Moderate Regime Research Articles

Optimal control of the SIR model with constrained policy, with an application to COVID-19

This article considers the optimal control of the SIR model with both transmission and treatment uncertainty. It follows the model presented in Gatto and Schellhorn (2021). We make four significant improvements on the latter paper. First, we prove the existence of a solution to the model. Second, our interpretation of the control is more realistic: while in Gatto and Schellhorn (2021) the control α is the proportion of the population that takes a basic dose of treatment, so that α>1 occurs only if some patients take more than a basic dose, in our paper, α is constrained between zero and one, and represents thus the proportion of the population undergoing treatment. Third, we provide a complete solution for the moderate infection regime (with constant treatment). Finally, we give a thorough interpretation of the control in the moderate infection regime, while Gatto and Schellhorn (2021) focused on the interpretation of the low infection regime. Finally, we compare the efficiency of our control to curb the COVID-19 epidemic to other types of control.

Short-dated smile under rough volatility: asymptotics and numerics

In Friz et al. [Precise asymptotics for robust stochastic volatility models. Ann. Appl. Probab, 2021, 31(2), 896–940], we introduce a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small-noise formulae for option prices, using the framework [Bayer et al., A regularity structure for rough volatility. Math. Finance, 2020, 30(3), 782–832]. We investigate here the fine structure of this expansion in large deviations and moderate deviations regimes, together with consequences for implied volatility. We discuss computational aspects relevant for the practical application of these formulas. We specialize such expansions to prototypical rough volatility examples and discuss numerical evidence.

STRUCTURAL ATTRIBUTES, DIVERSITY AND MANAGEMENT OF SOME VAN PANCHAYAT FOREST STANDS OF GARHWAL HIMALAYA

Oak (Quercus oblongata) is an important component of mid-altitude ecosystem of the Central Himalaya which are exposed to over-exploitation making conditions favourable for the invasion by light-demanding conifers such as chirpine (Pinus roxburghii). The present study provides information on woody vegetation structure, composition, regeneration and management of four broadleaved forest stands of Garhwal Himalaya managed by Village Panchayat. Quercus oblongata was the most important and dominant species in all the stands. Although dominance was shared by a number of species, no single species was found to complete with this climax species. The presence of Alnus nepalensis (a nitrogen-fixing species) depicts the poor nitrogen status of these forest stands. High density values and low basal cover suggest that these community forest stands are younger than the natural oak reserve forests of the Central Himalaya. The richness index shows that the seedling strata are ecologically richer than the tree, sapling and/or shrub strata. High richness in the seedling strata is attributed to the low magnitude of biotic interferences in these communities based conserved forest stands. The regeneration potential of Quercus oblongata is much higher than the natural oak forests of Central Himalaya managed by the forest department. This supports the view that moderate disturbance regimes are more conducive to satisfactory regeneration of this species. Since the management of these forest stands is looked after by the Village Panchayat, they are introducing some conifers for their vested interests. This may add an additional competition of the broadleaved climax species with conifers as has been witnessed in most of the broadleaved oak forests of this altitudinal range.

The effect of the Ni/Cu ratio on H-induced ductility loss and its mechanism in Cu–Ni binary alloy system

The effect of the Ni/Cu ratio on hydrogen embrittlement (HE) behavior is studied in the context of the Cu–Ni binary alloy system. When classifying HE sensitivity as a function of the Ni fraction, two regimes are obtained: Regime 1 (wherein Ni fraction is less than 80 wt%) with moderate HE and Regime 2 (where Ni fraction exceeds 80 wt%) with more severe HE, although hydrogen- (H-)induced intergranular (IG) cracking is noted to be the common primary cause of H-induced degradation. Necessities of H-transportation towards grain boundaries (GBs) via H–dislocation interaction and/or dynamic H-diffusion are discussed via the slow strain rate tensile tests at −196 °C. Specifically, in Regime 1, H-transportation is necessary for the triggering of IG cracking. Conversely, in Regime 2, such H-transportation plays a minor role and the initially concentrated hydrogen along GBs can sorely cause IG cracking.

