Realistic Fluctuations Research Articles

Enhancing valuation of variable annuities in Lévy models with stochastic interest rate

This paper extends the valuation and optimal surrender framework for variable annuities with guaranteed minimum benefits in a Lévy equity market environment by incorporating a stochastic interest rate described by the Hull-White model. This approach frames a more dynamic and realistic financial setting compared to previous literature. We exploit a robust valuation mechanism employing a hybrid numerical method that merges tree methods for interest rate modeling with finite difference techniques for the underlying asset price. This method is particularly effective for addressing the complexities of variable annuities, where periodic fees and mortality risks are significant factors. Our findings reveal the influence of stochastic interest rates on the strategic decision-making process concerning the surrender of these financial instruments. Through comprehensive numerical experiments, and by comparing our results with those obtained through the Longstaff-Schwartz Monte Carlo method, we illustrate how our refined model can guide insurers in designing contracts that equitably balance the interests of both parties. This is particularly relevant in discouraging premature surrenders while adapting to the realistic fluctuations of financial markets. Lastly, a comparative statics analysis with varying interest rate parameters underscores the impact of interest rates on the cost of the optimal surrender strategy, emphasizing the importance of accurately modeling stochastic interest rates.

Caught between two states: The compromise in acclimation of photosynthesis, transpiration and mesophyll conductance to different amplitudes of fluctuating irradiance.

While dynamic regulation of photosynthesis in fluctuating light is increasingly recognized as an important driver of carbon uptake, acclimation to realistic irradiance fluctuations is still largely unexplored. We subjected Arabidopsis thaliana (L.) wild-type and jac1 mutants to irradiance fluctuations with distinct amplitudes and average irradiance. We examined how irradiance fluctuations affected leaf structure, pigments and physiology. A wider amplitude of fluctuations produced a stronger acclimation response. Large reductions of leaf mass per area under fluctuating irradiance framed our interpretation of changes in photosynthetic capacity and mesophyll conductance as measured by three separate methods, in that photosynthetic investment increased markedly on a mass basis, but only a little on an area basis. Moreover, thermal imagery showed that leaf transpiration was four times higher under fluctuating irradiance. Leaves growing under fluctuating irradiance, although thinner, maintained their photosynthetic capacity, as measured through light- and CO2-response curves; suggesting their photosynthesis may be more cost-efficient than those under steady light, but overall may incur increased maintenance costs. This is especially relevant for plant performance globally because naturally fluctuating irradiance creates conflicting acclimation cues for photosynthesis and transpiration that may hinder progress towards ensuring food security under climate-related extremes of water stress.

In the heat of the moment: Including realistic thermal fluctuations results in dramatically altered key population parameters.

Temperature is commonly acknowledged as one of the primary forces driving ectotherm vector populations, most notably by influencing metabolic rates and survival. Although numerous experiments have shown this for a wide variety of organisms, the vast majority has been conducted at constant temperatures and changes therein, while temperature is far from constant in nature, and includes seasonal and diurnal cycles. As fluctuating temperatures have been described to affect metabolic processes at (sub)cellular level, this calls for studies evaluating the relative importance of temperature fluctuations and the changes therein. To gain insight in the effects of temperature fluctuations on ectotherm development, survival, and sex ratio, we developed an inexpensive, easily reproducible, and open-source, Arduino-based temperature control system, which emulates natural sinusoidal fluctuations around the average temperature. We used this novel setup to compare the effects of constant (mean) temperatures, most commonly used in experiments, block schemes, and natural sinusoidal fluctuations as well as an extreme variant with twice its amplitude using the cosmopolitan mosquito species Culex pipiens s.l. as a study organism. Our system accurately replicated the preprogrammed temperature treatments under outdoor conditions, even more accurately than traditional methods. While no effects were detected on survival and sex ratio within the ranges of variation evaluated, development was sped up considerably by including temperature fluctuations, especially during pupation, where development under constant temperatures took almost a week (30%) longer than under natural fluctuations. Doubling the amplitude further decreased development time by 1.5 days. These results highlight the importance of including (natural) oscillations in experiments on ectotherm organisms - both aquatic and terrestrial - that use temperature as a variable. Ultimately, these results have major repercussions for downstream effects at larger scales that may be studied with applications such as ecological niche models, disease risk models, and assessing ecosystem services that rely on ectotherm organisms.

