scholarly journals Laws for the size distribution of Khasyreis

2019 ◽  
Vol 488 (6) ◽  
pp. 655-657
Author(s):  
A. S. Victorov ◽  
T. V. Orlov ◽  
M. V. Arkhipova

The paper presents the results of empirical verification of the theoretical law, validated in a mathematical model of the morphological structure of thermokarst plains with fluvial erosion - the exponential distribution of the areas of khasyreis. The empirical testing based on the remote sensing data of high resolution involved 18 key sites at different regions of the cryolithozone in different natural environments. Eighty percent of the testing samples confirmed this theoretical statement. This result validates the suggested model and provides for the conclusion about the khasyrei radii corresponding to the Rayleigh distribution in different natural environments.

Author(s):  
A. S. Viktorov ◽  
V. N. Kapralova ◽  
M. V. Arkhipova

The paper deals with the results of the analysis of the dynamic mathematical model for the morphological pattern of thermokarst plains with fluvial erosion basing on the mathematical morphology of landscape approach and remote sensing data. The theoretical analysis resulted in the dynamic mathematical model for the morphological pattern of thermokarst plains with fluvial erosion, which was empirically tested at a set of the key sites. The empirical testing confirms the theoretical results about the exponential distribution of khasyrei areas in different natural environments with a broad geological and geocryological spectrums. Moreover, the area distribution of thermokarst lakes obeys both gamma and lognormal distributions. We have found that the average radius and diameter distributions should be the Raleigh one. The analysis shows that the variant of the thermokarst synchronous start is the most common for the taken key sites. Besides, the model allows us to assess certain dynamic parameters of the processes using landscape metrics from a single time slice.


Author(s):  
A. S. Victorov ◽  
T. V. Orlov ◽  
S. A. Sadkov ◽  
O. N. Trapeznikova

The aim of this paper is to show approaches for the quantitative evaluation of natural hazards using the remote sensing data and basing on the results of the mathematical morphology of landscape. The mathematical model of the morphological pattern for lacustrine thermokarst plains with fluvial erosion was taken for the decision of the problem in case of an asynchronous start of the thermokarst process with the continuous generation of new thermokarst depressions. The mathematical analysis of assumptions taken in the model gives us the regularities of the morphological pattern for the thermokarst plains with fluvial erosion including exponential distribution for khasyrei areas, integral-exponential distribution for lake areas, and the Poisson distribution for a quantity of either khasyreis or lakes within the key sites. Besides, analyzing the development of the territory in question by the approaches used in mathematical morphology of landscape we found out that in case of asynchronous start under very general conditions a dynamic equilibrium is established in generating thermokarst lakes and turning them into khasyreis after a long time. At the same time, the distribution density of thermokarst foci and their sizes, as well as process damage and the dimensions of khasyreis tend to some final levels specified by the expressions described above. The results obtained were empirically tested at 17 key sites. Generally, the empirical testing shows that the asynchronous start takes place within thermokarst plains with fluvial erosion at a sufficient number of sites, and the theoretically obtained regulations are valid. The regulations obtained were used for the mathematical solution of the probabilistic task for damage of a linear structure crossing the thermokarst plain with fluvial erosion.


2019 ◽  
Author(s):  
Xiaochu Li ◽  
Floricel Gonzalez ◽  
Nathaniel Esteves ◽  
Birgit E. Scharf ◽  
Jing Chen

AbstractCoexistence of bacteriophages, or phages, and their host bacteria plays an important role in maintaining the microbial communities. In natural environments with limited nutrients, motile bacteria can actively migrate towards locations of richer resources. Although phages are not motile themselves, they can infect motile bacterial hosts and spread in space via the hosts. Therefore, in a migrating microbial community coexistence of bacteria and phages implies their co-propagation in space. Here, we combine an experimental approach and mathematical modeling to explore how phages and their motile host bacteria coexist and co-propagate. When lytic phages encountered motile host bacteria in our experimental set up, a sector-shaped lysis zone formed. Our mathematical model indicates that local nutrient depletion and the resulting inhibition of proliferation and motility of bacteria and phages are the key to formation of the observed lysis pattern. The model further reveals the straight radial boundaries in the lysis pattern as a tell-tale sign for coexistence and co-propagation of bacteria and phages. Emergence of such a pattern, albeit insensitive to extrinsic factors, requires a balance between intrinsic biological properties of phages and bacteria, which likely results from co-evolution of phages and bacteria.Author summaryCoexistence of phages and their bacterial hosts is important for maintaining the microbial communities. In a migrating microbial community, coexistence between phages and host bacteria implies that they co-propagate in space. Here we report a novel phage lysis pattern that is indicative of this co-propagation. The corresponding mathematical model we developed highlights a crucial dependence of the lysis pattern and implied phage-bacteria co-propagation on intrinsic properties allowing proliferation and spreading of the microbes in space. Remarkably, extrinsic factors, such as overall nutrient level, do not influence phage-bacteria coexistence and co-propagation. Findings from this work have strong implications for dispersal of phages mediated by motile bacterial communities, which will provide scientific basis for the fast-growing applications of phages.


