Schr\"odinger-Poisson equations with singular potentials in R3R^3

The existence and $L^{\infty}$ estimate of positive solutions are discussed for the following Schr\"{o}dinger-Poisson system {ll} -\Delta u +(\lambda+\frac{1}{|y|^\alpha})u+\phi (x) u =|u|^{p-1}u, x=(y,z)\in \mathbb{R}^2\times\mathbb{R}, -\Delta\phi = u^2,\ \lim\limits_{|x|\rightarrow +\infty}\phi(x)=0, \hfill y=(x_1,x_2) \in \mathbb{R}^2 with |y|=\sqrt{x_1^2+x_2^2}, where $\lambda\geqslant0$, $\alpha\in[0,8)$ and $\max\{2,\frac{2+\alpha}{2}\}<p<5$.Comment: 23page

Global strong solutions to the compressible Navier-Stokes system with potential temperature transport

We study the global strong solutions to the compressible Navier-Stokes system with potential temperature transport in $\mathbb{R}^n.$ Different from the Navier-Stokes-Fourier system, the pressure is a nonlinear function of the density and the potential temperature, we can not exploit the special quasi-diagonalization structure of this system to capture any dissipation of the density. Some new idea and delicate analysis involved in high or low frequency decomposition in the Besov spaces have to be made to close the energy estimates.Comment: 12page

Numerical evaluation of wind effects on buildings

The wind environment around buildings and the wind pressures on building surfaces are studied by scale-model experiments in wind tunnels and confirmed by full scale measurements. Such experiments are often expensive and time consuming. Computational wind engineering as a new branch of computational fluid dynamics has been developed recently to evaluate the interaction between wind and buildings numerically. In the current study, a systematic examination of wind effects on buildings and wind flow conditions around buildings has been carried out numerically. Contrary to the usual numerical evaluations which were only performed on rectangular buildings, the current study evaluates the wind effects on buildings of different shapes such as L-shapes and Z-shapes. The steady state Reynolds averaged Navier-Stokes equations and the k-$\varepsilon$ turbulence model have been adopted for the numerical studies. These equations have been solved with the SIMPLE method. Some researchers declared that the discrepancies between the computed results with the k-$\varepsilon$ model method and the experimental data on the flat roof of a rectangular building are caused by the coarse grid used. To check this, a systematic evaluation of the k-$\varepsilon$ model method in predicting the wind pressure on flat roofs has been attempted by using grids of various densities. Computations were made for a low building and a taller building. Both the advantages and limitations of this most widely used method in computing the wind pressure on flat roofs under normal and oblique wind conditions have been discussed. This study revealed that these discrepancies can be attributed not only to the coarse grid arrangement but also to the k-$\varepsilon$ model itself. To keep the advantages of k-$\varepsilon$ model in representing the fully turbulent flow in the external region far from solid walls and to avoid its shortcomings for the near wall flows, a two-layer methodology combining the k-$\varepsilon$ model in external flow region with either a one-equation model or a modified k-$\varepsilon$ model in the near wall area has been adopted in this study to predict the wind conditions around a cubic building. The two-layer method based on the modified k-$\varepsilon$ model has not been found effective. The two-layer method based on a one-equation model, however, has been proved very effective in predicting the separation above the roof surface and near the side walls of a cubic building which was not possible with the usual k-$\varepsilon$ model method; as a result, the prediction of the wind pressure on the roof and side walls has also been apparently improve

Construction of a Fish-like Robot Based on High Performance Graphene/PVDF Bimorph Actuation Materials.

