Diffusion Approximation Research Articles

Optimal Reinsurance–Investment Strategy Based on Stochastic Volatility and the Stochastic Interest Rate Model

This paper studies insurance companies’ optimal reinsurance–investment strategy under the stochastic interest rate and stochastic volatility model, taking the HARA utility function as the optimal criterion. It uses arithmetic Brownian motion as a diffusion approximation of the insurer’s surplus process and the variance premium principle to calculate premiums. In this paper, we assume that insurance companies can invest in risk-free assets, risky assets, and zero-coupon bonds, where the Cox–Ingersoll–Ross model describes the dynamic change in stochastic interest rates and the Heston model describes the price process of risky assets. The analytic solution of the optimal reinsurance–investment strategy is deduced by employing related methods from the stochastic optimal control theory, the stochastic analysis theory, and the dynamic programming principle. Finally, the influence of model parameters on the optimal reinsurance–investment strategy is illustrated using numerical examples.

Information encoded in gene-frequency trajectories

In this work we present a systematic mathematical approximation scheme that exposes the way that information, about the evolutionary forces of selection and random genetic drift, is encoded within gene-frequency trajectories. We determine approximate, time-dependent, gene-frequency trajectory statistics, assuming additive selection. We use the probability of fixation to test and illustrate the approximation scheme introduced. For the case where the strength of selection and the effective population size have constant values, we show how a standard diffusion approximation result, for the probability of fixation, systematically emerges when increasing numbers of approximate trajectory statistics are taken into account. We then provide examples of how time-dependent parameters influence gene-frequency statistics.

Fuel loading pattern optimization of ALLEGRO fast reactor using the tabu search metaheuristic technique

In this work an improved tabu search (TS) optimization technique is used to find the optimal fuel loading pattern in the experimental fast reactor ALLEGRO. The penalty function method is used to solve this multi-objective combinatorial optimization problem. The objective function and constrains are computed via an interface between the developed optimizer and the ERANOS 2.3 deterministic code. To reduce the running time, the operating cycle simulation is carried out using the diffusion approximation and a 7-group neutron energy structure. The proposed objective function maximizes the k-eff value at the end of cycle, satisfying the maximum power factor, the excess hot reactivity, and the linear heat generation rate constraints. A novel procedure developed in ERANOS to perform fuel assembly swaps for neighbor search is presented. The algorithm performed as expected throughout the iterative process and, unlike other metaheuristics based on local search, did not get stuck in local optima, which is a well-known advantage of tabu search technique.

Asymptotic Diffusion Method for Retrial Queues with State-Dependent Service Rate

In this paper, we consider a retrial queue with a state-dependent service rate as a mathematical model of a node of FANET communications. We suppose that the arrival process is Poisson, the delay duration is exponentially distributed, the orbit is unlimited, and there is multiple random access from the orbit. There is one server, and the service time of every call is distributed exponentially with a variable parameter depending on the number of calls in the orbit. The service rate has an infinite number of values. We propose the asymptotic diffusion method for the model study. The asymptotic diffusion approximation of the probability distribution of the number of calls in the orbit is derived. Some numerical examples are demonstrated.

An inverse source problem for linearly anisotropic radiative sources in absorbing and scattering medium

We consider in a two dimensional absorbing and scattering medium, an inverse source problem in the stationary radiative transport, where the source is linearly anisotropic. The medium has an anisotropic scattering property that is neither negligible nor large enough for the diffusion approximation to hold. The attenuating and scattering properties of the medium are assumed known. For scattering kernels of finite Fourier content in the angular variable, we show how to recover the anisotropic radiative sources from boundary measurements. The approach is based on the Cauchy problem for a Beltrami-like equation associated with A-analytic maps. As an application, we determine necessary and sufficient conditions for the data coming from two different sources to be mistaken for each other.

Albedo method applied for gamma radiation shielding

Mathematical tools for calculating radiation shielding usually have difficult notations that could only be solved by computational methods. The Albedo’s method applied for calculation of shielding proves to be an excellent substitute in determining the incident beam fractions that are reflected, absorbed and transmitted, avoiding the use of the transport equation and diffusion approximation that are extremely important in nuclear reactor designs and irradiation calculations. Based on the simple following of the radiation current path, the method can be characterized as a graphical and analytical solution. This work explores the Albedo’s Method applied to 4-slab shielding with incidence of gamma radiation to an energy group compared to ANISN, computational method consecrated in the area of ​​nuclear calculations.

