Phase Space Model Research Articles

SRCES: a simulation program for collective effects in electron storage rings

Collective effects are important in the physics design of electron storage rings, especially for the fourth-generation synchrotron light source, where the collective effects are more severe than before and limit maximum stored beam current. To estimate beam collective effects, besides theoretical analysis, numerical tracking methods are necessary for obtaining more accurate and comprehensive results. To systematically study the comprehensive influence of wakefields and various damping mechanisms, we developed a new code Storage Ring Collective Effects Simulator (SRCES), which is a tracking code based on macroparticle model in 6-dimensional phase space. Several models are employed to handle various processes of particle motion. The modified transfer matrix and high order Taylor transfer map are used to solve particle motion under external electro-magnetic fields. A simplified equivalent damping and excitation model is used to represent the effects of synchrotron radiation on particle motion. The kick model is used to represent the influence of wakefields and RF cavity. Furthermore, the wake function data can be input as numerical arrays directly or through specific impedance models. In this paper, we describe the basic theory foundation, functions and benchmarked results of the code SRCES. Then, SRCES is used to conduct preliminary research on the collective effects of the Hefei Advanced Light Facility storage ring.

Integrated Control of Intelligent Vehicle Driving Stability Using Three-Dimensional Phase Space

<div>To enhance vehicle dynamic stability during driving, we developed a three-dimensional phase space model that incorporates the sideslip angle of center of mass, yaw rate, and lateral load transfer rate. This model enabled real-time evaluation and active control of vehicle stability. First, longitudinal and lateral controllers were implemented to ensure precise vehicle trajectory. Second, a hierarchical control strategy was designed to actively manage the desired sideslip angle, yaw rate, and roll angle based on the vehicle’s destabilizing conditions, thereby maintaining the vehicle within a stable state space. We simulated and tested the stability analysis methods and integrated control strategies for both cars and trucks under DLC (double lane change) and CDC (circular driving condition) scenarios using joint simulations with CarSim/TruckSim and Simulink. The proposed integrated stability control strategy, which combined MPC-based trajectory tracking with direct yaw moment control and active suspension control, enhanced the vehicle’s directional and roll stability. This approach effectively mitigated vehicle instability under extreme conditions. Compared to the MPC lateral tracking control system, the performance of the integrated control system was significantly improved. In the DLC scenario, the maximum values of the sedan’s lateral deviation, sideslip angle, yaw rate, and vehicle roll angle decreased by 22.6%, 33.9%, 5.5%, and 1.2%, respectively. In the CDC scenario, the truck’s lateral acceleration, sideslip angle, yaw rate, and vehicle roll angle decreased by 7.5%, 46.8%, 8.2%, and 80%, respectively. Additionally, open-loop simulation tests were conducted under fishhook steering conditions for both passenger cars and trucks. The results further validated the effectiveness of the integrated control strategy, demonstrating its ability to significantly improve yaw rate and roll response, thereby enhancing overall vehicle stability under challenging driving conditions.</div>

Asymptotic smoothness effects and global attractor for a peridynamic model with energy damping

AbstractIn this paper, we consider a peridynamic model with energy damping inspired by the works of Balakrishnan and Taylor on “damping models” based on the instantaneous total energy of the system. We study the asymptotic behavior of solutions, in the sense of attractors, of these peridynamic models in suitable phase space; more precisely, we prove a result of existence and characterization of compact global attractors with a nonlinear strongly continuous semigroup approach based in the asymptotic smoothness property thanks to Chueshov and Lasiecka and Nakao's lemma.

Complex Fluid Models of Mixed Quantum–Classical Dynamics

Several methods in nonadiabatic molecular dynamics are based on Madelung’s hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential leads to severe computational challenges and one often seeks to neglect its contribution, thereby approximating nuclear motion as classical. The resulting model couples classical hydrodynamics for the nuclei to the quantum motion of the electronic component, leading to the structure of a complex fluid system. This type of mixed quantum–classical fluid models has also appeared in solvation dynamics to describe the coupling between liquid solvents and the quantum solute molecule. While these approaches represent a promising direction, their mathematical structure requires a certain care. In some cases, challenging higher-order gradients make these equations hardly tractable. In other cases, these models are based on phase-space formulations that suffer from well-known consistency issues. Here, we present a new complex fluid system that resolves these difficulties. Unlike common approaches, the current system is obtained by applying the fluid closure at the level of the action principle of the original phase-space model. As a result, the system inherits a Hamiltonian structure and retains energy/momentum balance. After discussing some of its structural properties and dynamical invariants, we illustrate the model in the case of pure-dephasing dynamics. We conclude by presenting some invariant planar models.

