using cross-sections in three projection planes, for the four changes of Chua’s circuit parameters. It is known that due to changing the parameters, the Chua’s circuit can be characterized not only by stable limit cycle, but also by one double scroll chaotic attractor, two single scroll chaotic attractors or other two stable limit cycles. Chua’s circuit can even start working as a binary memory. It is not known yet, how changes in parameters, and consequently in at- tractors in the circuit, will affect the morphology of the boundarysurface. The boundarysurface separates the double scroll chaotic attractor from the stable limit cycle. In a variation of the parameters presented in this paper, the boundarysurface will separate even single scroll cha- otic attractors from each other. Dividing the state space into regions of attraction for different attractors, however, remains fundamentally the same.
For several decades perturbation methods have been considered inadequate for the treat- ment of problems of wave scattering, and only few of the many discussions, mainly in the area scattering by corrugated surfaces, have been based on perturbative techniques. Low order perturbative approaches include the rst order calculation of Rayleigh  and, much more recently, that of Wait . For higher order methods, the literature seems to reduce to the work of Meecham . Low order methods are only appropriate for very small departures from an exactly solvable geometry, and, in particular, they cannot be applied to scatterers in the resonance region [21, 31]. The approach of Meecham, on the other hand, produces the scattering from a corrugated surface as a Neumann series whose n -th term is given by an n -fold convolution of the Green's function. This method, which has not been implemented
selection is determined on the basis of the electric field values alone. This approach was devised to account for the varying initiating wind speeds, likely dependent on the speed required to lift snow and ice particles into the air under varying ice surface conditions, for which a rapid increase in the electric field values is observed (Burns et al. 1995). An initial rejection of the minute- averaged data is made on the basis of the fields ex- ceeding 300 V m 21 at Vostok, or 333 V m 21 for the higher field values at Concordia, over widened time in- tervals of 2 h from the times of the fields exceeding these thresholds. This extended time interval is a conservative allowance for the influence of lifting snow and ice before and after the cut-off electric field value is reached. Rapid variations below these thresholds are also rejected, at two levels of severity, on the basis of jumps in the field within a 5-min interval. Data within 30 min of a jump of 30 V m 21 (within 5 min) at Vostok or 33 V m 21 at Con- cordia are rejected and are designated ‘‘strong vari- ability rejection’’ (svr). These svr selection criteria are similar to those used for the 1998–2001 Vostok electric field measurements (Burns et al. 2005, 2012). When specifically for Vostok the designation of the data re- maining is Vos E s
Convection can be described as the motion of fluid which is driven by differential body forces or by surface forces which are acting on the boundary of the fluid. A differential body force can occur if there is a difference in the fluid’s density while it is in a gravitational field. This is a well known case and is an example of natural convection. Convection due to surface forces can be induced by a pump or fan which forces the fluid to move. This is an example of forced convection. Most types of convection can by categorized in one of these groups. However, there are other mechanisms possible. Consider a system which contains a fluid and is heated from below. Due to this heating, the density of the fluid changes locally, resulting in a lighter fluid in the bottom and a heavier fluid on top. This does however not guarantee convective motion. The thermal diffusivity and viscosity of the fluid will try to prevent the onset of this instability. If we induce a large enough temperature gradient between the bottom and top of the system, or in other words, if we heat the system sufficiently, the state becomes unstable and the convective motion becomes visible. This is illustrated in Figure 1.1.
Up to this point in the course, most of the emphasis has been upon the basic definitions of key concepts (various sorts of integrals, “nice” regions in the coordinate plane and 3 – space, potential functions, surface area, flux of a vector field, … ) and methods for computing various integrals and functions, including statements of several fundamentally important theorems like the Change of Variables Rule and Green’s Theorem. While these points are also central to the remaining sections of the course, there will also be an additional factor: We shall also focus on the logical derivations of some important formulas that play crucial roles in the applications of vector analysis to the sciences and engineering.
Rotation of Earth Surface ocean currents do not simply flow in a straight line away from the equator. The rotation of Earth causes the flow to curve to the right above the equator, and to the left below the equator. This natural phenomenon is called the Coriolis effect. Because of this effect, surface ocean currents can flow in a circular pattern called a gyre. Each ocean basin contains a gyre. Gyres north of the equator—like the North Atlantic Gyre below—turn in a clockwise direction. Gyres south of the equator turn in a counter-clockwise direction. It takes about three years for water to complete the path of the North Atlantic Gyre. This rate was determined by tracking bathtub toys that had spilled into the Atlantic Ocean (Figure 6.6)! Heat energy Surface ocean currents move an enormous amount of heat energy away from the equator. Find New York and England on the map below. You can see that England is farther north of the equator than New York. Find the Gulf Stream part of the North Atlantic Gyre. The Gulf Stream carries so much heat energy that England is as warm as New York! Moving this amount of heat energy is
we have N + 1 inequivalent boundary conditions, which have to correspond to different solutions of the boundary Yang-Baxter equation. Due to the fact that the boundary interaction does not involve any flavor-changing terms, we should be able to find diagonal solutions for the BYBE, which will be done in section 4. In this section, following Ghoshal analysis, we exhibit solutions for the free and fixed boundary conditions, which serves as a warm-up for the more general case.
