Isotropic Point Research Articles

Monte Carlo calculations of electrons impinging on a copper target: A comparison of EGSnrc, Geant4 and MCNP5

A simple geometry is used to compare several of the available Monte Carlo software codes for radiation transport. EGSnrc, Geant4 and MCNP5 are all used to calculate the photon fluence produced from electrons incident on a copper target. Four energies for the isotropic point source are chosen to simulate the average and maximum emission energies of 32P and 90Y: (0.7, 1.71)MeV and (0.93, 2.28)MeV, respectively. The energy deposition in the copper target, the electron current at the target and the computational efficiency are also calculated. EGSnrc is found to be the only self-consistent code when comparing results calculated using the default transport parameters of the condensed history mode with those calculated in the single scattering mode.

Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain

We study the return probability and its imaginary (τ) time continuation after a quench from a domain wall initial state in the XXZ spin chain, focusing mainly on the region with anisotropy . We establish exact Fredholm determinant formulas for those, by exploiting a connection to the six-vertex model with domain wall boundary conditions. In imaginary time, we find the expected scaling for a partition function of a statistical mechanical model of area proportional to , which reflects the fact that the model exhibits the limit shape phenomenon. In real time, we observe that in the region the decay for long time t is nowhere continuous as a function of anisotropy: it is Gaussian at roots of unity and exponential otherwise. We also determine that the front moves as , by the analytic continuation of known arctic curves in the six-vertex model. Exactly at , we find the return probability decays as . It is argued that this result provides an upper bound on spin transport. In particular, it suggests that transport should be diffusive at the isotropic point for this quench.

Abstract ID: 184 OpenDNA: An OpenCL-based GPU Monte Carlo simulation code for microdosimetry

Introduction Geant4-DNA [1] , [2] is a Geant4 module that simulates the track structure of charged particles (electron/positron, proton and ions) in water as well as the radiolysis process that follows. Unlike the condensed-history technique in normal Geant4 simulations, Geant4-DNA implements an analogue Monte Carlo (AMC) technique that gives the event-by-event history of primary particle and all its descendants. Due to this, the simulation is extremely slow. To provide a faster alternative, this work implements a GPU-based AMC using the OpenCL parallel programming framework, OpenDNA. Methods For electrons and positron, ionization, excitation and elastic scattering were implemented. For protons, ionization and excitation were implemented. The low energy cut is 10 eV (10 keV) for electron (proton). The physical models and cross section data were extracted from Geant4-DNA. OpenDNA was preliminarily benchmarked against Geant4-DNA by radial dose distribution (RDD) simulations. For electron, a spherical geometry was used for a isotropic point source of E = 30 keV for both codes. For proton, a cylindrical geometry was used and a E = 800 keV proton was initiated along its axis. The ratio of OpenDNA RDD over Geant4-DNA RDD was computed to evaluate the consistency. 1,000,000 (and 100,000) primary histories were simulated for the electron (proton) case. The codes were run in a Mac Pro with two AMD FirePro D700 GPUs (for OpenDNA, using 100 threads) and a 2.7 GHz 12-Core Intel Xeon E5 CPU (Geant-DNA). Results The RDDs of OpenDNA and Geant4-DNA are consistent with each other within 1% for both particles. The simulation time of the electron (proton) case was reduced to 1/12 (1/10). Conclusion An analogue MC code was implemented using OpenCL and therefore is supposed to run in all OpenCL-conformed GPU. Future work include the simulation of physicochemical and chemical processes.

Yang–Baxter solution of dimers as a free-fermion six-vertex model

It is shown that Dimers is Yang–Baxter integrable as a six-vertex model at the free-fermion point with crossing parameter . A one-to-many mapping of vertices onto dimer configurations allows the free-fermion solutions to be applied to the anisotropic dimer model on a square lattice where the dimers are rotated by compared to their usual orientation. This dimer model is exactly solvable in geometries of arbitrary finite size. In this paper, we establish and solve inversion identities for Dimers with periodic boundary conditions on the cylinder. In the particle representation, the local face tile operators give a representation of the fermion algebra, and the fermion particle trajectories play the role of nonlocal (logarithmic) degrees of freedom. In a suitable gauge, the dimer model is described by the Temperley–Lieb algebra with loop fugacity . At the isotropic point, the exact solution allows for the explicit counting of rotated dimer configurations on a periodic rectangular lattice. We show that the modular invariant partition function on the torus is the same as that of symplectic fermions and critical dense polymers. We also show that nontrivial Jordan cells appear for the dimer Hamiltonian on the strip with vacuum boundary conditions. We therefore argue that, in the continuum scaling limit, the dimer model gives rise to a logarithmic conformal field theory with central charge , minimal conformal weight and effective central charge .