Optimal Change-Point Detection With Training Sequences in the Large and Moderate Deviations Regimes

This paper investigates a novel offline change-point detection problem from an information-theoretic perspective. In contrast to most related works, we assume that the knowledge of the underlying pre- and post-change distributions are not known and can only be learned from the training sequences which are available. We further require the probability of the estimation error to decay either exponentially or sub-exponentially fast (corresponding respectively to the large and moderate deviations regimes in information theory parlance). Based on the training sequences as well as the test sequence consisting of a single change-point, we design a change-point estimator and further show that this estimator is optimal by establishing matching (strong) converses. This leads to a full characterization of the optimal confidence width (i.e., half the width of the confidence interval within which the true change-point is located at with high probability) as a function of the undetected error, under both the large and moderate deviations regimes.

Numerical analysis of the wake of complex-shaped snow particles at moderate Reynolds number

Climate model parametrization relies strongly on the prediction of snow precipitation, which in turn depends upon the snowflakes falling motion in air. The falling attitudes of such particles are elaborate because of the particles' irregular shapes, which produce meandering and turbulent wakes and give rise to convoluted trajectories. This also has an impact on the drag experienced by the particle. Especially for large snow particles falling close to the ground, Stokesian dynamics is not applicable, and the dependency of drag coefficient on Reynolds number becomes non-linear. This trend arises from the complex interaction between snowflakes and the surrounding air. We investigate the wake of complex-shaped snow particles using a validated delayed-detached eddy simulation model of airflow around a fixed snowflake, combined with experimental observations of free-falling, 3D-printed snowflake analogs. This novel approach allows us to analyze the wake topology and decompose its momentum flux to investigate the influence of shape and wake flow on the drag coefficient and its implications on falling attitudes by comparison with experiments. At low Re, the presence of separated vortex rings is connected to particle porosity and produces an increase in the drag coefficient. At moderate flow regimes, the particle flatness impacts the shear layer separation and the momentum loss in the wake, while at high Re the drag coefficient has almost the same value among the tested geometries although the contribution of different momentum flux terms differs. These results represent a further step toward a deeper understanding the drag of complex-shaped particles.

Rigorous Derivation of Population Cross-Diffusion Systems from Moderately Interacting Particle Systems

Population cross-diffusion systems of Shigesada–Kawasaki–Teramoto type are derived in a mean-field-type limit from stochastic, moderately interacting many-particle systems for multiple population species in the whole space. The diffusion term in the stochastic model depends nonlinearly on the interactions between the individuals, and the drift term is the gradient of the environmental potential. In the first step, the mean-field limit leads to an intermediate nonlocal model. The local cross-diffusion system is derived in the second step in a moderate scaling regime, when the interaction potentials approach the Dirac delta distribution. The global existence of strong solutions to the intermediate and the local diffusion systems is proved for sufficiently small initial data. Furthermore, numerical simulations on the particle level are presented.

An experimental study of the transition in the wear regime of brake friction materials

AbstractBrake friction materials (BFMs) are designed to have low wear rate under different conditions of contact pressure, temperature, and sliding velocity. The conditions to ensure a low wear rate (i.e., a moderate wear regime) between the disc and the BFM are not well established. The present article aims to enhance the comprehension about the wear regimes for BFMs. For this purpose, a commercial BFM was slid against a gray cast iron rotor (disc). Tests were performed under different sliding velocities and with both increasing and decreasing steps of pressure levels. Tribofilm formed on the disc's surface and BFM's wear were monitored during the tests. It was possible to conclude that the previous condition of the surface of the disc, with respect to the presence or absence of tribofilm, affects the required conditions for the transition in the wear regime. The removal of tribofilm on the surface of the disc was affected by high contact pressures and high sliding velocities. Those conditions led to a severe wear regime with a destruction of contact plateaus and an increase in friction and BFM's wear.