Effects of atlas-based anatomy on modelled light transport in the neonatal head

Objective. Diffuse optical tomography (DOT) provides a relatively convenient method for imaging haemodynamic changes related to neuronal activity on the cerebral cortex. Due to practical challenges in obtaining anatomical images of neonates, an anatomical framework is often created from an age-appropriate atlas model, which is individualized to the subject based on measurements of the head geometry. This work studies the approximation error arising from using an atlas instead of the neonate's own anatomical model. Approach. We consider numerical simulations of frequency-domain (FD) DOT using two approaches, Monte Carlo simulations and diffusion approximation via finite element method, and observe the variation in (1) the logarithm of amplitude and phase shift measurements, and (2) the corresponding inner head sensitivities (Jacobians), due to varying segmented anatomy. Varying segmentations are sampled by registering 165 atlas models from a neonatal database to the head geometry of one individual selected as the reference model. Prior to the registration, we refine the segmentation of the cerebrospinal fluid (CSF) by separating the CSF into two physiologically plausible layers. Main results. In absolute measurements, a considerable change in the grey matter or extracerebral tissue absorption coefficient was found detectable over the anatomical variation. In difference measurements, a small local 10%-increase in brain absorption was clearly detectable in the simulated measurements over the approximation error in the Jacobians, despite the wide range of brain maturation among the registered models. Significance. Individual-level atlas models could potentially be selected within several weeks in gestational age in DOT difference imaging, if an exactly age-appropriate atlas is not available. The approximation error method could potentially be implemented to improve the accuracy of atlas-based imaging. The presented CSF segmentation algorithm could be useful also in other model-based imaging modalities. The computation of FD Jacobians is now available in the widely-used Monte Carlo eXtreme software.

Heat transfer properties of dusty radiative cooling surface: Modeling and experimental studies

Radiative cooling has shown great potential for energy saving in different sectors. However, performance of a radiative cooling surface is easily affected by dust deposition at outdoors. In this work, we employed the equivalent particle model and the Rosseland diffusion approximation model to predict the heat transfer properties of radiative cooling surface with three different levels of dust deposition (low / medium / high). The models were then validated by experimental data. Theoretical and experimental results show that at low level of dust deposition, the reduction of net cooling power is about 7.1 W/m2 for every 0.1 mg/cm2 increase of dust mass. At medium level of dust deposition, the heat flow characteristics of dusty radiative cooling surface changes from outflow (i.e., cooling) to inflow (i.e., heating). The net heat gain is about 6.4 W/m2 for every 0.1 mg/cm2 increase of dust mass. At high level of dust deposition, the net heat gain gradually increases to a constant value with the increasing of dust mass, and even if the surface is fully covered by dust, it could still reduce the net heat gain by at least 10% in comparison with the concrete roof. This work could provide new insights into the heat transfer processes of dusty radiative cooling surface.

The magnetic field design of a solenoid for the cold-cathode Penning ion source of a miniature neutron tube

A high-yield and beam-stable neutron tube can be applied in many fields. It is of great significance to the optimal external magnetic field intensity of the cold-cathode Penning ion source (PIS) and precisely controls the movement of deuterium (D), tritium (T) ions and electrons in the source of the neutron tubes. A cold-cathode PIS is designed based on the solenoidal magnetic field to obtain better uniformity of the magnetic field and higher yield of the neutron tube. The degree of magnetic field uniformity among the magnetic block, double magnetic rings and solenoidal ion sources is compared using finite element simulation methods. Using drift diffusion approximation and a magnetic field coupling method, the plasma distribution of hydrogen and the relationship between plasma density and magnetic field intensity at 0.06 Pa pressure and a solenoid magnetic field are obtained. The results show that the solenoidal ion source has the most uniform magnetic field distribution. The optimum magnetic field strength of about 0.1 T is obtained in the ion source at an excitation voltage of 1 V. The maximum average number density of monatomic hydrogen ions (H+) is 1 × 108 m−3, and an ion-beam current of about 14.51 μA is formed under the −5000 V extraction field. The study of the solenoidal magnetic field contributes to the understanding of the particle dynamics within the PIS and provides a reference for the further improvement of the source performance of the neutron tube in the future.

The spatial Λ-Fleming–Viot process in a random environment

We study the large scale behaviour of a population consisting of two types which evolve in dimension d=1,2 according to a spatial Lambda-Fleming–Viot process subject to random time-independent selection. If one of the two types is rare compared to the other, we prove that its evolution can be approximated by a super-Brownian motion in a random (and singular) environment. Without the sparsity assumption, a diffusion approximation leads to a Fisher–KPP equation in a random potential. The proofs build on two-scale Schauder estimates and semidiscrete approximations of the Anderson Hamiltonian.