Matrix methods and teaching the fundamentals of fluid and gas mechanics in higher education institutions

Problem. The instruction of physical and mathematical disciplines in higher education institutions employing cutting-edge methods and universal approaches, which seamlessly integrate scientific and engineering activities of future specialists, remains one of the pertinent and priority tasks. The utilization of multidimensional or even infinite-dimensional spaces has become an effective and nearly indispensable tool in mathematical modeling of physical phenomena. This circumstance is directly linked to the increasing level of abstraction and the refinement of mathematical methods. The use of geometric methods inherent in vector algebra and vector analysis as the foundation for studying mechanics, despite their illustrative nature, is losing its relevance. Methods built upon matrix formalism are evolving as substitutes. The matrix framework enables the exploitation of phase space advantages to derive canonical equations of motion for continuous media and electromagnetic field equations in covariant forms. The electromagnetic potential acquires mechanical significance, allowing the utilization of electromechanical analogies at a fundamental level rather than on a merely formal basis, as done in classical electrodynamics. Goal. The aim of this research is to study and justify the advantages of matrix methods for deriving equations of motion for fluids and gases from the canonical equations of mechanics by utilizing a continuum model in phase and physical space. The research is directed towards demonstrating the connection between the internal microscopic and macroscopic motion of fluids and gases, as well as highlighting the potential of matrix formalism both in terms of modeling and the utilization of computational tools. Methodology. The methodological basis for selecting matrix methods lies in the application of tensor analysis and its generalizations for modeling the motion of fluids and gases in physical and phase space. Results. It has been demonstrated that the matrix method, previously applied to classical and relativistic mechanics, allows for the consideration of the molecular structure of the environment by folding the multidimensional phase space of the mechanical system, represented by a particle of the medium, and thereby deriving equations of motion for fluids and gases from the canonical equations of classical mechanics and the equations of momentum balance of the medium. Originality. The combination of canonical equations as a result of applying the conservation law of matter in the form of balance equations in phase space and momentum balance equations in physical space allows for elucidating the relationship between macroscopic and microscopic motions of the medium, as well as the mathematical structure of the equations of motion for fluids and gases. Practical value. The proposed method allows, while remaining within the standard mathematical training offered by technical educational institutions, to effectively formalize the equations of motion for fluids and gases and provide them with an invariant form. By guiding oneself through invariance, both fundamental laws (such as the law of universal gravitation) and partial laws (the generalized Newton's law) can be obtained.

Are early-type galaxies quenched by present-day environment? A study of dwarfs in the Fornax Cluster.

Galaxies undergo numerous transformative processes throughout their lifetimes that ultimately lead to the expulsion of gas and the cessation of star-forming activity. This phenomenon is commonly known as quenching, and in this study, we delve into the possibility that this process is caused by the environmental processes associated with the surrounding cluster. To this end, we used the results of our previous paper ---where we analyzed dwarf galaxies in the survey together with massive galaxies from the survey--- to compute the quenching time of each galaxy and compare it with the infall time into the cluster. Using as an approximation of the quenching time and deriving the infall time from phase-space models, we determined the probability of the quenching being produced by the local environment of galaxies. Our results reveal a relation between galaxy mass and quenching probability. Massive galaxies, down to exhibit a low, almost zero probability of quenching, suggesting their independence of environmental effects. As we move into the mass regime of dwarf galaxies, the probability increases with decreasing mass, highlighting their sensitivity to environmental quenching. For dwarfs, 36pm 9<!PCT!> of our observational data are consistent with this hypothesis, challenging the idea that the present-day cluster, Fornax, is the primary driver of quenching in the low-mass galaxies of our sample with stellar mass from to To further investigate the importance of environmental processes, we compared these results with cosmological simulations, selecting galaxies under similar conditions to our observational sample. Remarkably, the simulated sample shows lower quenching probabilities as we move down in mass, and barely 5pm 1<!PCT!> of galaxies meet the quenching criteria. This discrepancy between observations and simulations underlines the fact that the modelling of quenching is still in its infancy. In general, the number of observed galaxies quenched by their environment is lower than expected, which suggests that preprocessing plays a larger role in galaxy evolution. Ultimately, our results highlight the need for higher-quality simulations and refinement of galaxy formation and evolution models.

