The contributions of coherent bright‐field phase and incoherent dark‐field amplitude contrast are investigated for thick biological specimens. A model for a T4 phage is constructed and images simulated for both TEM and STEM phase contrast using a multislice code. For TEM, the fraction of the illumination intensity available for phase contrast imaging is limited by the fraction of electrons in the zero loss peak, the plasmon peak, or the Landau distribution peak for very thick specimens. These were measured from electron energy loss spectra recorded from various thicknesses of vitreous ice. The incoherent amplitude contrast is simulated using the Penelope Monte Carlo code. Noise limits the features that can be distinguished under the low‐dose conditions required for cryo‐EM, even for high electron exposures of 100 electrons/Å2. Since in STEM post specimen optics are not used to form the image inelastically scattered electrons contribute to the recorded intensity. In principle STEM should have an advantage over TEM not just for incoherent amplitude contrast but also for coherent phase contrast beyond the limit of weak phase. The simulations suggest that it should be possible to image features in the phage embedded in 1 µm of vitreous ice when collection angles are optimised for bright or dark‐field signals, with best contrast achieved for accelerating voltages of about 700 keV.

We present a simulation configuration for the electron beam profile consistent with experiments on the linear accelerator UERL-10-15S2, focusing on determining electron energy and beam size. Two essential aspects of the electron beam described in the simulation configuration are the initial energy distribution and the initial beam size with the flux distribution. Notably, we introduce a new mathematical function by modifying the approximated Landau distribution. This new function offers a better fit than our previous mathematical function and, more importantly, accurately reflects the physical nature of the energy spectrum of electrons passing through a thin layer of matter. Using this configuration, we have simulated the irradiation of zeolite ETS-10 by the electron beam. This irradiated simulation was set up with various electron energy distributions, yielding results on the dose rate distribution (2D dose map) and the mean absolute percentage deviation of the absorbed dose rate within the irradiated titanosilicate. With the improvements in this paper, we have provided a solution to enhance the linear accelerator’s application in scientific research besides conventional industrial irradiation applications. Published by the American Physical Society 2025

Abstract Assuming the beam spectrum at the accelerator output follows a Gaussian distribution and its attenuation in air is described by a Landau distribution, the ill-posed problem of electron energy spectrum reconstruction using depth-dose distribution was reduced to finding the electron spectrum at the phantom surface as a convolution of the Landau and Gaussian distributions. The algorithm proposed in the study uses the experimentally measured depth dose distributions generated by Varian TrueBeam medical accelerator operating at 6 MeV and 9 MeV modes in water-equivalint and aluminium phantoms and reconstructs the electron spectra in targeted materials. The algorithm uses reference depth dose distributions from monoenergetic electrons calculated using Geant4 toolkit. It was found that the spectra reconstructed using experimental depth dose distributions in solid water and aluminium differ by less than 5%, and reconstructed depth dose distributions corresponding to the reconstructed spectra deviate from experimentally measured ones by no more than 5%.

The exponential dispersion model (EDM) generated by the Landau distribution, denoted by EDM-EVF (exponential variance function), belongs to the Tweedie scale with power infinity. Its density function does not have an explicit form and, as of yet, has not been used for statistical aspects. Out of all EDMs belonging to the Tweedie scale, only two EDMs are steep and supported on the whole real line: the normal EDM with constant variance function and the EDM-EVF. All other absolutely continuous steep EDMs in the Tweedie scale are supported on the positive real line. This paper aims to accomplish an overall picture of all generalized linear model (GLM) applications belonging to the Tweedie scale by including the EDM-EVF. This paper introduces all GLM ingredients needed for its analysis, including the respective link function and total and scaled deviance. We study its analysis of deviance, derive the asymptotic properties of the maximum likelihood estimation (MLE) of the covariate parameters, and obtain the asymptotic distribution of deviance, using saddlepoint approximation. We provide numerical studies, which include estimation algorithm, simulation studies, and applications to three real datasets, and demonstrate that GLM using the EDM-EVF performs better than the linear model based on the normal EDM. An R package accompanies all of these.