Isotropic Lifshitz point in the O(N) theory

The presence of an isotropic tricritical Lifshitz point for the O(N) scalar theory is investigated at large N in the improved Local Potential Approximation (LPA′) by means of the Functional Renormalization Group equations. At leading order, the non-trivial Lifshitz point is observed if the number of dimensions d is taken between d=4 and d=8, and the eigenvalue spectrum of the associated eigendirections is derived. At order 1/N of the LPA′ the anomalous dimension ηN is computed and it is found to vanish both in d=4 and d=8. The dependence of our findings on the infrared regulator is discussed.

Computation of Green’s Function of 3-D Radiative Transport Equations for Non-isotropic Scattering of P and Unpolarized S Waves

In this work, I propose to model the propagation of high-frequency seismic waves in the heterogeneous Earth by means of a coupled system of radiative transfer equations for P and S waves. The model describes the propagation of both coherent and diffuse waves in a statistically isotropic heterogeneous medium and takes into account key phenomena such as scattering conversions between propagation modes, scattering anisotropy and absorption. The main limitation of the approach lies in the neglect of the shear wave polarization information. The canonical case of a medium with uniform scattering and absorption properties is studied in details. Using an adjoint formalism, Green’s functions (isotropic point source solutions) of the transport equation are shown to obey a reciprocity relation relating the P energy density radiated by an S source to the S energy density radiated by a P source. A spectral method of calculation of the Green’s function is presented. Application of Fourier, Hankel and Legendre transforms to time, space and angular variables, respectively, turns the equation of transport into a numerically tractable penta-diagonal linear system of equations. The implementation of the spectral method is discussed in details and validated through one-to-one comparisons with Monte Carlo simulations. Numerical experiments in different propagation regimes illustrate that the ratio between the correlation length of heterogeneities and the incident wavelength plays a key role in the rate of stabilization of the P-to-S energy ratio in the coda. The results suggest that the rapid stabilization of energy ratios observed in the seismic coda is a signature of the broadband nature of crustal heterogeneities. The impact of the texture of the medium on both pulse broadening and generation of converted S wave arrivals by explosion sources is illustrated. The numerical study indicates that smooth media enhance the visibility of ballistic-like S arrivals from P sources.

Double cone of eigendirections in optically active ethylenediammonium selenate crystals.

Circular birefringence (CB) is generally responsible for only a small perturbation to the state of light polarization in crystals that also exhibit linear birefringence (LB). As such, the magnetoelectric tensor of gyration, which gives rise to CB and optical activity, is less well determined than the electric permittivity tensor in optical models of the Mueller matrix. To visualize the effect of the magnetoelectric tensor on polarimetric measurements, reported here are experimental mappings of the Mueller matrix and of the CB in a new chiral crystal with accidental null LB at an accessible optical frequency. Single crystals of ethylenediammonium selenate (EDSeO4) were synthesized and characterized by X-ray diffraction and Mueller matrix measurements in transmission and reflection. The crystals are isomorphous with the corresponding sulfate salt. They are tetragonal, space group P41(3)212. The constitutive relations of EDSeO4 were recovered using a partial wave summation of incoherent reflections. The extraordinary and ordinary refractive indices cross at 364 nm (3.41 eV), a scenario commonly called the 'isotropic point' or 'iso-index point'. At this wavelength, the magnetoelectric tensor fully describes the polarization transformation, giving rise to a double cone of eigendirections.

