Papers by Leonid Kalachev
ABSTRACT . The age dynamics of a natural forest is modeled by the von-Foerster partial differenti... more ABSTRACT . The age dynamics of a natural forest is modeled by the von-Foerster partial differential equation for the age density, while the seedling density is obtained as a solution of an integro-differential equation. This seedling density equation contains a small parameter, the ratio of seedling re-establishment time and the life span of an average tree in the forest. Several models are introduced that take into account various mortality curves and growth functions of trees, the dependence of seedlings carrying capacity on forest size, and different types of seedlings re-establishment. Asymptotic, analytic and numerical methods are used to solve typical example problems.
Mathematical medicine and biology, Aug 2, 2010
Macroparasites include worms, ticks, mites, bugs and fleas. These parasites are well known to ind... more Macroparasites include worms, ticks, mites, bugs and fleas. These parasites are well known to induce morbidity effects including a reduction in the hosts' reproductive output and survival. An important scenario is the introduction of a new macroparasite into an established host population which may be caused by the climate change and by the transport of domestic animals. The aim of the article is to demonstrate an interesting feature of this scenario using a mathematical model with four dimensionless parameters. Six possible scenarios of introducing a new macroparasite into a host colony, ranging from the elimination of the new pathogen, through guaranteed host and parasite coexistence, to the collapse of the host colony are distinguished. The threshold surfaces in the space of parameters which separate the different scenarios are found. Some special limit cases are discussed.
Mathematical Notes, Jun 1, 1986
ABSTRACT A compact model for threshold voltages of SOI MOSFETs with ultra-thin top Si layer is pr... more ABSTRACT A compact model for threshold voltages of SOI MOSFETs with ultra-thin top Si layer is presented. The model is based on potential distribution solution of the two-dimensional Poisson equation using an asymptotic method. The validity of the model is verified by comparison with results of two-dimensional numerical simulations.
Foundations of data science, 2023
Trends in mathematics, 2019
Excitatory Amino Acid Transporters (EAATs) operate over wide time scales in the brain. They maint... more Excitatory Amino Acid Transporters (EAATs) operate over wide time scales in the brain. They maintain low ambient concentrations of the primary excitatory amino acid neurotransmitter glutamate, but they also seem to play a significant role in clearing glutamate from the synaptic cleft in the millisecond timescale process of chemical communication that occurs between neurons. The detailed kinetic mechanisms underlying glutamate uptake and clearance remain incompletely understood. In this work we used a combination of methods to model EAAT kinetics and gain insight into the impact of transport on glutamate dynamics in a general sense. We derive reliable estimates of the turnover rates of the three major EAAT subtypes expressed in the mammalian cerebral cortex. Previous studies have provided transporter kinetic estimates that vary over an order of magnitude. The values obtained in this study are consistent with estimates that suggest the unitary transporter rates are approximately 20-fold slower than the time course of glutamate in the synapse. A combined diffusion/transport model provides a possible mechanism for the apparent discrepancy.
Sleep, May 1, 2023
Results: Participants had an average of 58.2μg±63.8 PM2.5 exposure during a day until they went t... more Results: Participants had an average of 58.2μg±63.8 PM2.5 exposure during a day until they went to bed and 0.8μg±2.6 PM2.5 exposure during sleep. Because there was minimal night PM2.5 exposure, only the day exposure was correlated to sleep measures. There was no significant effect of PM2.5 exposure on sleep efficiency, sleep onset latency, wake after sleep onset, and total sleep time as measured from the Dreem headband. There was a modest but significant effect of PM2.5 on perceived sleep quality, as participants rated poorer sleep quality (r(141)=.17, p=.042) and higher fatigue levels (r(141)=.26, p=.002) the next morning. Conclusion: These findings suggest acute PM2.5 exposure levels were not high enough to affect sleep metrics but did affect one's perceived sleep. Future studies should examine longer period to assess whether there is a chronic effect of PM2.5 exposure on sleep. Support (if any):
Computational Mathematics and Mathematical Physics, Sep 1, 1992
The Michaelis-Menten-Henri (MMH) mechanism is one of the paradigm reaction mechanisms in biology ... more The Michaelis-Menten-Henri (MMH) mechanism is one of the paradigm reaction mechanisms in biology and chemistry. In its simplest form, it involves a substrate that reacts (reversibly) with an enzyme, forming a complex which is transformed (irreversibly) into a product and the enzyme. Given these basic kinetics, a dimension reduction has traditionally been achieved in two steps, by using conservation relations to reduce the number of species and by exploiting the inherent fast-slow structure of the resulting equations. In the present article, we investigate how the dynamics change if the species are additionally allowed to diffuse. We study the two extreme regimes of large diffusivities and of small diffusivities, as well as an intermediate regime in which the time scale of diffusion is comparable to that of the fast reaction kinetics. We show that reduction is possible in each of these regimes, with the nature of the reduction being regime dependent. Our analysis relies on the classical method of matched asymptotic expansions to derive approximations for the solutions that are uniformly valid in space and time.
U.S.S.R. computational mathematics and mathematical physics, 1988
A singularly perturbed system of two parabolic equationswhichdescribes combustion in the case of ... more A singularly perturbed system of two parabolic equationswhichdescribes combustion in the case of an autocatalytic first-order reaction allowing for diffusion and heat transfer is considered. An asymptotic expansion for the solution of this problem in the case when the reaction proceeds non-explosively is constructed on the basis of the boundary function method and proved.