Exploring Semi-Inclusive Two-Nucleon Emission in Neutrino Scattering: A Factorized Approximation Approach

The semi-inclusive cross-section of two-nucleon emission induced by neutrinos and antineutrinos is computed by employing the relativistic mean field model of nuclear matter and the dynamics of meson-exchange currents. Within this model, we explore a factorization approximation based on the product of an integrated two-hole spectral function and a two-nucleon cross-section averaged over hole pairs. We demonstrate that the integrated spectral function of the uncorrelated Fermi gas can be analytically computed, and we derive a simple, fully relativistic formula for this function, showcasing its dependency solely on both missing momentum and missing energy. A prescription for the average momenta of the two holes in the factorized two-nucleon cross-section is provided, assuming that these momenta are perpendicular to the missing momentum in the center-of-mass system. The validity of the factorized approach is assessed by comparing it with the unfactorized calculation. Our investigation includes the study of the semi-inclusive cross-section integrated over the energy of one of the emitted nucleons and the cross-section integrated over the emission angles of the two nucleons and the outgoing muon kinematics. A comparison is made with the pure phase-space model and other models from the literature. The results of this analysis offer valuable insights into the influence of the semi-inclusive hadronic tensor on the cross-section, providing a deeper understanding of the underlying nuclear processes.

Twitter Self-Organization to the Edge of a Phase Transition: Discrete-Time Model and Effective Early Warning Signals in Phase Space

Many real-world systems of various origins are capable of self-organization to the edge of a phase transition, characterized by avalanche-like behavior. Therefore, it is important, by observing the behavior of early warning measures for dynamical series generated by systems, to timely see the early warning signals (precursors) of such self-organization and, if necessary, take preventive measures. To date, convincing evidence of self-organization to the edge of a phase transition has been obtained, but no effective precursors for this self-organization have been found. This research explores precursors for the Twitter self-organization based on the analysis of the behavior of measures directly related to the critical slowdown of the network and measures of the phase space reconstructed by the Takens method for the series of the number of network users creating avalanches of retweets in the network, corresponding to the three debates of the 2016 United States Presidential Election. We hydrated the relevant Tweet IDs, which were obtained from the Harvard Dataverse using the Social Feed Manager, to form this series. Preliminarily, we explore the potential of measures for early detection of self-organization of sandpile cellular automata as systems with Twitter-equivalent self-organization mechanisms. The equivalence is justified in the proposed discrete-time model for Twitter self-organization to the edge of a phase transition. It is found that there are more moments of the Twitter self-organization than the moments of time when debates started, and Twitter stays at the edge of a phase transition longer than the debate lasts. The effective measures, as the measures with the lowest number of false early warning signals, among all studied measures and for all studied systems, are dispersion and correlation dimension. Obtained results are practically important in the design and implementation of early warning systems for the systems with similar mechanisms for sandpile cellular automata self-organization to the edge of a phase transition.

Statistical Models for the Dynamics of Heavy Particles in Turbulence

When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy particles, with mass densities larger than that of the carrying fluid, can detach from the flow. This results in preferential sampling, small-scale fractal clustering, and large relative velocities. To describe these effects of particle inertia, one must consider both particle positions and velocities in phase space. In recent years, statistical phase-space models have significantly contributed to our understanding of inertial-particle dynamics in turbulence. These models help to identify the key mechanisms and nondimensional parameters governing the particle dynamics and have made qualitative and, in some cases, quantitative predictions. This article reviews statistical phase-space models for the dynamics of small, yet heavy, spherical particles in turbulence. We evaluate their effectiveness by comparing their predictions with results from numerical simulations and laboratory experiments, and we summarize their successes and failures.

Multilayer Perceptron Network Optimization for Chaotic Time Series Modeling.

Chaotic time series are widely present in practice, but due to their characteristics-such as internal randomness, nonlinearity, and long-term unpredictability-it is difficult to achieve high-precision intermediate or long-term predictions. Multi-layer perceptron (MLP) networks are an effective tool for chaotic time series modeling. Focusing on chaotic time series modeling, this paper presents a generalized degree of freedom approximation method of MLP. We then obtain its Akachi information criterion, which is designed as the loss function for training, hence developing an overall framework for chaotic time series analysis, including phase space reconstruction, model training, and model selection. To verify the effectiveness of the proposed method, it is applied to two artificial chaotic time series and two real-world chaotic time series. The numerical results show that the proposed optimized method is effective to obtain the best model from a group of candidates. Moreover, the optimized models perform very well in multi-step prediction tasks.

