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EN
We consider a second order regular differential operator whose coefficients are nonselfadjoint bounded operators acting in a Hilbert space. An estimate for the resolvent and a bound for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.
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EN
This paper presents a numerical algorithm for the study of the absolute instability of a vortex street with external axial velocities and finite length vortices. The aim is that this will be of relevance to the study of the flow over slender bodies at yaw. The algorithm is based on the vortex dynamics momentum equation. Special core treatments have been implemented to tackle the problem of infinite self-induced velocity. A small pertubation method is then used to formulate the eigenvalue problem.
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EN
Four years after the end of its uprising against the Gaddafi regime, Libya remains in chaos. It is worth noting that for the third time since their independence in 1951, the Libyans’ attempts to create a modern and powerful state seem to be ‘wishful thinking’. The first two failed attempts – in 1951 and 1969 – were essentially local affairs without significant consequences beyond the country’s borders. The ongoing turmoil which followed in the wake of the Arab Spring in 2011 is leading to serious regional and international destabilization. This paper discusses the main factors of the instability in post‑Gaddafi Libya. According to the authors’ analysis, there are the following main obstacles in the process of transition toward democracy and peace: two competing governments, multiplicity of militias and combat groups operating in Libya, jihadism rising in power as well as the regional and ethnic claims for recognition and autonomy. The last part of this paper is devoted to potential scenarios for the future of Libya.
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Open Physics
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2008
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tom 6
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nr 4
903-911
EN
In this paper, we use a thin filament two dimensional Gaussian beam to model the self-trapping filament. The instability of the propagation of a Gaussian beam through a nonlinear refractive index media is investigated, theoretically and numerically. Specifically, the small scale instability of the beam is examined. The numerical results show that the propagation of the two dimensional Gaussian beam presents one or more nonlinear focal points.
5
Content available remote Climate of long internal waves and resuspension on the coastal shelf
100%
EN
Observations of the shelf environment rarely associate internal solitary waves (ISWs) with the impact of their passage. An experiment observed during the Coastal Mixing and Optics 1996 (CMO '96), a sequence of long internal waves on a coastal shelf is reported, including both mode-1 and mode-2 waves, together with evidence related to the interaction of propagating ISWs and the benthic boundary layer. The observed ISW dynamics is shown to present a repetitive pattern or "climate cycle". The ISW-associated benthic signature described here occurs frequently (at least once a day) in the CMO '96 coastal area and suggests that ISWs under calm, summer-like conditions may have a decisive influence on the fate of near-bottom pollutants or biological processes in shelf regions.
EN
A fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves of wave-steepness up to 0.25, is used here to investigate the effect of randomness on stability of deep-water surface gravity waves in the presence of wind blowing over water. A spectral transport equation for narrow band Gaussian surface wave is derived. With the use of this transport equation stability analysis is made for an initial homogeneous wave spectrum having a very simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained, in which higher order contribution comes from only one of the fourth order terms in the evolution equation, which is responsible for wave-induced mean flow. This higher order contribution in this expression for growth rate of instability produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and ultimately the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order terms in the evolution equation.
EN
Fourth order nonlinear evolution equations are derived for two Stokes wave trains in deep water in the presence of air flowing over water. The importance of the fourth order term in the evolution equation was pointed out by Dysthe (1979). Stability analysis is then made for uniform two Stokes wave trains in the presence of air flowing over water. From these evolution equations the expressions for the maximum growth rate of instability, the wave number at marginal stability and the wave number separation of fastest growing side band are derived and graphs are plotted for the above three expressions against the wave steepness. Significant improvements can be achieved from the results obtained from the two coupled third order nonlinear Schrödinger equations.
8
Content available remote Positive unstable electrical circuits
75%
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2012
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tom R. 88, nr 5a
187-192
EN
The instability for the positive linear electrical circuits composed of resistors, coils, condensators and voltage (current) sources are addressed. Three different classes of the positive unstable linear electrical circuits are proposed and analyzed. It is shown that positive electrical circuits are unstable for all values of their parameters if the electrical circuit has at least one mesh containing only inductances and source voltages.
PL
W artykule rozpatrywane są niestabilne dodatnie liniowe obwody elektryczne złożone z rezystorów, cewek, kondensatorów i źródeł napięcia lub prądu. Analizowane są trzy różne klasy dodatnich obwodów elektrycznych, które są niestabilne dla wszystkich wartości swoich parametrów tzn. rezystancji, indukcyjności i pojemności. Wykazano, że dodatnie obwody elektryczne są niestabilne dla wszystkich wartości swoich parametrów jeżeli zawierają one przynajmniej jedno oczko złożone tylko z cewek i źródeł napięcia.