Ground state properties of the bond alternating spin-1/2 anisotropic Heisenberg chain

Ground state properties, dispersion relations and scaling behaviour of spin gap of a bond alternating spin-$\frac{1}{2}$ anisotropic Heisenberg chain have been studied where the exchange interactions on alternate bonds are ferromagnetic (FM) and antiferromagnetic (AFM) in two separate cases. The resulting models separately represent nearest neighbour (NN) AFM-AFM and AFM-FM bond alternating chains. Ground state energy has been estimated analytically by using both bond operator and Jordan-Wigner representations and numerically by using exact diagonalization. Dispersion relations, spin gap and several ground state orders have been obtained. Dimer order and string orders are found to coexist in the ground state. Spin gap is found to develop as soon as the non-uniformity in alternating bond strength is introduced in the AFM-AFM chain which further remains non-zero for the AFM-FM chain. This spin gap along with the string orders attribute to the Haldane phase. The Haldane phase is found to exist in most of the anisotropic region similar to the isotropic point.

4D in vivo ultrafast ultrasound imaging using a row-column addressed matrix and coherently-compounded orthogonal plane waves

4D ultrafast ultrasound imaging was recently shown using a 2D matrix (i.e. fully populated) connected to a 1024-channel ultrafast ultrasound scanner. In this study, we investigate the row-column addressing (RCA) matrix approach, which allows a reduction of independent channels from N × N to N + N, with a dedicated beamforming strategy for ultrafast ultrasound imaging based on the coherent compounding of orthogonal plane wave (OPW). OPW is based on coherent compounding of plane wave transmissions in one direction with receive beamforming along the orthogonal direction and its orthogonal companion sequence. Such coherent recombination of complementary orthogonal sequences leads to the virtual transmit focusing in both directions which results into a final isotropic point spread function (PSF).In this study, a 32 × 32 2D matrix array probe (1024 channels), centered at 5 MHz was considered. An RCA array, of same footprint with 32 + 32 elements (64 channels), was emulated by summing the elements either along a line or a column in software prior to beamforming. This approach allowed for the direct comparison of the 32 + 32 RCA scheme to the optimal fully sampled 32 × 32 2D matrix configuration, which served as the gold standard.This approach was first studied through PSF simulations and then validated experimentally on a phantom consisting of anechoic cysts and echogenic wires. The contrast-to-noise ratio and the lateral resolution of the RCA approach were found to be approximately equal to half (in decibel) and twice the values, respectively, obtained when using the 2D matrix approach. Results in a Doppler phantom and the human humeral artery in vivo confirmed that ultrafast Doppler imaging can be achieved with reduced performances when compared against the equivalent 2D matrix. Volumetric anatomic Doppler rendering and voxel-based pulsed Doppler quantification are presented as well. OPW compound imaging using emulated RCA matrix can achieve a power Doppler with sufficient contrast to recover the vein shape and provides an accurate Doppler spectrum.

Quenching in Chern insulators with satellite Dirac points: The fate of edge states

We perform a sudden quench on the Haldane model with long range interactions, more specifically generalising to the next to next nearest neighbour hopping, referred to as the $N3$ model in our work. Such a model possesses both isotropic and multiple anisotropic (satellite) Dirac points which lead to a rich topological phase diagram consisting of phases with higher Chern number ($C$). Quenches between the topological and the non-topological phases of such an infinite system probe the effect of the presence of the anisotropic Dirac points on the non-equilibrium response of the topological system. Interestingly, the Chern number remains the same before and after the quench for both the quenching protocols, even when the quench of the system is carried out between two different topological phases. {However, for a finite system, we establish that the initial edge current asymptotically decays to zero when the system is quenched to the non-topological phase although the Chern number for the corresponding periodically wrapped system remains unaltered; what is remarkable is that when the Hamiltonian is quenched from $|C|=2$ phase to the non-topological phase the edge current associated with the inner channel decays at a faster rate than the outer channel resembling a situation in which the system passes through the phase with $|C|=1$ before ending up in the phase $C=0$.

4-D light field reconstruction by irradiance decomposition

Common light sources such as an ordinary flashlight with lenses and/or reflectors make complex 4-D light field that cannot be represented by conventional isotropic distribution model nor point light source model. This paper describes a new approach to estimate 4-D light field using an illuminated diffuser. Unlike conventional works that capture a 4-D light field directly, our method decomposes observed intensities on the diffuser into intensities of 4-D light rays based on inverse rendering technique with prior knowledge. We formulate 4-D light field reconstruction problem as a non-smooth convex optimization problem for mathematically finding the global minimum.

