified to be a better technique for a limited number of projections. The reconstruction program is benchmarked with the TraceWin beam dynamics code and implemented on the measured beam profiles to recreate the phase space distribution at the beginning of LEBT. Further, the tomographic reconstruction method is compared with the solenoid scan method and the rms emittance values are found to be in good agreement. The measured tomographic phase space distribution has then been used as TraceWin input for LEHIPA end-end beam dynamics simulations and the LEHIPA beam line parameters are re-optimized for minimum beam emittance growth. This paper presents the simulations of CT technique, benchmarking simulations with TraceWin, phase space reconstruction with measured beam profiles and beam dynamics studies of LEHIPA using the reconstructed beam distributions.

Analytical Solution to the Steady Navier-Stokes Equation for a Supersonic Cone in the Area of Boundary Layer Behind the Shock Wave by Means Tunnel Mathematics

The means of tunnel mathematics (the theory of functions of a spatial complex variable) allow for an analytical solution to the problem of supersonic flow around a cone in the area of the boundary layer and beyond. The peculiar feature of the Navier-Stokes equations is that they allow for the determination of analytical velocity fields of fluids only for a small number of simple problems. Of course, the problem of the supersonic motion of fluid around a cone is not included in this number. Tunnel mathematics is a method for finding analytical vector velocity fields for steady flows of fluids with axial symmetry. The Navier-Stokes equations are then used to determine pressure and temperature distributions. The main theorem of tunnel mathematics allows for the determination of these distributions for planes z = const (similar to constructing slices of a brain in an MRI procedure). By collecting these “slices,” we can obtain full space distributions of pressure and temperature around a supersonic cone. At this stage of investigation, the conclusions obtained through tunnel mathematics make it possible to qualitatively assess the thickness of the boundary layer on the cone's surface, the shape of the shock wave, and whether the shock wave intersects the boundary layer. First of all, we focused on ensuring that the resulting solutions corresponded to the physical pattern of phenomena. No doubt, solutions obtained through tunnel mathematics must be confirmed experimentally.

Synergistic effects of aggregate-void distribution on low-temperature fracture performance and crack propagation of asphalt concrete under mode I and mode II fracturing

Mesoscopic structures of asphalt concrete play an important role in low-temperature cracking behavior. Existing studies mainly focus on a single feature of the mesoscopic structure, neglecting the spatial distribution and synergistic effects of aggregates and voids, especially in Mode II fracturing. The results show that: in the case of −5 °C and Mode I fracturing, the fracture trend is less affected by the spatial distribution of mesoscopic structure, and tending to spread through aggregate and asphalt mastic along the shortest path. In the case of −5 °C and Mode II fracturing, the crack is easily affected by the distribution of large particle size aggregates in the initial zone, but not by the uneven distribution of voids. In the case of 10 °C and Mode I fracturing, the dominant large aggregate particle size influence on the path is weakened, and the effect of void distribution on the cracking path is perceptibly increased. In the case of 10 °C and Mode II fracturing, the location of large-particle aggregate determines the main streak of fractures, and the uneven distribution of void space determines the occurrence of fracture bending.

Anionic COF nanosheets construct porous and charged interlayer for the preparation of high-performance desalination membranes

Polyamide (PA) membranes prepared by interfacial polymerization (IP) provide an effective solution for efficient desalination. The IP reaction, as a diffusion-controlled polymerization reaction, regulates the storage and diffusion of monomers in the IP process to achieve effective regulation of the PA membrane structure. Higher initial monomer concentration and slower monomer release rate can effectively reduce the membrane thickness and enhance the permeance of the membrane. Herein, ionic covalent organic framework (iCOF) materials with well-developed and ordered pore channels bearing high-density –SO3H groups are used to construct a porous and charged interlayer to regulate the release process of monomers during the IP process. The well-ordered pore structure of iCOF provides sufficient storage space for amine monomers and uniform monomer distribution, accelerating the closure of the incipient film. Moreover, the electrostatic interactions between the high density of negatively charged anionic groups on iCOF and the positively charged amine monomer can reduce the diffusion coefficient of the amine monomer by a factor of two. The above two effects resulted in a nearly 10-fold reduction in the thickness of the PA separation layer and an increase in water permeance up to 24.8 L m−2 h−1 bar−1, nearly three times improvement compared to unmodified PA membrane.