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PL
W artykule opisano zjawiska nieciągłości i histerezy charakterystyk promieniowych wieńców sprężających. Omówiono zjawisko oderwania wirującego i przedstawiono jego interpretację literaturową. Opierając się o wyniki badań własnych oraz obcych przedstawiono przykłady charakterystyk wentylatorów i dmuchaw promieniowych, w których zachodzi histereza. W zakończeniu zaproponowano program badań w tej dziedzinie.
EN
The phenomena of discontinuity and hysteresis shown on performance curves of radial compressing cascades have been described. The rotating stall has been discussed and its interpretation in the literature is presented. On the basis of the results of own investigations as well as those conducted by the others, some examples of performance curves of radial fans and blowers, in which hysteresis takes place, have been presented. Finally, a programme for further investigations in this area has been proposed.
PL
Przedstawiono teoretyczne przesłanki prawidłowego doboru kształtu narzędzi do wyciskania promieniowego wyrobów. Za pomocą programów komputerowych DEFORM-2 i FORGE3 analizowano różne warunki płynięcia metalu. Udowodniono, że w przypadku nieprawidłowego doboru kształtu narzędzi dochodzi do niestateczności plastycznego płynięcia, która ujawnia się promieniowym podziałem wyciskanego materiału. Wykazano, że zbyt małe kąty nachylenia powierzchni wykrojów matrycowych przyczyniają się do obwodowego rozciągania warstw zewnętrznych kształtowanego metalu, co prowadzi do niekontrolowanego płynięcia metalu i utraty stateczności plastycznego płynięcia. Wyniki symulacji zostały potwierdzone badaniami eksperymentalnymi procesów wyciskania przeprowadzonymi na zimno i gorąco, a także w stanie półciekłym. Stwierdzono, że symulacje przeprowadzone metodą elementów skończonych pozwalają sprawdzić zachowanie stateczności plastycznego płynięcia, a tym samym ocenić przydatność zaprojektowanych narzędzi do zastosowań praktycznych.
EN
Theoretical premises for correct choice of tool shape for radial extrusion of products have been presented. The different conditions of metal flow were analyzed using DEFORM-2 and FORGE3 programme. It was proved that, in the case of incorrect choice of tool shape, instability of plastic flow occurs, which leads to radial partition of extruded material. It has been show that too small angles of inclination of die surfaces cause a circumferential tension of the external layer of deformed metal, which guides to the uncontrolled metal flow, and the loss of flow stability. The results of simulations have been confirmed by experimental investigations for radial extrusion processes carried out under cold and hot forming conditions, and also in semi-liquid state. It was found that the flow analysis using FEM solutions permits to check the stability of plastic flow and evaluates the usefulness of tools designed.
EN
By exact numerical computation Yuen (1984) obtained regions of type-I instability for waves propagating at the interface of two superposed fluids of infinite thickness in which the upper fluid has a constant streaming velocity. In the present paper it is shown that the long wavelength part of these instability regions can be obtained analytically from a fourth order nonlinear evolution equation for small but finite amplitude interfacial capillary gravity waves in the presence of air flowing over water.
EN
The goal of this study is to identify empirically how non-traditional activities affect directly the risk profiles and profitability of the banking sector. Through a dataset that covers 2678 European banks spanning the period 1996–2011 and the methodology of panel regression, the empirical findings document that investment banks have a negative effect on systemic risk in the banking sector. To show the heterogeneity of systemic risk determinants, the study sample was divided according to the economic development of a country into two groups: advanced and developing countries. We examine the implications of banks’ activity and risk-taking that manifest themselves as spreading and growing instability in the banking system. Then we explore the implications of the interaction between banking risk and structural, macroeconomic and financial market determinants. The findings have implications for both bank risk management and regulators. This paper advances the agenda of making macroprudential policy operational.
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2012
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tom Vol. 11, nr 2
93-101
EN
In this paper, the results of numerical studies on vibration and instability of a geometrically nonlinear column subjected to Euler's load are presented. The system is loaded by external axial force P applied at the free end of the column. Additional concentrated mass is localised on one of column's rods. The Hamilton principle was used to formulate the boundary problem. Due to the geometrical nonlinearity, the solution of the problem was performed by means of the small parameter method. The main purpose of this paper is to investigate an influence of the concentrated mass on divergence instability and critical loading and natural vibration frequency.
14
Content available remote Evolution of a random field of surface gravity waves in a two fluid domain
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EN
A spectral transport equation is derived here that governs the evolution of a random field of surface gravity waves in a two layer fluid model. This equation is used to study the stability of an initially homogeneous Lorentz spectrum under long wave length perturbations. It is observed that the effect of randomness is to reduce the growth rate of instability. An increase in the thickness of the upper fluid results in an increase in the extent of instability. It is also found that the extent of instability becomes less for a smaller density difference of the two fluids.