Multiphysics modeling of a reactivity insertion transient at different fidelity levels in support to the safety assessment of a SMART-like small modular reactor

Typical design basis accidents such as the control Rod Ejection Accident (REA) will need to be evaluated during the safety analysis in support the licensing processes for most of the current Small Modular Reactors (SMRs) designs. In this paper a study related to the neutronic and thermal-hydraulic coupled modelling of a REA transient for a boron-free SMART-like core at different fidelity levels is presented. Two different solutions for the core at hot zero power state (HZP) are provided; the first one is based on the standard nodal two-steps approach using the diffusion approximation and the second one is characterized by a more accurate high-fidelity scheme based on Monte Carlo neutronics coupled to subchannel-level thermal-hydraulics allowing performing full core pin-by-pin transient analysis. In the paper the details of the two different modelling approaches are presented and the corresponding results are compared one to each other, allowing on one side to verify the results of the high-fidelity modelling against a standard nodal-based solution and on the other side to highlight the added value when using a better resolution which allows to compute safety parameters at the local level with the consequent possibility to reduce the safety margins.

Numerical Simulation of a Light Field Structure in an Integrating Sphere via the Monte Carlo Method

The integrated cavity absorption meter is designed to measure the seawater absorption coefficient spectra which are necessary for studying ocean productivity and heat balance. The performed numerical simulations of a light field structure made it possible to improve the measurement technique. Its results showed that the use of the Lambertian model allows to reduce the calculation time by two orders of magnitude with an acceptable loss of accuracy for these calculations. It is shown that in the case of an integrating sphere made of fluorilon, the use of different volume scattering functions does not affect the calculation result, which is not true in the case of using a sphere with a mirror coating. The effect of an air layer between quartz and fluorilon is considered, and the applicability of the diffusion approximation is verified. Examples of field measurements of the seawater absorption coefficient and its components performed in different water areas of the World Ocean in 2020–2022 are presented.

Assessment of Drying Temperature and Initial Moisture on Beans and Corn Seeds Drying Kinetics and Transport Properties

The purpose of this study is to assess the drying temperature and initial moisture content on beans and corn seeds drying kinetics and transport properties. It was verified that the best empirical lumped models fitting whereas obtained by Approximation of Diffusion and Hii, Law and Cloke models. This was expected because the fitting tends to improve as the model has more parameters. However, despite having only two parameters, the Page model showed good fitting in all conditions analyzed, therefore, this generalized model could predict experimental data with a maximum global deviation of around 10.0 %. The distributed parameter model assessed moisture content distribution inside the grain, which could predict experimental data with an overall deviation of around 10.0 %. Results indicated that both drying temperature and initial moisture have a significant influence on drying rates and mass transfer coefficients and verified that it is not advisable to neglect the influence of the initial moisture content and its distribution along the position inside the material for beans and corn seeds drying studies.

Physics-guided neural network for tissue optical properties estimation.

Finding the optical properties of tissue is essential for various biomedical diagnostic/therapeutic applications such as monitoring of blood oxygenation, tissue metabolism, skin imaging, photodynamic therapy, low-level laser therapy, and photo-thermal therapy. Hence, the research for more accurate and versatile optical properties estimation techniques has always been a primary interest of researchers, especially in the field of bioimaging and bio-optics. In the past, most of the prediction methods were based on physics-based models such as the pronounced diffusion approximation method. In more recent years, with the advancement and growing popularity of machine learning techniques, most of the prediction methods are data-driven. While both methods have been proven to be useful, each of them suffers from several shortcomings that could be complemented by their counterparts. Thus, there is a need to bring the two domains together to obtain superior prediction accuracy and generalizability. In this work, we proposed a physics-guided neural network (PGNN) for tissue optical properties regression which integrates physics prior and constraint into the artificial neural network (ANN) model. With this method, we have demonstrated superior generalizability of PGNN compared to its pure ANN counterpart. The prediction accuracy and generalizability of the network were evaluated on single-layered tissue samples simulated with Monte Carlo simulation. Two different test datasets, the in-domain test dataset and out-domain dataset were used to evaluate in-domain generalizability and out-domain generalizability, respectively. The physics-guided neural network (PGNN) showed superior generalizability for both in-domain and out-domain prediction compared to pure ANN.

Diffusion approximation of a network model of meme popularity

Diffusion approximation of a network model of meme popularity

“Gradient-free” diffuse approximations of the Willmore functional and Willmore flow

We introduce new diffuse approximations of the Willmore functional and the Willmore flow. They are based on a corresponding approximation of the perimeter that has been studied by Amstutz-van Goethem [Interfaces Free Bound. 14 (2012)]. We identify the candidate for the Γ-convergence, prove the Γ-limsup statement and justify the convergence to the Willmore flow by an asymptotic expansion. Furthermore, we present numerical simulations that are based on the new approximation.