Stable isotope hydrology of a polymictic lake: Capturing transience of groundwater interactions

Although there have been many studies of groundwater inflow to small lakes, no systematic attention has been paid to the role of the time interval in the reliability of transient flow analysis. We addressed this issue in a two-year study of the isotope hydrology and water budget of a small lake in eastern Washington State (USA) that has been subject to limited management over several decades. The weighted local meteoric water line is δ2H = 7.14 δ18O – 5.22, reflecting the impact of convective recycling in this semi-arid region of inland northwestern North America. Groundwater inflow to the lake was quantified over two years using a short-interval isotopic transient mass balance approach. Calculated inflow was less than a fifth of the lake’s total water budget. Unrealistic temporal fluctuation of the calculated inflow was apparently correlated with fluctuation of the observed isotopic ratio of lake water (δL). We obtained realistic lake fluctuation and groundwater–lake exchange estimates by experimenting with the time interval of the isotope mass balance. It is crucial to acknowledge that each lake possesses unique characteristics that influence hydrologic and isotopic variations. Therefore, the optimal time interval for sampling and calculating mass balance may vary among different small lakes. Our findings have implications for long-term studies with frequent interval sampling.

Retaining Landau quasiparticles in the presence of realistic charge fluctuations in cuprates

Retaining Landau quasiparticles in the presence of realistic charge fluctuations in cuprates

Experience with modeling values of the virtual catapult range

The development of a virtual catapult involves the synthesis of knowledge from several fields, namely physics, probability, statistics, regression analysis, and computer science. Our contribution is not focused on the description of the creation of the application from the software point of view, but it presents a method by which it is possible to generate the numerical values of the range of the virtual catapult along with their corresponding variability. When modeling these range values, it is possible to choose the classical theoretical approach, i. e., the physical approach using equations of motion, or to statistically process the measured values obtained by experimenting with a real catapult model. In our case, a statistical approach, specifically the Design of Experiments method, was chosen to estimate the values of the catapult range. The obtained appropriate regression model was used as the output of the statistical analysis of the measured data for point estimates of the range at specific settings of selected parameters of a real catapult. In order for the results of the simulated range values to correspond to the actual range values of the catapult, it was necessary to achieve a realistic fluctuation (randomness) of the results in the simulation of the catapult ranges around the predicted range value obtained from the regression model. This article suggests a way to ensure stochasticity when modeling such types of systems.

Impact of microwave beam scattering by density fluctuations on the electron–cyclotron power deposition profile in tokamaks

Electron–cyclotron waves are a tool commonly used in tokamaks, in particular to drive current. Their ability to drive current in a very localized manner renders them an optimal tool for MHD mode mitigation. However, such applications require high accuracy and good control of the power deposition location to efficiently target the magnetic islands. It has been indirectly observed that the suprathermal electron distribution, resulting from the wave absorption, is broader than what is expected from experimentally-constrained forward drift-kinetic modeling. The present paper explores the possibility that beam scattering through the turbulent edge of the plasma may explain this observed discrepancy. In particular, full-wave studies exhibit three beam broadening regimes, from superdiffusive to diffusive, with an intermediate regime characterized by a Lorentzian beam profile with a slightly increased full-width at half maximum with respect to the quiet plasma case. In the tokamak à configuration variable, dedicated plasma scenarios have been developed to test this hypothesis. A realistic worst-case fluctuation scenario falls into this intermediate beam broadening regime. By comparing the experimental hard x-ray emission from suprathermal electron Bremmstrahlung with the emission calculated by coupling a full-wave model to a Fokker–Planck solver, it is shown that, in the tested cases, the beam broadening is not sufficient to explain the aforementioned discrepancy between simulation and experiment and that another mechanism must play the main role in broadening the suprathermal electron distribution.