Scintillations of Gaussian vortex beams with effective spectrum

We undertake the aperture averaged scintillation derivation of Gaussian vortex beam using Rytov approximation. For this purpose, point-like scintillation is formulated initially and is then converted into the aperture averaging form via overlap procedure. The numeric values delivered by this aperture averaged derivation are plotted side by side against the results obtained from random phase screen simulation. There it is seen that similar to point-like scintillation, the range of validity of the aperture averaged scintillation of Rytov approximation is also limited to weak turbulence range. Incorporating the effective spectrum of spherical wave into the aperture averaged expression demonstrates that it is possible to extend the validity of the aperture averaged derivation based on Rytov approximation to moderate and strong turbulence regimes. Our tests show that additional source beam specific terms are needed to fully adapt the effective spectrum.

Constitutive activation of genes involved in triterpene saponins enhances the accumulation of saponins in three-year-old Panax notoginseng growing under moderate light intensity

Light is an important physical factor that regulates plant developmental patterns and induces the synthesis of secondary metabolites. The optimal light intensity for saponin accumulation in roots of medicinal plants with different ages is relatively poorly understood. After that, the correlation of light-driven biosynthesis of triterpene saponins with the expression of genes incorporated into the biosynthesis of triterpene saponins is still unknown. The expression levels of genes, the total saponin contents, and the biomass accumulation and allocation were examined in different age Panax notoginseng grown under different light intensities. A significant elevation in total saponin content was found in three-year-old plants grown under 9.6 % of full sunlight (FL) condition compared with the others. The expression level of dammarenediol-II synthase (DS) rapidly increased from one-year-old plants to three-year-old plants, which was consistent with the change in total saponins. Furthermore, there is a positive relationship between the expression level of DS and the content of saponins. Additionally, 9.6 % FL-driven biosynthesis of saponin has more activity in the three-year-old P. notoginseng, and the genes expression level of CYP716A47 was elevated. At the same time, the expression of geranylgeranyl pyrophosphate synthase (GGPS) and phosphomevalonate kinase (PMK) had no positive contribution to the accumulation of saponins in roots. Overall, DS and CYP716A47 might attribute to the accumulation of saponins in three-year-old P. notoginseng under a moderate light regime (about 10 % FL).

Free-stream coherent structures in parallel compressible boundary-layer flows at subsonic and moderate supersonic Mach numbers

As a first step towards the description of coherent structures in compressible shear flows, we present an asymptotic description of nonlinear travelling-wave solutions of the Navier–Stokes equations in the compressible asymptotic suction boundary layer (ASBL). We consider free-stream Mach numbers $M_\infty$ in the subsonic and moderate supersonic regime so that $0\leqslant M_\infty \leqslant 2$ . We extend the large-Reynolds-number asymptotic theory of Deguchi & Hall (J. Fluid Mech., vol. 752, 2014, pp. 602–625) describing ‘free-stream’ coherent structures in incompressible ASBL flow to describe a nonlinear interaction in a thin layer situated just below the free stream. Crucially, the nonlinear interaction equations for the velocity field in this layer are identical to those obtained in the incompressible problem, and thus the asymptotic analysis supporting free-stream coherent structures in compressible ASBL is easily deduced from its incompressible counterpart. The nonlinear interaction produces streaky disturbances to both the velocity and temperature fields, which can grow exponentially towards the wall. We complete the description of the growth of the velocity and thermal streaks throughout the flow by solving the compressible boundary-region equations numerically. We show that the velocity and thermal streaks obtain their maximum amplitude in the unperturbed boundary layer. Increasing the free-stream Mach number enhances the thermal streaks and suppresses the velocity streaks, whereas varying the Prandtl number suppresses the velocity streaks, and can either enhance or suppress the thermal streaks depending on whether the flow is in the subsonic or moderate supersonic regime. Such nonlinear equilibrium states have been implicated in shear transition in incompressible flows; therefore, our results indicate that a similar mechanism may also be present in compressible flows.

