Revisiting the stability of spatially heterogeneous predator-prey systems under eutrophication

We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, this framework allows us to more realistically describe the situation where movement of individuals occurs on a faster time scale than the demographic (population) time scale, and we cannot determine population growth based on local density. However, most of the results reported so far for such systems have only been verified numerically and for a particular choice of model functions, which obviously casts doubts about these findings. In this paper, we analyse a class of integro-differential predator-prey models with a highly mobile predator in a heterogeneous environment, and we reveal the main factors stabilizing such systems. In particular, we explore an ecologically relevant case of interactions in a highly eutrophic environment, where the prey carrying capacity can be formally set to 'infinity'. We investigate two main scenarios: (i) the spatial gradient of the growth rate is due to abiotic factors only, and (ii) the local growth rate depends on the global density distribution across the environment (e.g. due to non-local self-shading). For an arbitrary spatial gradient of the prey growth rate, we analytically investigate the possibility of the predator-prey equilibrium in such systems and we explore the conditions of stability of this equilibrium. In particular, we demonstrate that for a Holling type I (linear) functional response, the predator can stabilize the system at low prey density even for an 'unlimited' carrying capacity. We conclude that the interplay between spatial heterogeneity in the prey growth and fast displacement of the predator across the habitat works as an efficient stabilizing mechanism.Comment: 2 figures; appendices available on request. To appear in the Bulletin of Mathematical Biolog

Гетерофазный синтез феррита кобальта

Objectives. The study aimed to develop new methods for the synthesis of cobalt ferrite (CoFe2O4), which is a precursor for the synthesis of CoFe2O4-based functional materials, as well as to study the physicochemical properties of the obtained phases.Methods. Two methods were used for the synthesis of CoFe2O4: (1) heterophase interaction of hydrated iron oxide with cobalt(II, III) oxide and (2) heterophase interaction of hydrated iron oxide with an aqueous solution of cobalt(II) sulfate (CCo = 0.147 mol/L, solid/liquid = 1:43). In both cases, the precursor was hydrated iron oxide (Fe2O3, 84.4 wt %), which was obtained by the heterophase interaction of iron(III) chloride with a concentrated ammonia solution (6.0–9.5 mol/L). The resulting intermediate products were subjected to thermal treatment at 750 °C (synthesis 1) and at 900 °C (synthesis 2) for 10–30 h in increments of 10 h. The synthesized phases and products of their thermolysis were studied by differential thermal analysis and differential thermogravimetry (DTA–DTG), X-ray diffraction analysis (XRDA), and granulometry.Results. The hydrated iron oxide sample remained amorphous even up to the crystallization temperature of 445 °C, which corresponds to the exothermic effect on the DTA curve. Further heating led to the α-modification of iron(III) oxide of the hexagonal system (a = b = 5.037 ± 0.002 Å; c = 13.74 ± 0.01 Å), which has an average particle size of 1.1 μm. XRDA results showed that a synthesis temperature of 750 °C (synthesis 1) and a heat treatment duration of 30 h were sufficient for the formation of a single-phase cobalt ferrite (a = 8.388 ± 0.002 Å) with an average particle diameter of 1.9 μm. For synthesis 2, a higher temperature of 900 °C was used because sample weight loss (about 12.5%) was observed in the temperature range of 720–810 °C based on the DTA results, which was due to the removal of SO2 and SO3. Moreover, when synthesis temperature and duration were at 900 °C and 30 h, respectively, CoFe2O4 with a = 8.389 ± 0.002 Å was formed. The results of the granulometric analysis showed that particles of different diameters were formed. The smallest particle size (1.5 μm) of cobalt ferrite was obtained by the heterophase interaction of hydrated iron(III) oxide (Fe2O3, 84.4 wt %) with an aqueous solution of cobalt sulfate with CCo = 0.147 mol/L. Conclusions. Depending on the method used for the synthesis of cobalt ferrite, particles of different diameters are formed. The smallest particle size of cobalt ferrite was obtained from the heterophase interaction of hydrated iron(III) oxide with an aqueous solution of cobalt(II) sulfate.Цели. Разработка новых методов синтеза феррита кобальта (CoFe2O4), являющегося предшественником для синтеза функциональных материалов на его основе, а также исследование физико-химических свойств полученных фаз.Методы. Гидратированный оксид железа и феррит кобальта получали гетерофазным методом. Синтезированные фазы и продукты их термолиза изучали методами дифференциально-термического анализа и дифференциальной термогравиметрии (ДТА–ДТГ), рентгенофазового анализа (РФА) и гранулометрии.Результаты. В статье изложены результаты двух методов синтеза феррита кобальта (CoFe2O4) и исследования полученных фаз. В обоих случаях в качестве предшественника выступал гидратированный оксид железа(III) с содержанием Fe2O3 – 84.4 мас. %, полученный гетерофазным взаимодействием хлорида железа(III) с концентрированным раствором аммиака (6.0–9.5 моль/л). Первый способ заключался во взаимодействии гидратированного оксида железа(III) с оксидом кобальта(II, III), второй – во взаимодействии гидратированного оксида железа(III) с водным раствором сульфата кобальта(II) с концентрацией ССо = 0.147 моль/л (Т : Ж = 1 : 43). Получившиеся промежуточные продукты подвергали термической обработке при 750 °C (синтез 1) и 900 °C (синтез 2) в течение 10–30 ч с шагом 10 ч.Выводы. Феррит кобальта (CoFe2O4) получен двумя способами. С использованием комплекса методов (РФА, ДТА–ДТГ, гранулометрии) исследованы физико-химические свойства синтезированных образцов. Установлено, что гидратированный оксида железа(III) вплоть до температуры кристаллизации (445 °C), соответствующей экзотермическому эффекту на кривой ДТА, остается рентгеноаморфным. Дальнейшее нагревание его приводит к образованию α-модификации оксида железа(III) гексагональной сингонии (a = b = 5.037 ± 0.002 Å; c = 13.74 ± 0.01 Å), средний размер частиц которой равен 1.1 мкм. Согласно данным РФА, в синтезе 1 при 750 °C и продолжительности термообработки 30 ч образуется однофазный феррит кобальта (a = 8.388 ± 0.002 Å) со средним диаметром частиц 1.9 мкм. В интервале температур 720–810 °C в образце наблюдается убыль массы (около 12.5%), связанная с удалением SO2 и SO3. Поэтому в синтезе 2 температуру нагревания увеличивали до 900 °C. Показано, что при 900 °C и продолжительности синтеза 30 ч также образуется феррит кобальта (CoFe2O4) (a = 8.389 ± 0.002 Å). Результаты гранулометрического анализа указывают на зависимость диаметра образующихся частиц от способа получения феррита кобальта. Наименьший размер частиц (1.5 мкм) обнаружен у феррита кобальта, полученного гетерофазным взаимодействием гидратированного оксида железа(III) (Fe2O3 – 84.4 мас. %) с водным раствором сульфата кобальта с концентрацией С(Со2+) = 0.147 моль/л

