Effect of droplets convective heating and their evaporation on the shielding properties of fire-fighting water curtain

Представлено подальший розвиток раніше отриманих результатів математичного моделювання водяних завіс протипожежного призначення. Предметом теоретичного аналізу є плоскі струмені розпиленої води, що створюються щілинними дренчерними зрошувачами. Основною метою роботи є теоретичне дослідження процесу конвективного нагрівання й випаровування крапель у нагрітому повітрі поблизу осередку пожежі та його впливу на екрануючі властивості протипожежної водяної завіси. Отримано розрахункову формулу і виконано чисельні розрахунки для залежності рівноважної температури крапель від температури повітря. Отримано розрахункові формули для часу випаровування крапель різних діаметрів в гарячому повітрі і для часу прольоту крапель уздовж осі водяної завіси. Згідно з виконаними розрахунками, для типових параметрів водяних завіс нагрівання крапель і їх випаровування внаслідок конвективного теплообміну з гарячим повітрям не мають істотного впливу на екрануючі властивості протипожежних водяних завіс. Застосування отриманих результатів до математичної моделі теплозахисту дозволило розширити її можливості для практичного застосування. Модель може використовуватися для проектування водяних завіс протипожежного призначення, а також для визначення оптимальних режимів їх застосування.Purpose. This work represents further development of earlier received results of simulation of water curtains used as fire protection walls. Subject of the theoretical analysis is the flat fan sprays which flow from the slot-hole sprinkler. The central objective of the study is theoretical research of processes of droplets convective heating and their evaporation in heated air near the fire seat and their influence on the shielding properties of a fire-fighting water curtain. Approach. In this study the earlier published literary data are applied to fulfill the calculations. The calculated formula allowed to have received numerical results for graphic dependence of droplet equilibrium temperature on air temperature. Other calculated formulae allowed to have executed calculations of the droplet evaporation time and of the time of droplet flight along an axis of a water curtain. According to the executed calculations, for typical parameters of water curtain the droplets heating and their evaporation owing to heat convection with hot air have no significant effect on the shielding properties of fire-fighting water curtain. Findings. Application of this formula to earlier developed mathematical model of thermal shielding allowed expanding its opportunities for practical use. This model can be used for designing of water curtains of fire-prevention appointment, and also for definition of optimum modes of their operation.Представлено дальнейшее развитие ранее полученных результатов математического моделирования водяных завес противопожарного назначения. Предметом теоретического анализа являются плоские струи распыленной воды, которые создаются щелевыми дренчерными оросителями. Основной целью работы является теоретическое исследование процесса конвективного нагрева и испарения капель в нагретом воздухе вблизи очага пожара и его влияния на экранирующие свойства противопожарной водяной завесы. Получена расчетная формула и выполнены численные расчеты для зависимости равновесной температуры капель от температуры воздуха. Получены расчетные формулы для времени испарения капель различных диаметров в горячем воздухе и для времени пролета капель вдоль оси водяной завесы. Согласно выполненным расчетам, для типичных параметров водяных завес нагрев капель и их испарение вследствие конвективного теплообмена с горячим воздухом не оказывают существенного влияния на экранирующие свойства противопожарных водяных завес. Применение полученных результатов к математической модели теплозащиты позволило расширить ее возможности для практического применения. Модель может использоваться для проектирования водяных завес противопожарного назначения, а также для определения оптимальных режимов их применения

Conservation laws for multidimensional systems and related linear algebra problems

We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model, and the Belousov-Zhabotinskii system. To achieve this, we solve over an arbitrary field the matrix equations SA=A^tS and SA=-A^tS for a quadratic matrix A and its transpose A^t, which may be of independent interest.Comment: 12 pages; proof of Theorem 1 clarified; misprints correcte

Orienting Role of Terminology in Context of Its Scientific-Popular Conceptualization