Since sonic sensor’s exciting energy change with energy consumption and the received amplitude could also make a difference. And if ordinary integrated op- erational amplifier is instead, amplitude identification method used in acoustic receiving may appear misconception phenomenon. Thus in order to create a similar amount of magnified pulse signal’s amplitude, automatic gain amplifying circuit should be eligible to amplifying signal and this type of functionality is usually realized by gain-programmed amplifier. Its working principle is sustain the magnified receipt signal’s peak sampling for long and the signal is used to control the gain-programmed amplifier’s amplification after A/D conversion, the output power can be kept stable finally. The deficiency of gain-programmed amplifier comprising so many switches and the circuit design is complex, worse still, the ever-changing magnification may contribute to circuit working instability. The chip VCA810 produced by the United States is used as Auto Gain Con- trol. It is a DC-coupled, continuously variable and voltage-controlled gain inte- grated amplifier with low-noise gain adjustable bandwidth and the frequency of bandwidth is 25 MHz. A linear correlation is found between the gain and control voltage, the slew rate is 300V s µ . The device provides a differential input to single output conversion with a high-impedance gain over −40 dB to 40 dB range linear in dB/V. In comparison with AD603, the noise control is superior to AD603 although frequency of bandwidth is lower than it. The external structure of VCA810 is shown in Figure 2.
In this paper, a high frequency driving circuit of surface acoustic wave trans- ducer has been designed to separate oil from oil/water mixed droplet. The transmission frequency of the surface acoustic wave transducer driving circuit can be up to 1 MHz. The transmit frequency of conventional ultrasonic driv- ing circuit is mostly 40 kHz. However, the high transmit frequency driving circuit presents a good stability and accuracy. By establishing the surface acoustic wave driving circuit model, the actual circuit and debugging verifica- tion, the driving circuit can excite the frequency signal required for the expe- riment. Thus, the surface acoustic wave driving circuit could provide neces- sary technical support for application in other fields.
The present work provides an analysis of the hydro-magnetic nanofluid boundary layer over a moving surface with variable thickness in the presence of nonlinear thermal radiation and convective boundary conditions. The governing partial differential equations system that describes the problem is converted to a system of ordinary differential equations by the similarity transformation method; such a system is solved numerically. The velocity, temperature, and nanoparticle concentration of the boundary layer are plotted and investigated in details. Moreover, the surface skin friction, rate of heat and mass transfer are deduced and explained in detail.
From Fig. 1, a steep increase of the velocity profile at low viscosity is evident. The velocity profile is characteristic especially for the air layer adhering to the surface of the tube (𝑐𝑐 = 0). When evaluating experiments using the PIV method (which cannot measure the velocity profile near the wall), it could be incorrectly judged from the figure, that the liquid slips along the wall of the tube. This is because we would have the last measured point where the first layer ends (the end of the blue color). That is why certain caution should be applied when evaluating results of the PIV experiments 6.
The temperature profiles of Ag-water nanofluid for dif- ferent values of convective parameter g when = 0.2 is presented in Figure 9. It is observed that the surface tem- perature increases with an increase in g for both solution branches, and in consequence, decreases the local Nus- selt number. It can be seen that from the convective boundary conditions (9), the value of θ (0) approaches 1, as g ® ∞ . Further, the convective parameter g as well as the Prandtl number Pr has no influence on the flow field, which is clear from Equations 7-9. Finally, it is worth mentioning that all the velocity and temperature profiles
Abstract. This paper examines a Markovian model for the optimal irreversible investment problem of a firm aiming at minimizing total expected costs of production. We model mar- ket uncertainty and the cost of investment per unit of production capacity as two independent one-dimensional regular diffusions, and we consider a general convex running cost function. The optimization problem is set as a three-dimensional degenerate singular stochastic control problem. We provide the optimal control as the solution of a reflected diffusion at a suit- able boundarysurface. Such boundary arises from the analysis of a family of two-dimensional parameter-dependent optimal stopping problems and it is characterized in terms of the family of unique continuous solutions to parameter-dependent nonlinear integral equations of Fredholm type.
a separation bubble has caused a thickening of the boundary layer that has a maximum depth of about 1mm. The effect of surface waviness on the boundary layer thickness is further emphasised in figure 13. All four flow cases are included in the figure to illustrate the strong amplification of the boundary layer due to both the wavy wall and separation. About the surface troughs, the boundary layer thickness grows considerably, but about the surface peaks δ decreases to smaller amplitudes than that associated with the non-wavy wing (solid line). The figure also suggests that there is a relationship between the amplitude of the waviness and the magnification or reduction of the boundary layer. The δ variations were found to vary linearly with the amplitude A about those locations where the boundary layer thickness decreases in size (X = 0.125, 0.225 etc.) On the other hand, when δ increases (X = 0.175, 0.275 etc.), the δ variations were found to be proportional to the square of A. However, this latter relationship is due to the flow separating within the troughs of the wavy surface for these particular flow systems (see figures 11(c, d)), causing δ to grow to larger magnitudes than what would be obtained if separation did not occur. This is confirmed by comparing boundary layer thicknesses for the flow systems with wavelengths L = 20 and 40, where amplitudes A ≤ 0.04 were not large enough to cause separation. Though not shown here, the δ variations for these two surface wavelengths were always found to vary linearly with the amplitude A, independent of the chord location used to compare flow characteristics.