PL
Ciepło generowane w hamulcach mechanicznych wywołuje odkształcenia termosprężyste tarcz hamulcowych, co prowadzi do zmiany rozkładu nacisków na powierzchniach ciernych tarcz. To wzajemnie powiązane ze sobą oddziaływanie prowadzi do wytworzenia tzw. gorących plam, jeżeli początkowa prędkość hamowania jest wystarczająco wysoka. Tak opisany proces nazywa się niestabilnością termosprężystą. W artykule przedstawiono zastosowanie metody elementów skończonych (MES) do modelowania tego procesu w hamulcach tarczowych maszyn wyciągowych. Przedstawiono wpływ wybranych parametrów konstrukcyjnych (grubość tarczy) i materiałowych tarczy (współczynnika rozszerzalności cieplnej, przewodności cieplnej i modułu sprężystości) na wartość prędkości krytycznej. Jako kryterium oceny przejścia ze sfery stabilności do niestabilności przyjęto kryterium dopuszczlnego odkształcenia osiowego tarczy hamulca.
EN
The heat generated in mechanical brakes causes thermoelastic distortion of disc and affects the distribution of contact pressure. This interaction is unstable if the sliding speed is sufficiently high leading eventually to the development of hot spots. The phenomenon is reffered to as frictionally-excited thermoelstic instability or TEI. This paper describes application of finite element modelling of the phenomenon in mining winding machine friction disc Breakes. The effects of friction material properties, disc material properties and disc thickness on the criterial speed were investigated. The most influential property was found to be the thermal expansion coefficient of disc material. As the criterion for stability/instability evaluation the axial disc diistortion-rise limit was applied in the finite element analysis.
16
63%
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2008
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tom Z. 1
43-54
PL
Celem opracowania jest przedstawienie warunków całkowitej energii chwiejności atmosfery (CAPE) nad Europą. Dane pomiarowe reprezentują 41 stacji aerologicznych w Europie między 10oW a 50oE oraz 35oN a 65oN. Wartość całkowitej energii chwiejności na wybranych stacjach zostały wyliczone dla sondaży z terminu 00UTC w latach 1991-2003. Przebieg wartości całkowitej energii chwiejności cechuje wyraźny cykl roczny z przypadającymi w lecie wartościami maksymalnymi. Najwyższe wartości powyżej 2500 J/kg zanotowano na stacjach w Mediolanie, na Sycylii, Stambule oraz w Kijowie, natomiast najniższe maksymalne wartości, nieprzekraczające1000 J/kg, na stacjach Brest i Stavanger. Rozkład przestrzenny średnich miesięcznych wartości całkowitej energii chwiejności pozwala na wyróżnienie trzech regionów, cechujących się odmiennym nasileniem niestabilności atmosfery. Pierwszy region, obejmujący obszary zachodniej i północnej Europy zaznacza się najsłabszą chwiejnością atmosfery. Wartości średnie miesięczne CAPE nie przekraczają 50 J/kg. Nie ma tu wyraźnego wzrostu niestabilności atmosfery w lecie. Drugi region, obejmujący wschodnią i środkową Europę, charakteryzuje się silniejsza niestabilnością atmosfery, szczególnie w porze letniej. Wtedy średnie miesięczne całkowitej energii chwiejności przekraczają 50 J/kg w Europie centralnej oraz przekraczają 200 J/kg we wschodniej Europie. Trzeci region, obejmujący południową Europę zaznacza się największymi średnimi miesięcznymi wskaźnika CAPE. W okresie od czerwca do września średnie miesięczne przekraczają 300 J/kg. Rozkład częstości wartości całkowitej energii chwiejności charakteryzuje się silną skośnością. Największą częstością odznaczają się wartości CAPE z przedziału 0-50 J/kg, powyżej 50% wszystkich przypadków, natomiast częstość większych wartości całkowitej energii chwiejności jest znacznie mniejsza. W przypadku stacji śródziemnomorskich szczególnie Mediolan, Sycylia, Stambuł wyróżniają się wzrostem częstości przypadków CAPE powyżej 1000 J/kg. Na tych stacjach w badanym okresie liczba dni z taka chwiejnością przekroczyła 100 przypadków.
EN
The main goal of this study is asses the spatial distribution of convective available potential energy (CAPE) in Europe. The analysis CAPE values is based on data from 41 stations (fig.1) which covered region from 35oN to 65oN and from 35oW to 50oE. The data used in this study were gathered during the thirteen years (1991-2003) measured every day at 00:00 UTC. The annual course of CAPE values shows summer maximum (fig.2). The maximum values reached above 2500 J/kg on Sicilian, Milan, Istanbul and Kiev and only 1000 J/kg on Brest. The spatial distribution and annual course of mean monthly of CAPE values shows three zones. The first one is located in west and north Europe where instability is very week. During all seasons the mean monthly values of CAPE reached minimum lover than 50 J/kg. The second zone, including central end east Europe is characterized by greater instability, especially during summer. During these season the mean monthly values of CAPE are noticed above 50 J/kg, especially in central Europe, and above 200 J/kg in east Europe. The third zone is located in south Europe. Between June to September the mean monthly values reached maximum above 300 J/kg. The frequency distribution of values of CAPE is positively skewed with long tail after the peak. The highest frequency is noticed for 0-50 J/kg in above 50% number of stations. Beyond these CAPE values frequency decreases. The special station are Milan, Sicilian and Istanbul where increases the number of cases above 1000J/kg. The frequency of CAPE index above 1000J/kg is shown (fig.6a) the greatest frequency of strong instability in south Europe (Sicilian, Italy, west Turkey above 100 cases).