A Novel Self-Expandable, Radioactive Airway Stent Loaded with 125I Seeds: A Feasibility and Safety Study in Healthy Beagle Dog.

Airway stent placement is an effective treatment for the immediate palliation of malignant airway obstruction. However, restenosis caused by tumor ingrowth and/or overgrowth after stenting is common. The purpose of this study was to investigate the feasibility and safety of a novel self-expandable stent loaded with 125I seeds in healthy beagle dog. Under fluoroscopic guidance, forty-eight self-expandable airway stents loaded with 125I seeds were perorally placed in the main trachea of 48 healthy beagle dogs, who were randomly divided into four groups (Group A: 0.3mCi; Group B: 0.6mCi; Group C: 0.9mCi; Control group: 0mCi). The estimated radiation dose was calculated using the isotropic point source approximation. Radiological follow-up examinations and histopathological examinations of stented tracheal segments and their adjacent organs and tissues were performed at 2, 4, 8, and 16weeks following the stenting. All stents were successfully deployed in the targeted tracheal segment in the beagle dogs without procedure-related complications. Tracheal stenosis became severe gradually in all the four groups, which was not associated with the radioactivity of 125I seeds (p>0.05). The tracheal injury scores increased along with the higher dose of radioactive seeds which reached peak at 8weeks and then turned back slightly at 16weeks. The adjacent tissue did not show pathohistological changes under microscope, while mild and reversible ultrastructure changes were showed under electronic microscope. This study demonstrates that it is feasible and safe to insert this novel self-expandable airway stent loaded with 125I seeds in healthy beagle dog.

Low-energy electron dose-point kernel simulations using new physics models implemented in Geant4-DNA

When low-energy electrons, such as Auger electrons, interact with liquid water, they induce highly localized ionizing energy depositions over ranges comparable to cell diameters. Monte Carlo track structure (MCTS) codes are suitable tools for performing dosimetry at this level. One of the main MCTS codes, Geant4-DNA, is equipped with only two sets of cross section models for low-energy electron interactions in liquid water (“option 2” and its improved version, “option 4”). To provide Geant4-DNA users with new alternative physics models, a set of cross sections, extracted from CPA100 MCTS code, have been added to Geant4-DNA. This new version is hereafter referred to as “Geant4-DNA-CPA100”.In this study, “Geant4-DNA-CPA100” was used to calculate low-energy electron dose-point kernels (DPKs) between 1keV and 200keV. Such kernels represent the radial energy deposited by an isotropic point source, a parameter that is useful for dosimetry calculations in nuclear medicine. In order to assess the influence of different physics models on DPK calculations, DPKs were calculated using the existing Geant4-DNA models (“option 2” and “option 4”), newly integrated CPA100 models, and the PENELOPE Monte Carlo code used in step-by-step mode for monoenergetic electrons. Additionally, a comparison was performed of two sets of DPKs that were simulated with “Geant4-DNA-CPA100” – the first set using Geant4′s default settings, and the second using CPA100′s original code default settings.A maximum difference of 9.4% was found between the Geant4-DNA-CPA100 and PENELOPE DPKs. Between the two Geant4-DNA existing models, slight differences, between 1keV and 10keV were observed. It was highlighted that the DPKs simulated with the two Geant4-DNA’s existing models were always broader than those generated with “Geant4-DNA-CPA100”. The discrepancies observed between the DPKs generated using Geant4-DNA’s existing models and “Geant4-DNA-CPA100” were caused solely by their different cross sections. The different scoring and interpolation methods used in CPA100 and Geant4 to calculate DPKs showed differences close to 3.0% near the source.

Fermionic algebraic quantum spin liquid in an octa-kagome frustrated antiferromagnet

We investigate the ground state and finite-temperature properties of the spin-1/2 Heisenberg antiferromagnet on an infinite octa-kagome lattice by utilizing state-of-the-art tensor network-based numerical methods. It is shown that the ground state has a vanishing local magnetization and possesses a $1/2$-magnetization plateau with up-down-up-up spin configuration. A quantum phase transition at the critical coupling ratio $J_{d}/J_{t}=0.6$ is found. When $0<J_{d}/J_{t}<0.6$, the system is in a valence bond state, where an obvious zero-magnetization plateau is observed, implying a gapful spin excitation; when $J_{d}/J_{t}>0.6$, the system exhibits a gapless excitation, in which the dimer-dimer correlation is found decaying in a power law, while the spin-spin and chiral-chiral correlation functions decay exponentially. At the isotropic point ($J_{d}/J_{t}=1$), we unveil that at low temperature ($T$) the specific heat depends linearly on $T$, and the susceptibility tends to a constant for $T\rightarrow 0$, giving rise to a Wilson ratio around unity, implying that the system under interest is a fermionic algebraic quantum spin liquid.