The paper comprehensively studies the natural exponential family and its associated exponential dispersion model generated by the Landau distribution. These families exhibit probabilistic and statistical properties and are suitable for modeling skewed continuous data sets on the whole real line. The study explores and further develops various probabilistic properties, including reciprocity, self-decomposability, reproducibility, unimodality, and characterizations. It delves into statistical aspects such as maximum-likelihood estimation, hypothesis testing, and generalized linear models.

Previously [D. K. Wilson, M. J. Kamrath, C. E. Haedrich, D. J. Breton, and C. R. Hart, J. Acoust. Soc. Am. 150(2), 783–800 (2021)], it was suggested that the probability distribution for sound levels in an urban environment could be usefully modeled with N randomly placed, independent sources in a circular region, with the receiver at the center. The sound decays away from the sources by a geometrical spreading law. With these assumptions, the received sound power consists of the sum of N Pareto-distributedrandom variables. Although an analytical solution for this sum is unavailable, some positively skewed, heavy-tailed distributions, such as the exponentially modified Gaussian distribution, provide reasonable approximations. The present study is motivated by the observation that, in the limit of large N, the Pareto sum must converge to a stable distribution; in particular, for spherical spreading, the limiting distribution is a Landau distribution. We have furthermore found that when N is drawn from a Poisson distribution, the Landau distribution is nearly exact for as few as eight sources. Hence, the Landau distribution provides a suitable general model for urban noise and other situations involving multiple, randomly placed sources.

We consider a fluctuation test experiment in which cell colonies were grown from a single cell until they reach a given population size and were then exposed to treatment. While they grow, the cells may, with a low probability, acquire resistance to treatment and pass it on to their offspring. Unlike the classical Luria–Delbrück fluctuation test, and motivated by recent work on drug-resistance acquisition in cancer/microbial cells, we allowed the resistant cell state to switch back to a drug-sensitive state. This modification did not affect the central part of the Luria–Delbrück distribution of the number of resistant survivors: the previously developed approximation by the Landau probability density function applied. However, the right tail of the modified distribution deviated from the power law decay of the Landau distribution. Here, we demonstrate that the correction factor was equal to the Landau cumulative distribution function. We interpreted the appearance of the Landau laws from the standpoint of singular perturbation theory and used the asymptotic matching principle to construct uniformly valid approximations. Additionally, we describe the corrections to the distribution tails in populations initially consisting of multiple sensitive cells, a mixture of sensitive and resistant cells, and a cell with a randomly drawn state.

The ionization loss of a high-energy electron–positron pair in thin targets is considered. The targets not thinner than about 10 upmu m are discussed. The analogue of the Landau distribution function is derived for this loss under the condition when the Chudakov effect of the pair ionization loss suppression is manifested. Expression for the most probable value of the pair ionization loss E_{MP} is obtained. It is shown that the magnitude of Chudakov effect for E_{MP} can be noticeably different from the magnitude of this effect for the restricted mean value of the pair ionization loss.

Shashlik tower, which is composed of absorbers and scintillators alternately, surrounded by reflector and coupled with Silicon Photomultiplier (SiPM) by Wavelength-Shifting (WLS) fibers, is a significant component to measure the energy and position of photons and electrons in Electromagnetic Calorimeter (ECal), a key detector of the Multi Purpose Detector (MPD) at the Nuclotron-based Ion Collider facility (NICA) in Russia. In this paper, the effect of materials adopted for absorber, reflector and WLS fiber, the length and curvature of fibers and the electrons incident position on photons transmission performance of tower is simulated based on GEANT4 software. The impact of Gaussian deviation's electron beam energy and spread of 10% in the energy range on the energy resolution of tower is also studied. Results show that the low polishing degree absorber, the high polishing degree TiO_2 reflector and the type of Y-11 WLS fibers bent with a curvature radius of greater than 11 cm can significantly improve the light output. In addition, electrons injected along the centre of tower can make photons position distribution in SiPM more uniform. The generation time of photons in scintillators and time of arrival at the SiPM both obey the Landau distribution. Finally, the energy resolution of tower can be better than 3.8%/√(E) (GeV) for a Gaussian deviation's electron beam with an average energy of 3 GeV and spread of 10% in the energy range.