Considerations for realistic atmospheric environments: An application to corrosion testing

Measured salt compositions in dust collected over roughly the last decade from surfaces of in-service stainless-steel alloys at four locations around the United States are presented, along with the predicted brine compositions that would result from deliquescence of these salts. The salt compositions vary greatly from ASTM seawater and from laboratory salts (i.e., NaCl or MgCl2) commonly used on corrosion testing. The salts contained relatively high amounts of sulfates and nitrates, evolved to basic pH values, and exhibited deliquescence relative humidity values (RH) higher than seawater. Additionally, inert dust in components were quantified and considerations for laboratory testing are presented. The observed dust compositions are discussed in terms of the potential corrosion behavior and are compared to commonly used accelerated testing protocols. Finally, ambient weather conditions and their influence on diurnal fluctuations in temperature (T) and RH on heated metal surfaces are evaluated and a relevant diurnal cycle for laboratory testing a heated surface has been developed. Suggestions for future accelerated tests are proposed that include exploration of the effects of inert dust particles on atmospheric corrosion, chemistry considerations, and realistic diurnal fluctuations in T and RH. Understanding mechanisms in both realistic and accelerated environments will allow development of a corrosion factor (i.e., scaling factor) for the extrapolation of laboratory-scale test results to real world applications.

Development of a bioenergetics and population dynamics coupled model: A case study of chub mackerel

A bioenergetics and population dynamics coupled model that includes a full life cycle and size/growth-dependent mortality function was developed to better understand stock fluctuations. As an example, the model was applied to chub mackerel (Scomber japonicus) as it shows large stock fluctuations in the western North Pacific. The mortality dependency parameters for growth/size were adjusted to achieve realistic stock fluctuations in the model from 1998 to 2018. Two types of mortality functions were used in the model: one based on both size and growth, and the other based solely on size. An increasing trend of stock fluctuation of chub mackerel in the 2010s was reproduced in the simulation by contributions of several strong monthly cohorts that formed strong year classes using both types of mortality functions. The reproducibility of the stock fluctuation was not markedly different between the models with the two types of mortality functions, which indicates the importance of size-dependent mortality on the stock fluctuations of chub mackerel. The influence of sea surface temperature (SST) and chlorophyll-a was evaluated separately by using the climatological values for one of the forcings, and the model results revealed that the stock fluctuations of chub mackerel during 1998–2018 were mainly controlled by chlorophyll-a, whereas the increasing stock during 2010–2014 was strongly influenced by chlorophyll-a, and that after 2014 was influenced by SST. When integrated with different fishing pressures, the model showed that high fishing pressure hinders the recovery of chub mackerel stocks, highlighting the importance of effective fishery management.

Wind fluctuations affect the mean behaviour of naturally ventilated systems

We study the dynamics of a naturally ventilated room in which a point source provides a steady source of buoyancy and which is affected by an opposing unsteady wind. The wind is modelled as a stochastic forcing, which aims at simulating realistic velocity fluctuations as observed in the lower atmosphere. Our main finding is the occurrence of a “noise-induced transition”, namely a structural change of the mean behaviour of the system: the warm–cold air interface does not fluctuate around the elevation exhibited when wind is constant, but oscillations occur around a new (significantly lower) interface elevation. We provide the physical explanation for such a counter-intuitive behaviour and show its dependence on (i) wind characteristics (intensity and timescale of fluctuations) and (ii) relative strength of wind over thermal loads. A realistic example case shows that the behaviour highlighted here has potentially major implications in the design and management of naturally ventilated buildings.