17
Content available remote Application of element deletion method for numerical analyses of cracking
63%
EN
Purpose: To develop a numerical algorithm to simulate cracking and its evolution for machining, shearing and multi-pass hot bar rolling processes. Design/methodology/approach: Element deletion method was adopted for developing a numerical algorithm and implemented to a rigid-viscoplastic finite element program. Cockcroft-Latham and specific plastic work criteria were incorporated in the present investigation for simulating cracking and shearing processes. An instability condition for the tension was assumed to be valid to determine a critical damage factor for initiation of possible cracking. Findings: The developed element deletion algorithm was simple to be applied for simulating cracking and shearing patterns for the processes applied. Cockcroft-Latham and specific plastic work fracture criteria were reasonable in predicting the internal and external crack, respectively. Research limitations/implications: The research finding can be utilized for investigating occurrence of external and internal cracking involved with metal forming processes such as Chevron cracking in extrusion. Practical implications: By expanding the current approach to determine a processing map for extrusion the processing condition to prevent Chevron cracking can be determined easily and utilized in industry. Also, the current investigation can be easily expanded to other process design and control. Originality/value: Numerical algorithm based on the element deletion method was developed and implemented to the existing finite element program to examine the processes including cracking phenomenon. The applicability to utilize a critical damage factor for the fracture criteria based on the instability was evaluated.
18
Content available remote Relaxation and breakup of a cylindrical liquid column
63%
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2011
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tom Vol. 16, no 1
257-270
EN
Instability of a capillary wave and breakup of a square cylindrical liquid column during its relaxation have been investigated numerically by simulating three-dimensional Navier-Stokes equations. For this investigation a computer code based on the volume-of-fluid (VOF) method has been developed and validated with published experimental results. The result shows that the agreement of numerical simulation is quite good with the experimental data. The code is then used to study the capillary wave and breakup phenomena of the liquid column. The investigation shows the underlying physics during relaxation of the square cylindrical liquid column, illustrates the formation and propagation of the capillary wave and breakup processes. The breakup behavior for the present configuration of the liquid column shows some significant differences from those predicted by conventional jet atomization theories. The formation of the capillary wave is initiated by the surface tension on the sharp edge of the square end of the cylinder and the propagation of the wave occurs due to the effect of surface tension force on the motion of the fluid. The propagation of the capillary wave to the end of the liquid column causes a disturbance in the system and makes the waves unstable which initiates the breakup of the liquid column. The characteristics of the capillary wave show that the amplitude of the swell grows faster than the neck of the wave and that of the tip wave grows much faster than other waves. The velocity of the liquid particle is dominated by the pressure in the liquid column.
19
63%
EN
Meaning Holism and Contextualism are standardly acknowledged to be similar relativistic theories that often lead to similar troubles, in particular to issues concerning instability. On the other hand, the main rival of Contextualism, which is Minimalism, is taken to be resistant to these problems. In effect, it seems inevitable to see Meaning Holism and Minimalism as natural enemies. In my paper, I attempt to reject such a view. My argumentation consists of three main parts. First, I argue that Minimalism does not differ that much from Meaning Holism with respect to the instability issues as it also faces some of them (although in a slightly different way from the case of Holism of Contextualism). Second, I put forward several arguments to show that in fact Minimalism is not incompatible with the two versions of Meaning Holism I distinguish, namely Global Holism and Local Holism. I argue that a meaning holist has to accept some not uncontroversial principles to become an antiminimalist – and vice versa. Finally, I demonstrate that Minimalism and Meaning Holism can be reconciled. Such a possibility occurs when something I called ‘purely semantic processes’ is allowed. The role of these processes is, roughly speaking, to protect literal meanings from being affected by strong pragmatic factors.
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2010
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tom Vol. 9, nr 1
187-194
EN
In this paper, the results of numerical studies on the local and global instability and vibration of a geometrically nonlinear column subjected to Euler's load are presented. The Hamilton principle was used to formulate the boundary problem. Due to the geometrical nonlinearity, the solution of the problem was performed by means of the perturbation method. The magnitude of the bifurcation load of the nonlinear column, the local and global instability regions and characteristic curves have also been presented.
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