Linear harmonic oscillatory rarefied gas flow with arbitrary frequency in comb finger blocks

The linear oscillatory two-dimensional rarefied gas flow in the zig-zag channel between the shuttle and stator fingers of typical comb elements, due to the harmonic motion of the shuttle finger with arbitrary frequency, is numerically investigated, via the linearized unsteady Shakhov kinetic model equation, subject to purely diffuse boundary conditions. The amplitude and phase distributions of the velocity components, normal and shear stresses, density and temperature are thoroughly investigated in the whole range of the gas rarefaction and oscillation parameters, characterizing the flow. The low, moderate and high flow oscillation regimes are defined by the ratio of the gas rarefaction over the oscillation parameters. It is shown that in the low oscillation regime the flow may be approximated by the corresponding steady-state analysis, while in the high oscillation one by the superposition of the associated oscillatory one-dimensional normal sound propagation and Couette flows. In the former case edge and compressibility effects are considerable and in the latter one the flow is characterized by gas trapping along the shuttle finger. In the moderate oscillation regime the fully oscillatory two-dimensional flow must be analysed. Here, the antiresonance and resonance states of the flow are considered. The ratios of the gas rarefaction over the oscillation parameters, where the average normal and shear stresses acting on the shuttle finger are minimized are computationally specified. Changing the main geometry parameters of the comb finger block, significantly affects the normal and shear stresses acting on the shuttle finger, mainly in the low oscillation regime. The present work may be applied to minimize the damping forces in comb finger blocks, as well as to optimize the design of new generation devices operating in moderate and high frequencies.

Evolution of the interface microstructure of short-period Cr/Ti multilayers with increase in number of bi-layers

Evolution of interface microstructure with addition of more number of layers has been investigated on Cr/Ti multilayer which is important for application as a mirror or monochromator in the “water window” soft X-ray spectral regime. Two sets of Cr/Ti multilayers at moderate and low bi-layer thickness regime have been prepared for this purpose using Ion Beam Sputtering technique. In one set, Cr/Ti multilayer with 25, 50, 60 and 100 numbers of bilayers with moderate bi-layer thickness of 3.8 nm have been deposited. In another set, four samples each having low bilayer thickness of 2.4 nm with 25, 50, 75 and 100 number of bi-layers have been prepared and the multilayers have subsequently been characterized with Specular X-ray reflectivity and diffuse X-ray scattering measurements at grazing incidence with hard X-rays. It is observed that cumulative effect of interface imperfections became more pronounced with increasing number of bilayers resulting in continuous increase in the interface width in both the thickness regimes; however, its evolution is not exactly same for the two sets of samples. Diffuse X-ray scattering result reveals that for the first set of samples, interface imperfections are dominated by interface roughness with no change in the interface diffusion with increase in number of layers, while for the second set, both interface roughness as well as interface diffusion contribute towards the cumulative accumulation of interface imperfections which is also confirmed by cross-sectional Transmission Electron Microscopy. Finally, performance of the multilayers in water window regime has been checked by soft X-ray reflectivity measurements using synchrotron radiation. The above results have direct implication in utilisation of these multilayers over a wide bi-layer thickness regime required to cover the full ‘water-window’ spectrum.

Environmental legacy effects and acclimatization of a crustose coralline alga to ocean acidification

Prior exposure to variable environmental conditions is predicted to influence the resilience of marine organisms to global change. We conducted complementary 4-month field and laboratory experiments to understand how a dynamic, and sometimes extreme, environment influences growth rates of a tropical reef-building crustose coralline alga and its responses to ocean acidification (OA). Using a reciprocal transplant design, we quantified calcification rates of the Caribbean coralline Lithophyllum sp. at sites with a history of either extreme or moderate oxygen, temperature, and pH regimes. Calcification rates of in situ corallines at the extreme site were 90% lower than those at the moderate site, regardless of origin. Negative effects of corallines originating from the extreme site persisted even after transplanting to more optimal conditions for 20 weeks. In the laboratory, we tested the separate and combined effects of stress and variability by exposing corallines from the same sites to either ambient (Amb: pH 8.04) or acidified (OA: pH 7.70) stable conditions or variable (Var: pH 7.80-8.10) or acidified variable (OA-Var: pH 7.45–7.75) conditions. There was a negative effect of all pH treatments on Lithophyllum sp. calcification rates relative to the control, with lower calcification rates in corallines from the extreme site than from the moderate site in each treatment, indicative of a legacy effect of site origin on subsequent response to laboratory treatment. Our study provides ecologically relevant context to understanding the nuanced effects of OA on crustose coralline algae, and illustrates how local environmental regimes may influence the effects of global change.