3D trajectories and velocities of rainfall drops in a multifractal turbulent wind field

Abstract. Weather radars measure rainfall in altitude, whereas hydro-meteorologists are mainly interested in rainfall at ground level. During their fall, drops are advected by the wind, which affects the location of the measured field. The governing equation of a rain drop's motion relates the acceleration to the forces of gravity and buoyancy along with the drag force. It depends non-linearly on the instantaneous relative velocity between the drop and the local wind, which yields complex behaviour. Here, the drag force is expressed in a standard way with the help of a drag coefficient expressed as a function of the Reynolds number. Corrections accounting for the oblateness of drops greater than 1–2 mm are suggested and validated through a comparison of the retrieved “terminal fall velocity” (i.e. without wind) with commonly used relationships in the literature. An explicit numerical scheme is then implemented to solve this equation for a 3+1D turbulent wind field, and hence analyse the temporal evolution of the velocities and trajectories of rain drops during their fall. It appears that multifractal features of the input wind are simply transferred to the drop velocity with an additional fractional integration whose level depends on the drop size, and a slight time shift. Using an actual high-resolution 3D sonic anemometer and a scale invariant approach to simulate realistic fluctuations of wind in space, trajectories of drops of various sizes falling form 1500 m are studied. For a strong wind event, drops located within a radar gate in altitude during 5 min are spread on the ground over an area of the size of a few kilometres. The spread for drops of a given diameter is found to cover a few radar pixels. Consequences on measurements of hydro-meteorological extremes that are needed to improve the resilience of urban areas are discussed.

Fractional neural sampling as a theory of spatiotemporal probabilistic computations in neural circuits

A range of perceptual and cognitive processes have been characterized from the perspective of probabilistic representations and inference. To understand the neural circuit mechanism underlying these probabilistic computations, we develop a theory based on complex spatiotemporal dynamics of neural population activity. We first implement and explore this theory in a biophysically realistic, spiking neural circuit. Population activity patterns emerging from the circuit capture realistic variability or fluctuations of neural dynamics both in time and in space. These activity patterns implement a type of probabilistic computations that we name fractional neural sampling (FNS). We further develop a mathematical model to reveal the algorithmic nature of FNS and its computational advantages for representing multimodal distributions, a major challenge faced by existing theories. We demonstrate that FNS provides a unified account of a diversity of experimental observations of neural spatiotemporal dynamics and perceptual processes such as visual perception inference, and that FNS makes experimentally testable predictions.

Aeroacoustic installation effects in multi-rotorcraft: Numerical investigations of a small-size drone model

The noise associated with the growing presence of unmanned aerial vehicles such as professional drones is becoming a concern. The buzzing noise emitted by multicopter drones is particularly distracting and annoying. The root mechanisms causing this tonal noise in multicopter configurations are however poorly understood and constitute the focus of this study. We developed a hybrid methodology that couples unsteady Reynolds-Averaged Navier-Stokes simulations with a computational aeroacoustic approach based on the Finite Element Method. This has permitted quantifying propeller-propeller and propeller-airframe aerodynamic installation effects, and the airframe scattering effects. The methodology is validated by comparing the predicted tones with existing acoustic measurements in the literature. The aerodynamic simulations indicate that the dominant sound sources are due to the unsteady interactions of the blade with the other propellers and supporting struts. This necessitates simulating the entire system in order to obtain realistic fluctuations of the aerodynamic forces. Similarly, the sound directivity results indicate that the acoustic scattering by the airframe has also a significant effect, both in the geometrical near- and far-field of the drone.

Assimilation and extension of particle image velocimetry data of turbulent Rayleigh\u2013B\xe9nard convection using direct numerical simulations