New insights into holonomic brain theory: implications for active consciousness

This pioneering research on how specific molecules deep inside our brains form a dynamic information holarchy in phase space, linking mind and consciousness, is not only provocative but also revolutionary. Holonomic is a dynamic encapsulation of the holonic view that originates from the word “holon” and designates a holarchical rather than a hierarchical, dynamic brain organization to encompass multiscale effects. The unitary nature of consciousness being interconnected stems from a multiscalar organization of the brain. We aim to give a holonomic modification of the thermodynamic approach to the problem of consciousness using spatiotemporal intermittency. Starting with quasiparticles as the minimalist material composition of the dynamical brain where interferences patterns between incoherent waves of quasiparticles and their quantum-thermal fluctuations constrain the kinetic internal energy of endogenous molecules through informational channels of the negentropically-derived quantum potential. This indicates that brains are not multifractal involving avalanches but are multiscalar, suggesting that unlike the hologram, where the functional interactions occur in the spectral domain, the spatiotemporal binding is multiscalar because of self-referential amplification occurring via long-range correlative information. The associated negentropic entanglement permeates the unification of the functional information architecture across multiple scales. As such, the holonomic brain theory is suitable for active consciousness, proving that consciousness is not fundamental. The holonomic model of the brain’s internal space is nonmetric and nonfractal. It contains a multiscalar informational structure decoded by intermittency spikes in the fluctuations of the negentropically-derived quantum potential. It is therefore, a more realistic approach than the platonic models in phase space.

New insights into holonomic brain theory: implications for active consciousness

This pioneering research on how specific molecules deep inside our brains form a dynamic information holarchy in phase space, linking mind and consciousness, is not only provocative but also revolutionary. Holonomic is a dynamic encapsulation of the holonic view that originates from the word “holon” and designates a holarchical rather than a hierarchical, dynamic brain organization to encompass multiscale effects. The unitary nature of consciousness being interconnected stems from a multiscalar organization of the brain. We aim to give a holonomic modification of the thermodynamic approach to the problem of consciousness using spatiotemporal intermittency. Starting with quasiparticles as the minimalist material composition of the dynamical brain where interferences patterns between incoherent waves of quasiparticles and their quantum-thermal fluctuations constrain the kinetic internal energy of endogenous molecules through informational channels of the negentropically-derived quantum potential. This indicates that brains are not multifractal involving avalanches but are multiscalar, suggesting that unlike the hologram, where the functional interactions occur in the spectral domain, the spatiotemporal binding is multiscalar because of self-referential amplification occurring via long-range correlative information. The associated negentropic entanglement permeates the unification of the functional information architecture across multiple scales. As such, the holonomic brain theory is suitable for active consciousness, proving that consciousness is not fundamental. The holonomic model of the brain’s internal space is nonmetric and nonfractal. It contains a multiscalar informational structure decoded by intermittency spikes in the fluctuations of the negentropically-derived quantum potential. It is therefore, a more realistic approach than the platonic models in phase space.

Dynamically Implementing the μ¯-Scheme in Cosmological and Spherically Symmetric Models in an Extended Phase Space Model

We consider an extended phase space formulation for cosmological and spherically symmetric models in which the choice of a given μ¯-scheme can be implemented dynamically. These models are constructed in the context of the relational formalism by using a canonical transformation on the extended phase space, which provides a Kuchař decomposition of the extended phase space. The resulting model can be understood as a gauge-unfixed model of a given μ¯-scheme. We use this formalism to investigate the restrictions to the allowed μ¯-scheme from this perspective and discuss the differences in the cosmological and spherically symmetric case. This method can be useful, for example, to obtain a μ¯-scheme in a top-down derivation from full LQG to symmetry-reduced effective models, where, for some models, only the μ0-scheme has been obtained thus far.

The Influence of Deformation Phase-Space on Spectra of Heavy Quarkonia in Improved Energy Potential at Finite Temperature Model of Shrodinger Equation Via the Generalized Boob’s Shift Method and Standard Perturbation Theory