Heterogeneous multiscale Monte Carlo simulations for gold nanoparticle radiosensitization.

To introduce the heterogeneous multiscale (HetMS) model for Monte Carlo simulations of gold nanoparticle dose-enhanced radiation therapy (GNPT), a model characterized by its varying levels of detail on different length scales within a single phantom; to apply the HetMS model in two different scenarios relevant for GNPT and to compare computed results with others published. The HetMS model is implemented using an extended version of the EGSnrc user-code egs_chamber; the extended code is tested and verified via comparisons with recently published data from independent GNP simulations. Two distinct scenarios for the HetMS model are then considered: (a) monoenergetic photon beams (20 keV to 1 MeV) incident on a cylinder (1 cm radius, 3 cm length); (b) isotropic point source (brachytherapy source spectra) at the center of a 2.5 cm radius sphere with gold nanoparticles (GNPs) diffusing outwards from the center. Dose enhancement factors (DEFs) are compared for different source energies, depths in phantom, gold concentrations, GNP sizes, and modeling assumptions, as well as with independently published values. Simulation efficiencies are investigated. The HetMS MC simulations account for the competing effects of photon fluence perturbation (due to gold in the scatter media) coupled with enhanced local energy deposition (due to modeling discrete GNPs within subvolumes). DEFs are most sensitive to these effects for the lower source energies, varying with distance from the source; DEFs below unity (i.e., dose decreases, not enhancements) can occur at energies relevant for brachytherapy. For example, in the cylinder scenario, the 20 keV photon source has a DEF of 3.1 near the phantom's surface, decreasing to less than unity by 0.7 cm depth (for 20 mg/g). Compared to discrete modeling of GNPs throughout the gold-containing (treatment) volume, efficiencies are enhanced by up to a factor of 122 with the HetMS approach. For the spherical phantom, DEFs vary with time for diffusion, radionuclide, and radius; DEFs differ considerably from those computed using a widely applied analytic approach. By combining geometric models of varying complexity on different length scales within a single simulation, the HetMS model can effectively account for both macroscopic and microscopic effects which must both be considered for accurate computation of energy deposition and DEFs for GNPT. Efficiency gains with the HetMS approach enable diverse calculations which would otherwise be prohibitively long. The HetMS model may be extended to diverse scenarios relevant for GNPT, providing further avenues for research and development.

Long-range Heisenberg models in quasiperiodically driven crystals of trapped ions

We introduce a theoretical scheme for the analog quantum simulation of long-range XYZ models using current trapped-ion technology. In order to achieve fully-tunable Heisenberg-type interactions, our proposal requires a state-dependent dipole force along a single vibrational axis, together with a combination of standard resonant and detuned carrier drivings. We discuss how this quantum simulator could explore the effect of long-range interactions on the phase diagram by combining an adiabatic protocol with the quasi-periodic drivings and test the validity of our scheme numerically. At the isotropic Heisenberg point, we show that the long-range Hamiltonian can be mapped onto a non-linear sigma model with a topological term that is responsible for its low-energy properties, and we benchmark our predictions with Matrix-Product-State numerical simulations.

On nonstationary radiation fields in an infinite one-dimensional homogeneous medium

This paper considers nonstationary monochromatic radiative transfer in an infinite onedimensional homogeneous medium. The medium is considered to be illuminated by a momentary isotropic point energy source. The optical properties of the medium are characterized by the absorption coefficient α, the single-scattering albedo λ, the mean time t 1 of photon stay in the absorbed state, and the mean time t 2 of its stay on the path between two consecutive scatterings. The exact solution of the nonstationary radiative transfer equation has been obtained for the case t 1 = t 2. Asymptotic expressions have been derived for the source function, for the average intensity, and for radiation flux when points of the medium are located at large optical distances from the power source |τ| ≫ 1 and for small absorption of light in the medium (1 − λ ≪ 1), assuming that t 1 ≫ t 2, t 1 ≪ t 2, or t 1 = t 2. These expressions are more precise than the ones previously known.