When a fast charged particle passes through matter, it loses some of its energy to the excitation and ionization of atoms. This energy loss is called ionization energy loss. In rather thin layers of matter, the value of such energy loss is stochastic. It is distributed in accordance with the law, which was first received by L.D. Landau. In amorphous substances, such a distribution (or spectrum), known as the Landau distribution, has a single maximum that corresponds to the most probable value of particle energy loss. When a particle moves in crystal in a planar channeling mode, the probability of close collisions of the particle with atoms decreases (for a positive particle charge) or increases (for a negative charge), which leads to a change in the most probable energy loss compared to an amorphous target. It has recently been shown that during planar channeling of negatively charged particles in a crystal, the distribution of ionization energy loss of the particles is much wider than in the amorphous target. In this case, this distribution can be two-humped, if we neglect the incoherent scattering of charged particles on the thermal oscillations of the crystal atoms and the electronic subsystem of the crystal. This paper explains the reason for this distribution of ionization energy loss of particles. The ionization energy loss distribution of high-energy negatively charged particles which move in the planar channeling mode in a silicon crystal are studied with the use of numerical simulation. The dependence of this distribution on the impact parameter of the particles with respect to atomic planes is considered. The dependence of the most probable ionization energy loss of particles on the impact parameter is found. It is shown that, for a large group of particles, the most probable ionization energy loss during planar channeling in a crystal is lower than in an amorphous target.

We report on silicon carbide (SiC) p-n junction diodes with a high blocking voltage over 3 kV. Although SiC radiation sensors have been developed with a Schottky barrier type due to a simple fabrication process in the early stages, p-n junction structures are advantageous due to lower sensitivity of the surface defects. Thus, this system provides an ideal condition to investigate the effect of bulk crystal defects on the characteristics of the radiation sensor. The p-n diodes were designed with a device simulator and fabricated with a 4-in 4H-SiC wafer. The epitaxial layer was grown on an n-type substrate with sufficiently low doping concentration of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N_{\mathrm{ d}}} - {N_{\mathrm{ a}}}=\sim 5\times 10^{14} {\mathrm{ cm}}^{-3}$ </tex-math></inline-formula> and an average thickness of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$52 ~\mu {\mathrm{ m}}$ </tex-math></inline-formula> . Fabricated p-n diodes with a relatively large leakage current still show a clear peak of the Landau distribution in the charge spectrum, suggesting their practical availability as minimum ionizing particle (MIP) detectors. The estimated electron–hole pair creation energy is consistent with the published studies and we expect good radiation tolerance. Feasibility based on the wafer processing indicates that the prototype devices are a good candidate for the muon beam monitor application in the COherent Muon-to-Electron Transition (COMET) experiment at Japan Proton Accelerator Research Complex (J-PARC).

We evaluate the hit rate of cosmic rays and their daughter particles on the Si:As IBC detectors in the IRAC instrument on the Spitzer Space Telescope. The hit rate follows the ambient proton flux closely, but the hits occur at more than twice the rate expected just from this flux. Toward large amplitudes, the size distribution of hits by single-charge particles (muons) follows the Landau Distribution. The amplitudes of the hits are distributed to well below the energy loss of a traditional “average minimum-ionizing proton” as a result of statistical fluctuations in the ionization loss within the detectors. Nonetheless, hits with amplitudes less than a few hundred electrons are rare; this places nearly all hits in an amplitude range that is readily identified given the read noises of modern solid-state detectors. The spread of individual hits over multiple pixels is dominated by geometric effects, i.e., the range of incident angles, but shows a modest excess probably due to: (1) showering and scattering of particles; (2) the energy imparted on the ionization products by the energetic protons; and (3) interpixel capacitance. Although this study is focused on a specific detector type, it should have general application to operation of modern solid-state detectors in space.

This paper presents the performance of a 3GEM in terms of identification of high and low beta energy radiation sources through the energy distribution of the main beta radiation sources used for industrial application 90Sr and 204Tl. We compare the beta radiation theoretical energy loss into the drift zone with experimental energy distribution at different 3GEM voltages. The experimental results show that the Most Probable Value (MPV) of the fitted Landau distribution obtained from 90Sr and 204Tl obtained a degree of error lower than 14% in comparison to the theoretical calculation. Additionally, high energy beta radiation source (90Sr) is identified in comparison to low energy (204Tl) - taking into account the MPV and sigma values from the fitted Landau distribution. These results are essential to design and implement a new application that utilizes the performance and special characteristics of the 3GEM for beta radiation detection and identification.