In this work, we obtain solutions of the deformed Schrödinger equation (DSE) with improved internal energy potential at a finite temperature model in a 3-dimensional nonrelativistic noncommutative phase-space (3D-NRNCPS) symmetries framework, using the generalized Bopp’s shift method in the case of perturbed nonrelativistic quantum chromodynamics (pNRQCD). The modified bound state energy spectra are obtained for the heavy quarkonium system such as charmonium cc- and bottomonium bb- at finite temperature. It is found that the perturbative solutions of the discrete spectrum are sensible to the discreet atomic quantum numbers (j,l,s,m) of the ( QQ- (Q=c,b)) state, the parameters of internal energy potential (T,αs(T), mD (T),β,c), which are the Debye screening mass mD (T), the running coupling constant αs(T) the critical temperature β, the free parameter c in addition to noncommutativity parameters (Θ,θ-). The new Hamiltonian operator in 3D-NRNCPS symmetries is composed of the corresponding operator in commutative phase-space and three additive parts for spin-orbit interaction, the new magnetic interaction, and the rotational Fermi-term. The obtained energy eigenvalues are applied to obtain the mass spectra of heavy quarkonium systems (cc- and bb-). The total complete degeneracy of the new energy levels of the improved internal energy potential changed to become equal to the new value 3n2 in 3D-NRNCPS symmetries instead of the value n2 in the symmetries of 3D-NRQM. Our non-relativistic results obtained from DSE will possibly be compared with the Dirac equation in high-energy physics.

Varian Clinac 2100 linear accelerator simulation employing PRIMO phase space model

IntroductionThe lack of information concerning the geometry and the chemical elements that constitute the components of the linear accelerator is a real problem that is encountered by most researchers who wish to simulate these devices by Monte Carlo methods. MethodsTo overcome this problem, PRIMO represents a very attractive alternative that allows the simulation of different commercial linacs without disclosing their components. This solution was applied to simulate the Varian Clinac 2100 linear accelerator. The electron beam parameters for 6, 9 and 12 MeV are iteratively adjusted to match the measurement data. After validation of the simulation with PRIMO, the phase space models were generated and validated, for all the studied energy ranges in this work. Then, the results of this simulation were implemented in the GATE platform.The obtained simulation results by this method were compared to the measured data, to the GOLDEN DATA, and to the simulation data obtained from the direct simulation with PRIMO. ResultsThe simulation results found, for different field sizes and different energies, are in good agreement with the measured data and significantly better than those obtained by direct simulation with PRIMO. ConclusionsThis method gives very satisfactory results for all energies and all fields. The finding also shows how important it is for researchers to adopt this strategy to save the simulation time and the effort to find the shape and composite materials of the accelerator.

Phase-Space Modeling and Control of Robots in the Screw Theory Framework Using Geometric Algebra

The following paper talks about the dynamic modeling and control of robot manipulators using Hamilton’s equations in the screw theory framework. The difference between the proposed work with diverse methods in the literature is the ease of obtaining the laws of control directly with screws and co-screws, which is considered modern robotics by diverse authors. In addition, geometric algebra (GA) is introduced as a simple and iterative tool to obtain screws and co-screws. On the other hand, such as the controllers, the Hamiltonian equations of motion (in the phase space) are developed using co-screws and screws, which is a novel approach to compute the dynamic equations for robots. Regarding the controllers, two laws of control are designed to ensure the error’s convergence to zero. The controllers are computed using the traditional feedback linearization and the sliding mode control theory. The first one is easy to program and the second theory provides robustness for matched disturbances. On the other hand, to prove the stability of the closed loop system, different Lyapunov functions are computed with co-screws and screws to guarantee its convergence to zero. Finally, diverse simulations are illustrated to show a comparison of the designed controllers with the most famous approaches.

A New Model to Describe Quarkonium Systems under Modified Cornell Potential at Finite Temperature in pNRQCD

In the present work, the three-dimensional modified radial Schrödinger equation is analytically solved. The nonrelativistic interactions under new modified Cornell potential (NMCP, in short) at finite temperature, are extended to the symmetries of nonrelativistic noncommutative space phase (NRNSP, in short), using the generalized Bopp’s shift method in the case of perturbed nonrelativistic quantum chromodynamics (pNRQCD). W generalize this process by adding multi-variable coupling potentials , and together with the modified Cornell potential model in three-dimensional nonrelativistic quantum mechanics noncommutative phase space (3D-NCSP, in short). The new energy eigenvalues and the corresponding Hamiltonian operator are calculated in 3D-NCSP symmetries instead of solving the modified Schrödinger equation with the Weyl Moyal star product. The present results, in (3D-NCSP), are applied to the charmonium and bottomonium masses at finite temperature. The present approach successfully generalizes the energy eigenvalues at finite temperature in 3D-NCSP symmetries. It is found that the perturbative solutions of the discrete spectrum and quarkonium mass can be expressed by the Gamma function, the discreet atomic quantum numbers of the state and the potential parameters ( ), in addition to noncommutativity parameters ( and ). The total complete degeneracy of new energy levels of NMCP changed to become equals to the value instead the values in ordinary quantum mechanics. Our obtained results are in good agreement with the already existing literature in NCSP. Keywords: Schrödinger Equation, Heavy Quarkonium System, Cornell Potential, Noncommutative Space Phase, Bopp’s Shift Method. Subject Classification Numbers: 03.65.-w; 03.65.Ge; 03.65. Fd; 03.65.Ca

