22 research outputs found

    On a model of sequential point patterns

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    A sequential point process motivated by the cooperative sequential adsorption is studied. Analytical properties of the process are considered in details. It is shown that the point process is useful for modelling cluster point patterns. The test on the real life data is carried ou

    Gaussian fluctuations of random point measures generated by cooperative sequential adsorption

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    A finite number of points are sequentially allocated in a finite domain of d-dimensional space. The probability distribution of a point depends on all previously allocated points. We consider a situation when this dependence vanishes as the domain is saturated by points. The law of large numbers and the central limit theorem are proved for the generated sequence of random point measures as the number of points goes to infinit

    Limit theorems for random point measures generated by cooperative sequential adsorption

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    We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity of the model is that the probability distribution of a point depends on previously allocated points. We assume that the dependence vanishes as the concentration of points tends to infinity. Under this assumption the law of large numbers, the central limit theorem and Poisson approximation are proved for the generated sequence of random point measures.Comment: 17 page

    Volcano–Plutonic Complex of the Tumrok Range (Eastern Kamchatka): An Example of the Ural-Alaskan Type Intrusion and Related Volcanic Series

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    Zoned plutons, composed of dunites, pyroxenites, and gabbroic rocks, have been referred to as the Ural-Alaskan type complexes (UA-complexes) and occur in numerous paleo-arc settings worldwide. Many of these complexes are source rocks for economic placers of platinum-group metals. Thus, it is important to understand how UA-complexes form and the origin and behavior of platinum-group elements (PGEs). It is widely assumed that the UA-complexes result from differentiation of supra-subduction high-Ca high-Mg sub-alkaline magmas. However, there is a lack of direct evidence for the existence and differentiation of such magmas, mainly because cases of UA-complexes being spatially and temporally linked to co-genetic volcanics are unknown. We studied an UA-complex from the Tumrok range (Eastern Kamchatka) where a dunite-clinopyroxenite-gabbro assemblage is spatially and temporary related to high-Ca volcanics (i.e., picrites and basalts). Based on the mineral and chemical composition of the rocks, mineral chemistry, and composition of melt inclusions hosted within rock-forming minerals, we conclude that the intrusive assemblage and the volcanics are co-genetic and share the same parental magma of ankaramitic composition. Furthermore, the compositions of the plutonic rocks are typical of UA-complexes worldwide. Finally, the rocks studied exhibit a full differentiation sequence from olivine-only liquidus in picrites and dunites to eutectic crystallization of diopside or hornblende, plagioclase, and K-Na feldspar in plagio-wehrlites and gabbroic rocks. All these results make the considered volcano–plutonic complex a promising case for petrological studies and modelling of UA-complex formation

    BENCHOP - The BENCHmarking project in Option Pricing

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    The aim of the BENCHOP project is to provide the finance community with a common suite of benchmark problems for option pricing. We provide a detailed description of the six benchmark problems together with methods to compute reference solutions. We have implemented fifteen different numerical methods for these problems, and compare their relative performance. All implementations are available on line and can be used for future development and comparison

    Properties of Calcium Phosphate/Hydrogel Bone Grafting Composite on the Model of Diaphyseal Rat Femur’s Defect: Experimental Study

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    Background. The problem of bone defects replacement is relevant nowadays, that is why many scientists create new synthetic bone substitutes, but the ideal material has not been found so far. The aims of the study: 1) to determine the suitability of the monocortical defect model in the rat femur diaphysis with additional prophylactic reinforcement with a bone plate for assessing the biological properties of implanted materials using the commercially available ChronOS material as an example; 2) to assess of the osteoconductive properties of composite materials based on poly(ethylene glycol)diacrylate and octacalcium phosphate with architecture Kelvin and gyroid types on the developed model. Methods. A prospective study, level of evidence II. A monocortical defect of the rat femoral diaphysis (length 7 mm) was produced under anaesthesia in aseptic conditions and fixed with a polyetheretherketone plate and six titanium screws. In the control group, the defect was left empty. In other groups, blocks of one of three materials were implanted сhronOS and composites of poly(ethylene glycol)diacrylate and octacalcium phosphate with 3D-printed Kelvin and gyroid architectures. After 3 and 6 weeks, the rats were sacrificed, and histological examination of the defect zone was performed. The amount of newly formed bone tissue was histometricly assessed, followed by statistical processing of the results. Results. All rats have reached the planned endpoint, and there were no infectious complications or loss of fixation. Histological examination of the defect zone revealed minimal bone growth in the Control group, rather slow bone formation in the Gyroid group, and statistically significantly more pronounced bone formation in the pores of the materials in the Kelvin and Chronos groups. Conclusions. Bone defect in this model was not spontaneously filled with bone tissue and allowed us to study the biological properties of bone substitutes (the ability to biodegrade and osteoconductive properties). The osteoconductive properties of a composite material based on poly(ethylene glycol)diacrylate and octacalcium phosphate with a Kelvin architecture are higher than with a gyroid architecture and are comparable to that of the сhronOS

    Composition, crystallization conditions and genesis of sulfide-saturated parental melts of olivine-phyric rocks from Kamchatsky Mys (Kamchatka, Russia)

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    Highlights • Parental melts of sulfide-bearing KM rocks have near primary MORB-like composition. • Crystallization of these S-saturated melts occurred in near-surface conditions. • Extensive fractionation and crustal assimilation are not the causes of S-saturation. • S content in melts can be restored by accounting for daughter sulfide globules. Abstract Sulfide liquids that immiscibly separate from silicate melts in different magmatic processes accumulate chalcophile metals and may represent important sources of the metals in Earth's crust for the formation of ore deposits. Sulfide phases commonly found in some primitive mid-ocean ridge basalts (MORB) may support the occurrence of sulfide immiscibility in the crust without requiring magma contamination and/or extensive fractionation. However, the records of incipient sulfide melts in equilibrium with primitive high-Mg olivine and Cr-spinel are scarce. Sulfide globules in olivine phenocrysts in picritic rocks of MORB-affinity at Kamchatsky Mys (Eastern Kamchatka, Russia) represent a well-documented example of natural immiscibility in primitive oceanic magmas. Our study examines the conditions of silicate-sulfide immiscibility in these magmas by reporting high precision data on the compositions of Cr-spinel and silicate melt inclusions, hosted in Mg-rich olivine (86.9–90 mol% Fo), which also contain globules of magmatic sulfide melt. Major and trace element contents of reconstructed parental silicate melts, redox conditions (ΔQFM = +0.1 ± 0.16 (1σ) log. units) and crystallization temperature (1200–1285 °C), as well as mantle potential temperatures (~1350 °C), correspond to typical MORB values. We show that nearly 50% of sulfur could be captured in daughter sulfide globules even in reheated melt inclusions, which could lead to a significant underestimation of sulfur content in reconstructed silicate melts. The saturation of these melts in sulfur appears to be unrelated to the effects of melt crystallization and crustal assimilation, so we discuss the reasons for the S variations in reconstructed melts and the influence of pressure and other parameters on the SCSS (Sulfur Content at Sulfide Saturation)
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