A novel method for assimilating and extending measured turbulent Rayleigh–Bénard convection data is presented, which relies on the fractional step method also used to solve the incompressible Navier–Stokes equation in direct numerical simulations. Our approach is used to make measured tomographic particle image velocimetry (tomo PIV) fields divergence-free and to extract temperature fields. Comparing the time average of the extracted temperature fields with the temporally averaged temperature field, measured using particle image thermometry in a subdomain of the flow geometry, shows that extracted fields correlate well with measured fields with a correlation coefficient of C_{Ttilde{T}}=0.84. Additionally, extracted temperature fields as well as divergence-free velocity fields serve as initial fields for subsequent direct numerical simulations with and without feedback which generate small-scale turbulence initially absent in the experimental data. Although the tomo PIV data set was spatially under-resolved and did not include any information on the boundary layers, the here-proposed method successfully generates velocity and temperature fields featuring small-scale turbulence and thermal as well as kinetic boundary layers, without disturbing the large-scale circulation contained in the original experimental data significantly. The latter is underpinned by high vertical and horizontal velocity correlation coefficients—computed from velocity fields averaged in time and horizontal x-direction obtained from the measurement and from the simulation without feedback—of C_{vtilde{v}}=0.92 and C_{wtilde{w}}=0.91 representing the large-scale structure. For simulations with feedback, the generated velocity fields resemble the experimental data increasingly well for higher feedback gain values, whereas the temperature fluctuation intensity deviates noticeably from the values obtained from a direct numerical simulation without feedback for gain values alpha ge 1. Thus, a feedback gain of alpha =0.1 was found optimal with correlation coefficients of C_{vtilde{v}}=0.96 and C_{wtilde{w}}=0.95 as well as a realistic temperature fluctuation intensity profile. The xt-averaged temperature fields obtained from the direct numerical simulations with and without feedback correlate somewhat less with the extracted temperature field (C_{Ttilde{T}}approx 0.6), which is presumably caused by spatially under-resolved and temporally oscillating initial tomo PIV fields reflected by the extracted temperature field.Graphical abstract

Four dimensional wave propagation simulation in liquid metal with realistic thermal fluctuation

In this paper, we performed a four-dimensional numerical simulation to calculate wave propagation in a thermal fluctuating liquid metal in order to obtain detailed knowledge on a wave propagation in coolant material of a Sodium-cooled Fast reactor (SFR). The wave and the medium are described in three spatial and one temporal dimensions. We made use of a massive data set to describe the fluctuating situation of the medium. This data set was provided by Computational Fluid Dynamics (CFD) with a Large-Eddy Simulation (LES) model, which calculated the temperature field with a higher spatial resolution than Reynolds-Averaged Navier–Stokes turbulence models (RANS). This data set was furthermore obtained from other studies on a numerical and physical experiment called PLAJEST that created mixing jets of liquid metal in order to simulate the status of running SFRs. Because of the limitation of computational resources, previous acoustic studies applied to such a medium could only use the spatial–temporally averaged fluctuating heterogeneity of a medium calculated by RANS turbulence model. This limitation may overlook wave fluctuation because of the difference of the resolution between computational fluid dynamics and acoustic wave length. Our numerical effort allowed us to study the most realistic acoustic wave propagation in liquid metal than in any former studies. A new important result was obtained in this work as we demonstrated that ultrasonic measurements could follow thermal-hydraulic fluctuations in an opaque liquid with high sensitivity. This result was obtained through the definition of descriptors to analyze medium fluctuations along the wave path. We defined a very new measurement index, called hereafter Cumulated Temperature Fluctuation Intensity (CTFI), to correlate the variations in the thermal-hydraulic conditions to the wave variations. We demonstrated a good correlation between the second derivative of this index and the second derivative of several acoustic measurements, then we discussed the easiest measurements to be used in practice in an industrial setup.

Quantum gates with weak van der Waals interactions of neutral Rydberg atoms

Neutral atoms are promising for large-scale quantum computing, but accurate neutral-atom entanglement depends on large Rydberg interactions which strongly limit the interatomic distances. Via a phase accumulation in detuned Rabi cycles enabled by a Rydberg interaction of similar magnitude to the Rydberg Rabi frequency, we study a controlled-phase gate with an arbitrary phase and extend it to the controlled-NOT gate. The gates need only three steps for coupling one Rydberg state, depend on easily accessible van der Waals interaction that naturally arises between distant atoms, and have no rotation error in the weak interaction regime. Importantly, they can work with very weak interactions so that well-separated qubits can be entangled. The gates are sensitive to the irremovable fluctuation of Rydberg interactions, but can still have a fidelity over 98\% with realistic position fluctuation of qubits separated over 20~$\mu$m.

Gigantic tunneling magnetoresistance in magnetic Weyl semimetal tunnel junctions.