2022 ◽  
Vol 2022 ◽  
pp. 1-14
Author(s):  
Muhammad Ali ◽  
Alamgir Khalil ◽  
Wali Khan Mashwani ◽  
Sharifah Alrajhi ◽  
Sanaa Al-Marzouki ◽  
...  

In this article, a new lifetime model, referred to as modified Frechet–Rayleigh distribution (MFRD), is developed by accommodating an additional parameter in Rayleigh distribution on the basis of the modified Frechet method. Numerous statistical properties of the suggested model are derived and discussed. The technique of maximum likelihood (ML) estimation is adopted to get estimates of the parameters. The suggested model is very flexible and has the capability to model datasets having both monotonic and nonmonotonic failure rates. The proposed model is applied on two real datasets for checking its performance in comparison with available well-known models. The suggested model has shown outclass performance in comparison with the available versions of the Rayleigh distribution used in the literature.


2012 ◽  
Vol 47 (1) ◽  
pp. 137-142
Author(s):  
AA Rana ◽  
M Kamruzzaman ◽  
M Saha

Benzylation of o-cresol with benzyl alcohol (Bz-OH) in presence of 94% H2SO4 as catalyst was studied statistically with a two-levels threefactored   experimental design to study the effects of single factor and effects of their interactions on the yield of benzylated product. Reaction   temperature, molar ratio of o-cresol to Bz-OH and amount of 94% H2SO4 were considered as the major variables. A mathematical model   was derived to calculate the predicted yield of benzyl o-cresol as y = 0.419T+12.4055m+16.17w-0.0525Tm-2.606mw-   0.094Tw+0.0175Tmw-6.25; where, T = temperature (oC), m = o-cresol to Bz-OH molar ratio, w = amount of catalyst (% by wt. of o-cresol)   and y = yield. The adequacy of the suggested model was checked up and the discrepancies between the experimental and calculated values   did not exceed ± 0.79%. DOI: http://dx.doi.org/10.3329/bjsir.v47i1.10727 Bangladesh J. Sci. Ind. Res. 47(1), 137-142, 2012


2014 ◽  
Vol 20 (3) ◽  
pp. 484-506 ◽  
Author(s):  
Lijana Maskeliūnaitė ◽  
Henrikas Sivilevičius

The quality of multifaceted objects or phenomena can be hardly described or evaluated by a single criterion. The quality of the trip by train is described by a set of quantitative and qualitative criteria. The influence of all the criteria on the trip by international train may be evaluated by a comprehensive quality index (CQI) or quality index K. An additive model is offered for calculating CQI, which consists of the average weights of the criterion groups, as well as normalized weights and variables of the criteria, showing the correspondence of the real value of each criterion to the best, critical or allowable value. A mathematical model, which may be used for determining the quality of the trip by train based on the criteria describing the elements of the train and technical state of the railway track is also presented. Based on the use of 16 criteria describing the elements of the train and the parameters and the technical state of the railway track, the quantitative estimate KA (multiple criteria index) is obtained. The suggested model and the techniques used in the work may be applied to determining the quality or effectiveness of other objects or processes, which can be described by sets of criteria.


2016 ◽  
Vol 20 (2) ◽  
pp. 71-79
Author(s):  
Karol Garbiak ◽  
Jan Jurga

AbstractThe article presents analysis of the mathematical model for determination of a momentary dose of spray applied by the field sprayer nozzles which move on the curve with the forward speed the value of which may differ from the speed accepted for regulation. Regulation speed and regulation dose, real forward speed of a sprayer, angular velocity during the curve movement, and the coefficient of the nozzle location towards the axis of the sprayer turn are independent variables in the suggested model. Based on the mathematical model, plots were drawn and analyses of relation of the spray dose to particular variables were carried out including inter alia, a repeated field spray, application of a dose which considerably differs from the regulation dose and diversity of the dose on the working width of the sprayer.


1988 ◽  
Vol 1 (21) ◽  
pp. 119 ◽  
Author(s):  
Rolf Deigaard ◽  
Jorgen Fredsoe ◽  
Ida Broker Hedegaard ◽  
Julio A. Zyserman ◽  
Ole Holst Andersen

The littoral drift model developed at DHI and ISVA, see Deigaard et al. (1986b) has been extended to include the effects of the irregularity of the waves, of a coastal current and a wind acting on the surf zone. Further, a mathematical model to simulate the near-shore current pattern along a barred coast with rip channels has been developed. The influence on the littoral drift of the irregularity of waves, wind, coastal current, and rip channels is discussed. It is concluded that irregularity of waves and presence of rip channels must be considered while coastal current and wind action are of minor importance.


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