Three-dimensional density field of a screeching under-expanded jet in helical mode using multi-view digital holographic interferometry

A synchronised multi-axis digital holographic interferometry set-up is presented for the study of 3-D flow fields with large density gradients. This optical configuration provides instantaneous interferograms with fine spatial resolution in six directions of projection. A regularised tomographic approach taking into account the presence of possible shock waves is furthermore considered to reconstruct 3-D density fields. Applied to a screeching under-expanded supersonic jet with helical dynamics, this set-up is used to provide dense optical phase measurements in the initial region of the jet. The jet mean density field is shown to be satisfactorily estimated with sharply resolved density gradients. In addition, an approach based on azimuthal Fourier transform and snapshot proper orthogonal decomposition (POD) applied to the instantaneous flow observations is proposed to study the main coherent dynamics of the jet. Relying on a cluster analysis of the azimuthal POD mode coefficients, a reduced dynamical model in the POD mode phase space is used as an approximation of the two observed limit cycles. A clear 3-D representation of the density field of a helical instability associated with screech mode C is then evidenced, with two equally probable directions of rotation. Switching between the two directions is reported, highlighting intermittency in the feedback loop. This helical structure is particularly seen to extend to the jet core, driving its internal dynamics and inducing out-of-phase density fluctuations between the outer and inner shear layers. These out-of-phase motions are related to the non-uniform radial distribution of fluctuation phase associated with the outer-layer Kelvin–Helmholtz instability wave.

A phase space model of a Versa HD linear accelerator for application to Monte Carlo dose calculation in a real-time adaptive workflow.

PurposeThis study aims to develop and validate a simple geometric model of the accelerator head, from which a particle phase space can be calculated for application to fast Monte Carlo dose calculation in real‐time adaptive photon radiotherapy. With this objective in view, the study investigates whether the phase space model can facilitate dose calculations which are compatible with those of a commercial treatment planning system, for convenient interoperability.Materials and methodsA dual‐source model of the head of a Versa HD accelerator (Elekta AB, Stockholm, Sweden) was created. The model used parameters chosen to be compatible with those of 6‐MV flattened and 6‐MV flattening filter‐free photon beams in the RayStation treatment planning system (RaySearch Laboratories, Stockholm, Sweden). The phase space model was used to calculate a photon phase space for several treatment plans, and the resulting phase space was applied to the Dose Planning Method (DPM) Monte Carlo dose calculation algorithm. Simple fields and intensity‐modulated radiation therapy (IMRT) treatment plans for prostate and lung were calculated for benchmarking purposes and compared with the convolution‐superposition dose calculation within RayStation.ResultsFor simple square fields in a water phantom, the calculated dose distribution agrees to within ±2% with that from the commercial treatment planning system, except in the buildup region, where the DPM code does not model the electron contamination. For IMRT plans of prostate and lung, agreements of ±2% and ±6%, respectively, are found, with slightly larger differences in the high dose gradients.ConclusionsThe phase space model presented allows convenient calculation of a phase space for application to Monte Carlo dose calculation, with straightforward translation of beam parameters from the RayStation beam model. This provides a basis on which to develop dose calculation in a real‐time adaptive setting.

Search for the decay B0→ ϕμ+μ−

A search for the decay B0→ ϕμ+μ− is performed using proton-proton collisions at centre-of-mass energies of 7, 8, and 13 TeV collected by the LHCb experiment and corresponding to an integrated luminosity of 9 fb−1. No evidence for the B0→ ϕμ+μ− decay is found and an upper limit on the branching fraction, excluding the ϕ and charmonium regions in the dimuon spectrum, of 4.4 × 10−3 at a 90% credibility level, relative to that of the {B}_s^0 → ϕμ+μ− decay, is established. Using the measured {B}_s^0 → ϕμ+μ− branching fraction and assuming a phase-space model, the absolute branching fraction of the decay B0→ ϕμ+μ− in the full q2 range is determined to be less than 3.2 × 10−9 at a 90% credibility level.