Incommensurate spiral magnetic order on anisotropic triangular lattice: Dynamical mean-field study in a spin-rotating frame

We study the ground-state magnetism of the half-filled Hubbard model on the anisotropic triangular lattice, where two out of three bonds have hopping $t$ and the third one has $t^\prime$ in a unit triangle. Working in a spin-rotating frame and using the density matrix renormalization group method as an impurity solver, we provide a proper description of incommensurate magnetizations at zero temperature in the framework of the dynamical mean-field theory (DMFT). It is shown that the incommensurate spiral magnetic order for $t^\prime/t\gtrsim 0.7$ survives the dynamical fluctuations of itinerant electrons in the Hubbard interaction range from the strong-coupling (localized-spin) limit down to the insulator-to-metal transition. We also find that the magnetic moment reduction from the localized-spin limit is pronounced in the vicinity of the transition between the commensurate N\'eel and incommensurate spiral phases at $t^\prime/t\sim 0.7$. When the anisotropy parameter $t^\prime/t$ increases from the N\'eel-to-spiral transition, the magnitude of the magnetic moment immediately reaches a maximum and then rapidly decreases in the range of larger $t^\prime/t$ including the isotropic triangular lattice point $t^\prime/t=1$. This work gives a solid foundation for further extension of the study including nonlocal correlation effects neglected at the standard DMFT level.

Augmented design and analysis of computer experiments: a novel tolerance embedded global optimization approach applied to SWIR hyperspectral illumination design.

A novel meta-heuristic approach for minimizing nonlinear constrained problems is proposed, which offers tolerance information during the search for the global optimum. The method is based on the concept of design and analysis of computer experiments combined with a novel two phase design augmentation (DACEDA), which models the entire merit space using a Gaussian process, with iteratively increased resolution around the optimum. The algorithm is introduced through a series of cases studies with increasing complexity for optimizing uniformity of a short-wave infrared (SWIR) hyperspectral imaging (HSI) illumination system (IS). The method is first demonstrated for a two-dimensional problem consisting of the positioning of analytical isotropic point sources. The method is further applied to two-dimensional (2D) and five-dimensional (5D) SWIR HSI IS versions using close- and far-field measured source models applied within the non-sequential ray-tracing software FRED, including inherent stochastic noise. The proposed method is compared to other heuristic approaches such as simplex and simulated annealing (SA). It is shown that DACEDA converges towards a minimum with 1 % improvement compared to simplex and SA, and more importantly requiring only half the number of simulations. Finally, a concurrent tolerance analysis is done within DACEDA for to the five-dimensional case such that further simulations are not required.

The spin-half XXZ antiferromagnet on the square lattice revisited: A high-order coupled cluster treatment

We use the coupled cluster method (CCM) to study the ground-state properties and lowest-lying triplet excited state of the spin-half XXZ antiferromagnet on the square lattice. The CCM is applied to it to high orders of approximation by using an efficient computer code that has been written by us and which has been implemented to run on massively parallelized computer platforms. We are able therefore to present precise data for the basic quantities of this model over a wide range of values for the anisotropy parameter Δ in the range −1≤Δ<∞ of interest, including both the easy-plane (−1<Δ<1) and easy-axis (Δ>1) regimes, where Δ→∞ represents the Ising limit. We present results for the ground-state energy, the sublattice magnetization, the zero-field transverse magnetic susceptibility, the spin stiffness, and the triplet spin gap. Our results provide a useful yardstick against which other approximate methods and/or experimental studies of relevant antiferromagnetic square-lattice compounds may now compare their own results. We also focus particular attention on the behaviour of these parameters for the easy-axis system in the vicinity of the isotropic Heisenberg point (Δ=1), where the model undergoes a phase transition from a gapped state (for Δ>1) to a gapless state (for Δ≤1), and compare our results there with those from spin-wave theory (SWT). Interestingly, the nature of the criticality at Δ=1 for the present model with spins of spin quantum number s=12 that is revealed by our CCM results seems to differ qualitatively from that predicted by SWT, which becomes exact only for its near-classical large-s counterpart.