The U.S. Environmental Protection Agency, National Exposure Research Laboratory (EPA/NERL) has an instrumentation cluster that facilitates high- resolution temporal measurements near the surface. This ensemble consists of three portable trailers supporting an Aerovironment Model 4000 miniSODAR, Aerovironment Model 2000 SODAR and three- level 10 m micrometeorological tower. The emphasis here is on the diurnal structure of the surface layer using this observing system. Two 24 hr cases are inspected in which the meteorological conditions are dissimilar. The first observational period occurs during a high wind and deep cloud cover scenario; it is considered near neutral during both the daytime and nighttime hours. Conversely, little cloud cover and light wind govern the meteorology of the second case. For this case, the boundary layer is dominated by free convection during the day and strong thermal stability at night. An attempt is made to distinguish differences in the surface layer structure between two cases by examining the wind profiles, surface stability and SODAR observations.
The steady boundary layer flow of nanofluid over an exponential stretching surface is investigated analytically. The transport equations include the effects of Brownian motion parameter and thermophoresis parameter. The highly nonlinear coupled partial differential equations are simplified with the help of suitable similarity transformations. The reduced equations are then solved analytically with the help of homotopy analysis method (HAM). The convergence of HAM solutions are obtained by plotting h-curve. The expressions for velocity, temperature and nanoparticle volume fraction are computed for some values of the parameters namely, suction injection parameter a , Lewis number Le, the Brownian motion parameter Nb and thermophoresis parameter Nt.
where Ω ⊂ R 3 is an elastic body, y : Ω → R 3 a deformation ﬁeld, W the bulk stored energy function, and γ a surface stored energy function. The potentials W, γ are chosen such that W (F) denotes the energy per unit volume in an inﬁnite crystal under the deformation y ( x ) = Fx , while γ ( F, ν ) is the surface energy per unit area of a half-space with surface normal ν, under the deformation y(x) = Fx. Thus, W and γ are derived from the underlying atomistic model. For W this is a well-understood idea [1, 10, 12, 19]; the novel approach in the SCB method is to apply the same principle to the surface energy potential. We note, however, that a surface contribution as in (1.1) was previously derived in , as the ﬁrst-order expansion of an atomistic model with pair interactions. A more explicit form of the surface energy contribution in polygonal domains is given in . In contrast to the SCB method, most computational models (see, e.g., [13, 15, 40]) are based upon a ﬁnite element discretization of the governing surface elasticity equations of Gurtin and Murdoch , where the constitutive relation for the surface is linearly elastic or uses standard hyperelastic strain energy functions . The SCB model was successfully applied to various nanomechanical boundary value problems, including thermomechanical coupling , resonant frequencies, and elucidating the importance of nonlinear, ﬁnite defor- mation kinematics on the resonant frequencies of both FCC metal  and silicon nanowires [20, 21], bending of FCC metal nanowires , and electromechanical coupling in surface-dominated nanostructures . A fur- ther application that we aim to pursue in future work is the simulation of cracks in bulk crystalline materials (see [2–4] for related works), which requires the accurate description of the crack surface; in more than one dimension this will require the development of a coupling mechanism at crystal surfaces.
Abstract —Thin sheet models are essential to allow shielding effectiveness of composite enclosures and vehicles to be modelled. Thin dispersive sheets are often modeled using surface impedance models in finite-difference time-domain (FDTD) codes in order to deal efficiently with the multi-scale nature of the overall structure. Such boundary conditions must be applied to collocated tangential electric and magnetic fields on either side of the surface; this is usually done on the edges of the FDTD mesh cells at the electric field sampling points. However, these edge based schemes are difficult to implement accurately on stair- cased surfaces. Here we present a novel face centered approach to the collocation of the fields for the application of the boundary condition. This approach naturally deals with the ambiguities in the surface normal that arise at the edges on stair-cased surfaces, allowing a simpler implementation. The accuracy of the new scheme is compared to edge based and conformal approaches using both planar sheet and spherical shell canonical test cases. Stair-casing effects are quantified and the new face-centered scheme is shown have up to 3 dB lower error than the edge based approach in the cases considered, without the complexity and computational cost of conformal techniques.
overnight. Due to the hydrophilicity of the HZSM- 5 surface, addition of a small amount of water led to aggregation owing to the capillary force of water between particles. Under these conditions, it is ex- pected that only the outer surface of aggregates, in contact with organic phase can be modified with OTS. The partly modified sample was labeled w/o − HZSM- 5. Fully modified HZSM-5 (o-HZSM-5) was prepared without addition of water.