Mistiming Death: Modeling the Time-Domain Variability of Tumor Apoptosis and Implications for Molecular Imaging of Cell Death.

We have investigated the influence of a strong magnetic field on various aspects of a quantum Fermi plasma. Due to the strong magnetic field, the distribution function becomes anisotropic. First, we consider non-degenerate quantum, Landau and Kelly distribution function. It was found that the adiabatic equation is similar to the adiabatic equation for a Maxwell distribution function, when we include the magnetic field in the energy expression. Using the Kelly distribution for a degenerate, quantum Fermi gas, parallel and perpendicular components of the pressure were derived. It was found that perpendicular component of pressure never becomes zero and three-dimensional system always stay three-dimensional. Lastly, we investigated electron emission from metals and have shown the influence of the magnetic field. We calculated thermionic emission, the so-called Richardson effect. In addition, we investigate the influence of external electromagnetic radiation on the electron current density (Hallwachs effect) from metals.

The quality control of thin film thickness measurements through the transmission and counting of beta and X-ray radiation has achieved very competitive precision with values to 0.2%. However, when the attenuated intensities by the thin film under measurement is above 90%, the method of counting beta or X-ray radiation generates a dramatic degradation in the precision to 30%. This work presents a new method to obtain and analyze thicknesses of aluminum and copper thin films using energy distribution information provided by a triple gas electron multiplier detector (3GEM). The method is based on the ratio of the peak of the Landau distribution generated by the background detection and the peak of the Gaussian distribution of soft X-ray photons generated by the radiation transmission through the thin films emitted by a 55Fe radiation source. The results improve the thickness measurement precision with respect to the radiation counting method when the intensity attenuated by the thin film is greater than 95% compared to precision values less than or equal to 30% obtained with the counting method to values below 10% achieved with the newly reported energy distribution method.

Exploring the sampling rate effect on digital time of flight response for fast scintillator detectors

Quality assurance (QA) is required when performing pencil-beam scanning proton therapy, but the efficiency of QA is degraded in proportion to the energy of the protons. We developed a method to assess the preferred energy range and distal fall-off by combining multiple Bragg peaks to increase the efficiency of QA. Beams of 70, 110, 150, 190, and 230 MeV for exposure were planned using a treatment planning system. The Bragg curves for therapeutic proton beams were modeled using three different fitting function models, allowing the feasibility of a simple modeling of the Bragg curve to be investigated. The planned beams were exposed and measured using a multi-layered ionization chamber. Software developed using a Python tool could detect five Bragg peaks from the integrated curves that were fitted based on polynomial, cubic spline and Landau distributions. This software could calculate the range and distal fall-off of the five fitted peaks. For the verification of the accuracy of this method, the calculated results were compared with the range and distal falloff obtained by exposing and analyzing five single-energy beams individually. Comparisons of the Bragg peaks for the five energies exposed individually with the results obtained by exposing them all at once showed that the ranges of the energy beams when using the polynomial fitting and the cubic spline modes were 0.16 mm and 0.10 mm longer, respectively, while the distal fall-offs were 0.14 mm and 0.06 mm shorter, respectively. When using the Landau distribution fitting, the range was 0.06 mm longer and the distal fall-off was 0.04 mm shorter. Analyses of the ranges and distal fall-offs of the five energy beams exposed at once with single-beam loading by using the method developed in this study showed no significant differences from the results obtained by exposing the energy beams individually. Thus, range verification QA by using the proposed method is not only suitable for single-proton beams with multiple energies but also reduces the measurement time.

The impact of incorporating shell-corrections to energy loss in silicon

In this work, the results of the measurements of characteristics of 40-cm and 2-m scintillation counters irradiated by a particle beam with a momentum of 7 GeV/c from the accelerator of the Institute for High Energy Physics are presented. The scintillators used in counters are BC-404 and BC-408 scintillators. The counters are viewed from both ends by R1828-01 photomultiplier tubes. The PMT signal spectra are well described by a convolution of the Landau and Gaussian distributions. Their width is determined mainly by fluctuations of ionization energy losses. The time distributions of the signals obey the Gaussian law. For the 40-cm counter, the time resolution is σ(T) = 88 ps; for the 2-m counter, it varies from 120–160 ps in its center to ~100 ps near the end.