Immune phase transition under steroid treatment

The steroid hormone glucocorticoid (GC) is a well-known immunosuppressant that controls T-cell-mediated adaptive immune response. In this work, we have developed a minimal kinetic network model of T-cell regulation connecting relevant experimental and clinical studies to quantitatively understand the long-term effects of GC on pro-inflammatory T-cell (T_{pro}) and anti-inflammatory T-cell (T_{anti}) dynamics. Due to the antagonistic relation between these two types of T cells, their long-term steady-state population ratio helps us to characterize three classified immune regulations: (i) weak ([T_{pro}]>[T_{anti}]), (ii) strong ([T_{pro}]<[T_{anti}]), and (iii) moderate ([T_{pro}]∼[T_{anti}]), holding the characteristic bistability. In addition to the differences in their long-term steady-state outcome, each immune regulation shows distinct dynamical phases. In the presteady state, a characteristic intermediate stationary phase is observed to develop only in the moderate regulation regime. In the medicinal field, the resting time in this stationary phase is distinguished as a clinical latent period. GC dose-dependent steady-state analysis shows an optimal level of GC to drive a phase transition from the weak or autoimmune prone to the moderate regulation regime. Subsequently, the presteady state clinical latent period tends to diverge near that optimal GC level where [T_{pro}]:[T_{anti}] is highly balanced. The GC-optimized elongated stationary phase explains the rationale behind the requirement of long-term immune diagnostics, especially when long-term GC-based chemotherapeutics and other immunosuppressive drugs are administrated. Moreover, our study reveals GC sensitivity of clinical latent period, which might serve as an early warning signal in diagnosing different immune phases and determining immune phasewise steroid treatment.

Pomegranate plasticity to water stress: attempt to understand interactions between cultivar, year and stress level

This work investigated the effects of sustained deficit irrigation (SDI) on yield components and fruit physico-biochemical proprieties of two pomegranate cultivars, ‘Sefri’ and ‘Wonderful’ 21 trees each, in Sais plain (northern Morocco) over two consecutive seasons (2018–2019). Irrigation treatments consisted of a control, irrigation applied to fully satisfy crop evapotranspiration (100% ETC), and two SDI treatments: 70% ETC (SDI70) and 50% ETC (SDI50). The effects of the SDI treatments differed between cultivars and years. During the first year, yield and fruit weight were significantly reduced in ‘Sefri’ under SDI50. The same effect was also observed in the second year under SDI70. In ‘Wonderful’, a significant decrease in yield occurred in the second year under both SDI regimes. Fruit juice content was reduced in both cultivars, particularly under SDI50, with no significant effect on fruit aril content and aril weight. As for juice chemical properties, it was observed a decrease in total soluble solids, especially under SDI50. Furthermore, a significant decrease in juice soluble sugars content was observed in the first year for both cultivars. Total polyphenols content has significantly diminished in the second year in both cultivars. Likewise, total anthocyanins level displayed the same pattern, particularly in ‘Wonderful’. The findings suggest that SDI decreases yield and fruit quality even under moderate regime of 70% ETC. These negative effects may be dramatic depending on pomegranate genotypes, as observed in ‘Sefri’, compared to Wonderful variety. The great impact on species behavior toward water stress was particularly driven by the irrigation treatment, of which the interaction with the cultivar factor had the higher impact on the model. As many areas of how sustained deficit irrigation impacts pomegranate tree resilience are still needed to be investigated further, this study is a first attempt to explore water management in pomegranate in the Mediterranean semiarid lands.

A Perfect Andreev Reflection Induced by Anderson Disorder in a Normal–Superconductor Junction

The electronic transport properties of a 2D normal metal superconductor are studied by a nonequilibrium Green's function method. The normal metal is the non‐inverted HgTe/CdTe quantum well doped by electrons. It is found that Andreev reflection (AR) is enhanced in the weak disorder regime while weakened in the strong disorder regime. However, the AR coefficient can be perfect () with vanished fluctuations in the moderate disorder regime, whereas other scattering processes are forbidden. The mechanism goes that Anderson disorder leads to a topological Anderson insulator with bulk states localized while edge states still extensive. Multiple ARs and spin‐momentum locking cooperate to vanish the normal reflection and leave AR only. A detailed numerical study shows that fixing the Fermi surface in conduction band, a large enough junction width, and a strong coupling between the normal and superconducting leads are necessary for perfect AR.