The article examines the structural and functional properties of terms in popular scientific discourse. The authors aim to characterize the orientation of a term as a combination of its linguistic and functional properties, which define the concept expressed by the term, its connections with other concepts, and its place within the terminological system. The object of the study is linguistic and speech units in popular scientific texts, while the subject is the means of expressing orienting properties of terms in popular scientific discourse. The novelty of the research lies in studying the orienting properties of terms in popular scientific style based on their linguistic and speech properties, and providing a classification of these properties according to the scope and content of the expressed concepts. The relevance of the study is determined by the important role of these properties in the process of forming specialized concepts, understanding scientific, popular scientific, and educational discourses, and solving practical problems related to terminology use. The authors focus on the orienting function of a term, which is carried out through linguistic and speech means, with logical definitions, textual explanations, intercategorical connections expressed by elements of word formation and morpho-syntactic systems being the most active ones. The authors conclude that orienting properties of terms play a significant role in terminological conceptualization (formation of specialized concepts)

Potential Conservation Laws

We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially depend on potential variables. This statement provides a significant generalization of results of the recent paper by Bluman, Cheviakov and Ivanova [J. Math. Phys., 2006, V.47, 113505]. Moreover, we present extensions to gauged potential systems, Abelian and general coverings and general foliated systems of differential equations. An example illustrating possible applications of proved statements is considered. A special version of the Hadamard lemma for fiber bundles and the notions of weighted jet spaces are proposed as new tools for the investigation of potential conservation laws.Comment: 36 pages, extended versio

Coherence Enhanced Transient Lasing in XUV Regime

We report the effect of a coherent drive on transient lasing in three-level $\Lambda$ and $\Xi$ configurations ($c\leftrightarrow a\leftrightarrow b$). We show that the presence of a resonant coherent drive on the $a\leftrightarrow c$ optical transition can yield an order of magnitude enhancement of the output laser energy on a $a\rightarrow b$ XUV or X-ray transition than with no coherent drive. We demonstrate the crucial role of coherence $\varrho_{ac}$ for the laser power enhancement. Contrary to the forward direction (with respect to the pump), where forward gain can be enhanced for some choice of the drive Rabi frequency $\Omega_{c}$, coherent drive on the $ac$ transition always suppresses the backward gain.Comment: 8 pages, 11 figure

Results on the Wess-Zumino consistency condition for arbitrary Lie algebras

The so-called covariant Poincare lemma on the induced cohomology of the spacetime exterior derivative in the cohomology of the gauge part of the BRST differential is extended to cover the case of arbitrary, non reductive Lie algebras. As a consequence, the general solution of the Wess-Zumino consistency condition with a non trivial descent can, for arbitrary (super) Lie algebras, be computed in the small algebra of the 1 form potentials, the ghosts and their exterior derivatives. For particular Lie algebras that are the semidirect sum of a semisimple Lie subalgebra with an ideal, a theorem by Hochschild and Serre is used to characterize more precisely the cohomology of the gauge part of the BRST differential in the small algebra. In the case of an abelian ideal, this leads to a complete solution of the Wess-Zumino consistency condition in this space. As an application, the consistent deformations of 2+1 dimensional Chern-Simons theory based on iso(2,1) are rediscussed.Comment: 39 pages Latex file, 1 eps figure, typos and proof of lemma 5 correcte

Channel spaser

We show that net amplification of surface plasmons is achieved in channel in a metal plate due to nonradiative excitation by quantum dots. This makes possible lossless plasmon transmission lines in the channel as well as the amplification and generation of coherent surface plasmons. As an example, a ring channel spaser is considered

The Johnson-Segalman model with a diffusion term in Couette flow

We study the Johnson-Segalman (JS) model as a paradigm for some complex fluids which are observed to phase separate, or ``shear-band'' in flow. We analyze the behavior of this model in cylindrical Couette flow and demonstrate the history dependence inherent in the local JS model. We add a simple gradient term to the stress dynamics and demonstrate how this term breaks the degeneracy of the local model and prescribes a much smaller (discrete, rather than continuous) set of banded steady state solutions. We investigate some of the effects of the curvature of Couette flow on the observable steady state behavior and kinetics, and discuss some of the implications for metastability.Comment: 14 pp, to be published in Journal of Rheolog