We investigate the tunneling magnetoresistance in magnetic tunnel junctions (MTJs) comprised of Weyl semimetal contacts. We show that chirality-magnetization locking leads to a gigantic tunneling magnetoresistance ratio, an effect that does not rely on spin filtering by the tunnel barrier. Our results indicate that the conductance in the anti-parallel configuration is more sensitive to magnetization fluctations than in MTJs with normal ferromagnets, and predicts a TMR as large as 104 % when realistic magnetization fluctuations are accounted for. In addition, we show that the Fermi arc states give rise to a non-monotonic dependence of conductance on the misalignment angle between the magnetizations of the two contacts.

Fractional Neural Sampling: A Theory of Spatiotemporal Probabilistic Computations in Neural Circuits

A range of perceptual and cognitive processes have been characterized from the perspective of probabilistic representations and inference. To understand the neural circuit mechanism underlying these probabilistic computations, we develop a new theory based on complex spatiotemporal dynamics of neural population activity. We first implement and explore this theory in a biophysically realistic, spiking neural circuit. Population activity patterns emerging from the circuit capture the realistic variability or fluctuations of neural dynamics not only in time but also in space; such spatial fluctuations, however, are ignored in traditional models of neural computations. These activity patterns implement a new type of probabilistic computations that we call Fractional Neural Sampling (FNS). We further develop a normative model to reveal the algorithmic nature of FNS and its powerful computational advantages for representing multimodal distributions, a major challenge faced by existing theories. We show that FNS accounts for recent experimental observations of perceptual inference and makes experimentally testable predictions.

On the Response of Ultralean Combustion of CH4/H2 Blends in a Porous Burner to Fluctuations in Fuel Flow-an Experimental Investigation.

Fluctuations in the fuel flow rate may occur in practical combustion systems and result in flame destabilization. This is particularly problematic in lean and ultralean modes of burner operation. In this study, the response of a ceramic porous burner to fluctuations in the flow rate of different blends of methane and hydrogen is investigated experimentally. Prior to injection into the porous burner, the fuel blend is premixed with air at equivalence ratios below 0.275. The fuel streams are measured and controlled separately by programmable mass flow controllers, which impose sinusoidal fluctuations on the flow rates. To replicate realistic fluctuations in the fuel flow rate, the period of oscillations is chosen to be on the order of minutes. The temperature inside the ceramic foam is measured using five thermocouples located at the center of the working section of the burner. The flame embedded in porous media is imaged while the fuel flow is modulated. Analysis of the flame pictures and temperature traces shows that the forced oscillation of the fuel mixture leads to flame movement within the burner. This movement is found to act in accordance with the fluctuations in methane and hydrogen flows for both CH4(90%)–H2(10%) and CH4(70%)–H2(30%) mixtures. However, both fuel mixtures are noted to be rather insensitive to hydrogen flow fluctuation with a modulation amplitude below 30% of the steady flow. For the CH4(70%)–H2(30%) mixture, the flame in the porous medium can be modulated by fluctuations between 0 and 30% of steady methane flow without any noticeable flame destabilization.

High-Fidelity Simulations of Multi-Jet Impingement Cooling Flows

Abstract This article shows the first parametric study on turbulent multi-jet impingement cooling flows using large-eddy simulations (LES). We focus on assessing the influence of the inter-jet distance and the cross-flow conditions on the heat transfer at the impingement wall. The LES setup is thoroughly validated with both experimental and direct numerical simulation data, showing an excellent agreement. The inter-jet distance effect on the heat transfer is studied comparing three different distances, where the full Nusselt number profile decreases in amplitude when the jet distance is increased. To evaluate the cross-flow effects, we prescribe both laminar and turbulent inflow conditions at different cross-flow magnitudes ranging between 20% and 40% of the impinging jet speed. Large cross-flow intensities cause a jet deflection that reduces the maxima in the Nusselt number distribution, and it increases the heat transfer in the areas of the wall less affected by the jet impingement. Adding realistic turbulent fluctuations to the inflow enhances the cross-flow effects on the heat transfer at the impingement wall.