Smart actuators have many potential applications in various areas, so the development of novel actuation materials, with facile fabricating methods and excellent performances, are still urgent needs. In this work, a novel electromechanical bimorph actuator constituted by a graphene layer and a PVDF layer, is fabricated through a simple yet versatile solution approach. The bimorph actuator can deflect toward the graphene side under electrical stimulus, due to the differences in coefficient of thermal expansion between the two layers and the converse piezoelectric effect and electrostrictive property of the PVDF layer. Under low voltage stimulus, the actuator (length: 20 mm, width: 3 mm) can generate large actuation motion with a maximum deflection of about 14.0 mm within 0.262 s and produce high actuation stress (more than 312.7 MPa/g). The bimorph actuator also can display reversible swing behavior with long cycle life under high frequencies. on this basis, a fish-like robot that can swim at the speed of 5.02 mm/s is designed and demonstrated. The designed graphene-PVDF bimorph actuator exhibits the overall novel performance compared with many other electromechanical avtuators, and may contribute to the practical actuation applications of graphene-based materials at a macro scale

Raziskovanje udorov na kraških območjih z uporabo integriranih geofizikalnih metod: primer iz okrožja Conghua, mesta Guangzhou, Kitajska

Integrated geophysical methods were used to investigate the geological conditions of karst collapses in Aotou, Conghua District, Guangzhou City. Based on audio frequency magnetotelluric (AMT) soundings, high-density electric signals and microtremors, a series of features, including the soil structure and thickness, faults, and hidden karst, were detected from shallow to deep subsurface regions in three-dimensional (3-D) space. These were then compared with geologic and drilling data. The measurements of micro-vibrations and high-density electric signals revealed that the strata in the collapsed area consists of clay and medium-grain sand, which is approximately 8–15 m thick and arranged as a multiple-element structure. The AMT soundings uncovered a hidden structure in the subsurface, which lies at the core of a syncline and adjacent to a contact zone between soluble limestone and non-soluble granite. Combined with the geologic data, the survey using the high-density electric method also showed that the study area hosts the Shidengzi Formation from the Datang Stage of the lower Carboniferous, which contain carbonaceous micrite and dolomitic limestone, locally intercalated with thin quartz siltstone, with well-developed karst. Collectively, the soil structure, hidden structure in the subsurface, and karst development provide the primary conditions for collapses. The main triggering factors for the karst collapses are seasonal variations in groundwater levels and excessive groundwater withdrawals. These results can provide guidance for the selection and application of geophysical methods for the examination of this issue in other areas with similar geology.Pri raziskovanju geoloških razmer za pojav udorov na območju krasa v Aotouju, okrožju Conghua, mesta Guangzhou so bile uporabljene integrirane geofizikalne metode. Z uporabo avdiofrekvenčnih magnetno teluričnih (AMT) sondiranj, visokofrekvenčnih električnih signalov in mikrotremorjev smo zaznali razne elemente v podzemlju, kot so debelina in struktura prsti, prelomi in nepoznani podzemni prostori. Izsledki so bili primerjani s podatki geoloških kartiranj in napravljenih vrtin. Meritve mikrovibracij in električnih signalov so razkrile, da so formacije na območju udorov sestavljene iz gline in srednje zrnatega peska, v skupni debelini približno 8‒15 m. Magnetno telurično sondiranje je pod površjem razkrilo neznano strukturo, ki leži na jedru sinklinale ob stiku med topnim apnencem in netopnim granitom. Skupaj z geološkimi podatki je metoda z električnimi signali pokazala, da področje študije zajema formacijo Shidengzi, stopnje Datang iz spodnjega Karbona, ki vsebuje mikritni in dolomitni apnenec, ki se lokalno izmenjuje s tankimi plastmi kremenovega meljevca. Na tem območju je nastal dobro razviti kras. Ugodna sestava prsti, neznane strukture pod površjem in zakrasevanje zagotavljajo dobre razmere za nastanek udorov. Glavni dejavniki udora kraških območij so sezonska nihanja nivojev podzemne vode in čezmerna črpanja podtalnice. Pridobljeni izsledki zagotavljajo smernice za izbor in uporabo ustreznih geofizikalnih metod za raziskovanje teh težav v drugih regijah s podobno geologijo