Parole rayonnante d’une réalité impossible : trois récits de Maurice Blanchot

The oeuvre of M. Blanchot belongs to “the age of suspicion”: it explores various relations between reality and our capacity to report it. “Thomas l'obscur”, “Au moment voulu” and “Celui qui ne m'accompagnat pas” are “réсits” (event story), where the logic of narration is completely perturbated : while the language is very subjective (modal verbs, verbs of opinion, affectif adjectifs and adverbs etc.), the narrator is looking for its disappearance. It's the paradoxe ot the subjectivity in absentia. The instance of discourse is omnipresent in “réсits” of Blanchot and it seems to dislodge such traditional narratif structures as plot, hero or time and space of narration. The text is always in reciprocal relation with itself, so that creates nonsolvable space between the writing and the representation, between the signification and the text in its materiality

Evolution of a Polydisperse Ensemble of Ellipsoidal Crystals with Fluctuating Growth Rates in Supercooled Melts

In this paper, an analytical solution to the model of the evolution of ellipsoidal crystals with fluctuating growth rates at the intermediate step of bulk phase transition is presented. A complete system of integrodifferential equations describing the problem was derived and analytically solved using the Laplace integral method. The kinetics of supercooling removal in melts has been found. The particle-volume distribution function represents a pike-shaped curve decreasing its maximum with time. It is demonstrated the differences in the distribution function for ellipsoidal and spherical crystals. © 2021 Institute of Physics Publishing. All rights reserved.This work was supported by the Russian Science Foundation (grant no. 18-19-00008)