Toward an Estimation of the Optical Feedback Factor C on the Fly for Displacement Sensing.

In this paper, a method based on the inherent event-based sampling capability of laser optical feedback interferometry (OFI) is proposed to assess the optical feedback factor C when the laser operates in the moderate and strong feedback regimes. Most of the phase unwrapping open-loop OFI algorithms rely on the estimation of C to retrieve the displacement with nanometric precision. Here, the proposed method operates in open-loop configuration and relies only on OFI’s fringe detection, thereby improving its robustness and ease of use. The proposed method is able to estimate C with a precision of <5%. The obtained performances are compared to three different approaches previously published and the impacts of phase noise and sampling frequency are reported. We also show that this method can assess C on the fly even when C is varying due to speckle. To the best of the authors’ knowledge, these are the first reported results of time-varying C estimation. In addition, through C estimation over time, it could pave the way not only to higher performance phase unwrapping algorithms but also to a better control of the optical feedback level via the use of an adaptive lens and thus to better displacement retrieval performances.

Physiological, biochemical, and anatomical responses of Araucaria araucana seedlings to controlled water restriction

Water stress triggers acclimation responses and can damage plants, which varies by species and stress levels. Ongoing climate change is projected to result in longer and more intense water stress conditions leading to an alarming increase in drought-induced forest decline. The aim of this study was to evaluate the physiological responses of leaves and stem wood anatomy from Araucaria araucana pot-grown three-year old seedlings, a conifer tree from northwestern Patagonia. Plants were subjected to moderate and severe water restriction regimes and compared to well-watered controls. Severe water stress reduced relative leaf water content and triggered an accumulation of free proline in leaves, regardless of age. Epicuticular wax extrusions increased in apical leaf stomata while photosynthetic pigments decreased, resulting in differential oxidative damage. The concentration of phenolic compounds was not affected by water restrictions. Plants exposed to restricted water regimes showed diminished middle leaf biomass and expansion (~60% of total leaves), increased stem wood density, and experienced 7% and 30% mortality rates under moderate and severe water stress, respectively. Our findings suggest that under moderate water stress, analogous to short-term droughts, A. araucana seedlings activate physiological mechanisms that allow them to withstand short periods of drought, while more severe water stress and longer droughts can be severely harmful.

Physiological, developmental and growth responses to desiccation induced stress in four seed coat colour varieties of Vigna unguiculata (L. Walp).

Cowpea (Vigna unguiculata L. Walp) is a widely grown leguminous crop in Ghana. This study was conducted using four varieties of cowpea based on the colour of the seed coat namely; red, brown, black and cream cowpea varieties, and were subjected to three different watering regimes, namely: Normal, moderate and severe water stress regimes. These different watering regimes were used as potential screening criteria to determine their drought tolerance ability. We monitored changes in physiological, morphological and yield traits due to the effects of four seed coat colour varieties and imposed water regimes. The effects of seed coat colour on relative water content (RWC) was significant (F = 13.15; p ≤ 0.05). Red variety recorded the highest RWC (60.14%) with the lowest RWC (50.71%) in the Black seed colour, all under severe water stress. The Red and Cream seed coats had a soil moisture content (SMC) of 62.61 and 48.70% respectively when the severe water stress treatment was considered. There was a decreasing trend in chlorophyll content for all four cowpea varieties. The Brown and Red varieties recorded the highest chlorophyll contents under moderate and severe water stress respectively. Proline concentrations were high with increasing drought severity. The Red cowpea variety recorded the maximum concentration of free proline (5.7 µg/g) under severe water stress. Mean seed weight in Red seed coat, subjected to severe water stress, was 0.48 g. Results in this experiment revealed that the Red seed coat colour appeared to be tolerant to severe water stress compared to Cream, Black and Brown seed coats. Key words: Cowpea, seed coat colour, water stress, relative water content, soil moisture content.