Weakly interacting massive particle cross section limits from LOFAR observations of dwarf spheroidal galaxies

Context. Weakly interacting massive particles (WIMPs) can self-annihilate, thus providing us with a way to indirectly detect dark matter (DM). Dwarf spheroidal (dSph) galaxies are excellent places to search for annihilation signals because they are rich in DM and background emission is low. If O(0.1–10 μG) magnetic fields in dSph galaxies exist, the particles produced in DM annihilation emit synchrotron radiation in the radio band. Aims. We used the non-detection of 150 MHz radio continuum emission from dSph galaxies with the LOw Frequency ARray (LOFAR) to derive constraints on the annihilation cross section of WIMPs in electron–positron pairs. Our main underlying assumption is that the transport of the cosmic rays can be described by the diffusion approximation, which necessitates the existence of magnetic fields. Methods. We used observations of six dSph galaxies in the LOFAR Two-metre Sky Survey (LoTSS). The data were reimaged, and a radial profile was generated for each galaxy. We also used stacking to increase the sensitivity. In order to derive upper limits on the WIMP cross section, we injected fake Gaussian sources into the data, which were then detected with 2σ significance in the radial profile. These sources represent the lowest emission we would have been able to detect. Results. We present limits from the observations of individual galaxies as well as from stacking. We explored the uncertainty due to the choice of diffusion and magnetic field parameters by constructing three different model scenarios: optimistic (OPT), intermediate (INT), and pessimistic (PES). Assuming monochromatic annihilation into electron–positron pairs, the limits from the INT scenario exclude thermal WIMPs (⟨σv⟩≈2.2 × 10−26 cm3 s−1) below 20 GeV, and the limits from the OPT scenario even exclude thermal WIMPs below 70 GeV. The INT limits can compete with limits set by Fermi-LAT using γ-ray observations of multiple dwarf galaxies, and they are especially strong for low WIMP masses.

Jeans Instability of an Astrophysical Self-Gravitating Medium in the Presence of High Radiation Pressure and Diffuse Radiative Transfer

Within the problem of modeling the evolution of a protostellar disk, a discussion is presented on the effect of radiation on the Jeans gravitational instability for a self-gravitating optically thick (for intrinsic infrared radiation) gas-and-dust medium, taking into account the influence of radiation pressure perturbations and radiative diffusion transfer on the critical wavelength. Two radiative diffusion approximations are considered: the case of perfect thermal equilibrium with the same temperature of matter and radiation and the case of the time dependence of the radiation field with an energy separation between radiation and matter. An analysis of the normal regime of modes is used to derive dispersion relations, which enable the derivation of modifications of the classical Jeans instability criterion under the influence of radiation pressure and radiation diffusion. In particular, it is shown that, in contrast to the system’s local thermodynamic equilibrium, where the acoustic velocity of perturbed gas propagates with the isothermal speed of sound, in the case of different temperatures of radiation and gas, the perturbing wave propagates with the adiabatic speed of sound in gas. The results obtained are aimed at solving the problem of gravitational instability of individual massive protostellar disks or self-gravitating radiative media characterized by large optical depths for their dust-transformed intrinsic infrared radiation.

Large time behavior of solutions to a diffusion approximation radiation hydrodynamics model

This paper concerns the large time behavior of solutions to a diffusion approximation radiation hydrodynamics model when the initial data is a small perturbation around an equilibrium state. The global-in-time well-posedness of solutions is achieved in Sobolev spaces depending on the Littlewood-Paley decomposition technique together with certain elaborate energy estimates in frequency space. Moreover, the optimal decay rates of solutions are also derived provided the initial data satisfy an additional L1 condition. Meanwhile, the same decay rates of the solutions to the approximation system without thermal conductivity could also be established.

Evolution with recombination as Gibbs sampling

This work presents a population genetic model of evolution, which includes haploid selection, mutation, recombination, and drift. The mutation-selection equilibrium can be expressed exactly in closed form for arbitrary fitness functions without resorting to diffusion approximations. Tractability is achieved by generating new offspring using n-parent rather than 2-parent recombination. While this enforces linkage equilibrium among offspring, it allows analysis of the whole population under linkage disequilibrium. We derive a general and exact relationship between fitness fluctuations and response to selection. Our assumptions allow analytical calculation of the stationary distribution of the model for a variety of non-trivial fitness functions. These results allow us to speak to genetic architecture, i.e., what stationary distributions result from different fitness functions. This paper presents methods for exactly deriving stationary states for finite and infinite populations. This method can be applied to many fitness functions, and we give exact calculations for four of these. These results allow us to investigate metastability, tradeoffs between fitness functions, and even consider error-correcting codes.