We consider a singularly perturbed system of second-order dierential equations describing steady ... more We consider a singularly perturbed system of second-order dierential equations describing steady state of a chemical process that involves three species, two reactions (one of which is fast), and diusion. Formal asymptotic expansion of the solution is constructed. The theorem on estimation of the remainder is proved.
Transportation Research Part F: Traffic Psychology and Behaviour, 2021
Biomathematical models of fatigue can be used to predict neurobehavioral deficits during sleep/wa... more Biomathematical models of fatigue can be used to predict neurobehavioral deficits during sleep/wake or work/rest schedules. Current models make predictions for objective performance deficits and/or subjective sleepiness, but known differences in the temporal dynamics of objective versus subjective outcomes have not been addressed. We expanded a biomathematical model of fatigue previously developed to predict objective performance deficits as measured on the Psychomotor Vigilance Test (PVT) to also predict subjective sleepiness as self-reported on the Karolinska Sleepiness Scale (KSS). Four model parameters were re-estimated to capture the distinct dynamics of the KSS and account for the scale difference between KSS and PVT. Two separate ensembles of datasets - drawn from laboratory studies of sleep deprivation, sleep restriction, simulated night work, napping, and recovery sleep - were used for calibration and subsequent validation of the model for subjective sleepiness. The expanded model was found to exhibit high prediction accuracy for subjective sleepiness, while retaining high prediction accuracy for objective performance deficits. Application of the validated model to an example scenario based on cargo aviation operations revealed divergence between predictions for objective and subjective outcomes, with subjective sleepiness substantially underestimating accumulating objective impairment, which has important real-world implications. In safety-sensitive operations such as commercial aviation, where self-ratings of sleepiness are used as part of fatigue risk management, the systematic differences in the temporal dynamics of objective versus subjective measures of functional impairment point to a potentially significant risk evaluation sensitivity gap. The expanded biomathematical model of fatigue presented here provides a useful quantitative tool to bridge this previously unrecognized gap.
WSEAS Transactions on Mathematics archive, 2018
In this paper we describe a technique that we have used in a number of publications to find the “... more In this paper we describe a technique that we have used in a number of publications to find the “watershed” under which the initial condition of a positive solution of a nonlinear reaction-diffusion equation must lie, so that this solution does not develop into a traveling wave, but decays into a trivial solution. The watershed consists of the positive solution of the steady-state problem together with positive pieces of nodal solutions ( with identical boundary conditions). We prove in this paper that our method for finding watersheds works in Rk , k ≥ 1, for increasing functions f(z)/z. In addition, we weaken the condition that f(z)/z be increasing, and show that the method also works in R1 when f(z)/z is bounded. The decay rate is exponentia
Experiments reveal that thermal energy transfers as an acoustic wave near the critical point of a... more Experiments reveal that thermal energy transfers as an acoustic wave near the critical point of a classical fluid under microgravity. In this paper we use asymptotic methods and Fourier analysis to provide a complete mathematical proof of this piston effect. Our two-step method provides a “fast-time” solution describing the piston effect in detail, and a “slow-time” solution leading to solutions that agree in nature with those obtained by numerical methods applied to the original model system on “slow-time” scale.
Trends in Mathematics, 2019
Several reduced kinetic models for N-methyl-D-aspartate receptors were derived in order to suit d... more Several reduced kinetic models for N-methyl-D-aspartate receptors were derived in order to suit different experimental protocols. Their simultaneous application allows for a step-wise estimation of parameters of a conventional model that is otherwise overparameterized with respect to the existing data.
Journal of Physics: Conference Series, 2016
We present a simple model of experimental setup for in vitro study of drug release from drug elut... more We present a simple model of experimental setup for in vitro study of drug release from drug eluting stents and drug propagation in artificial tissue samples representing blood vessels. The model is further reduced using the assumption on vastly different characteristic diffusion times in the stent coating and in the artificial tissue. The model is used to derive a relationship between the times at which the measurements have to be taken for two experimental platforms, with corresponding artificial tissue samples made of different materials with different drug diffusion coefficients, to properly compare the drug release characteristics of drug eluting stents.
Nature Communications, May 17, 2021
Polymeric drug carriers are widely used for providing temporal and/or spatial control of drug del... more Polymeric drug carriers are widely used for providing temporal and/or spatial control of drug delivery, with corticosteroids being one class of drugs that have benefitted from their use for the treatment of inflammatory-mediated conditions. However, these polymer-based systems often have limited drug-loading capacity, suboptimal release kinetics, and/or promote adverse inflammatory responses. This manuscript investigates and describes a strategy for achieving controlled delivery of corticosteroids, based on a discovery that low molecular weight corticosteroid dimers can be processed into drug delivery implant materials using a broad range of established fabrication methods, without the use of polymers or excipients. These implants undergo surface erosion, achieving tightly controlled and reproducible drug release kinetics in vitro. As an example, when used as ocular implants in rats, a dexamethasone dimer implant is shown to effectively inhibit inflammation induced by lipopolysaccharide. In a rabbit model, dexamethasone dimer intravitreal implants demonstrate predictable pharmacokinetics and significantly extend drug release duration and efficacy (>6 months) compared to a leading commercial polymeric dexamethasone-releasing implant.
Forest Ecology and Management
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Papers by Leonid Kalachev