Drag on a sphere in a fluid

Summary The possible acceleration dependence of the drag on a sphere, executing a translatory motion in a fluid, is examined in detail. After revisiting the standard derivations of this dependence, it is pointed out that the result might be connected with the scheme of incompressible fluids. That the adoption of this scheme is crucial is made evident by showing that a striking contradiction would arise in compressible fluids. Next a procedure is applied which, in a suitable linear approximation, leads to an explicit expression for the drag in compressible fluids. The drag turns out to depend both on the present value and on the history of the speed of the sphere.

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Riassunto Si considera una sfera in moto traslatorio in un fluido e si esamina il problema dell’eventuale dipendenza della forza resistiva dall’accelerazione. Sulla base delle derivazioni classiche di tale dipendenza, si mette in evidenza che il risultato potrebbe essere conseguenza diretta dell’adozione del modello di fluido incomprimibile. Che tale modello sia realmente cruciale è provato anzitutto osservando che l’analoga trattazione, nel caso di fluidi comprimibili, conduce ad una contraddizione. Successivamente, seguendo un’opportuna approssimazione lineare, si perviene all’espressione esplicita della forza resistiva in un fluido comprimibile. Tale forza risulta dipendente sia dal valore attuale sia dalla storia della velocità della sfera.

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Резюме Рассматривается трансияционное движение сферы в жидкости и исследуется проблема эффективной зависимости силы сопротивления от ускорения. После анализа стандартных подходов для вывода этой зависимости отмечается, что исследуемый результат может быть связан с выбранной моделью несжимаемой жидкости. Тот факт, что выбор модели является сушественнум, иллюстрируется в случае сжимаемых жидкостей, где возникает противоречие. Затем развивается линейное приближение, которое приводит к явному выражению для сопротивления в сжимаемых жидкостях. Оказывается, что сопротивление зависит не только от скорости в данный момент, но и от истории скорости сферы.

     

Research on a flash imaging lidar based on a multiple-streak tube

A flash imaging lidar based on a multiple-streak tube is presented in this paper; a fiber remapping optics maps light from an area in the focal plane of an imaging lens to multiple rows of fibers on the streak tube’s photocathode. The lidar system contains a multiple-streak tube, laser, transmitting and receiving telescope, remapping optical fibers, and CCD to capture stripe images from the streak tube’s phosphor screen. Data processing yields 48 × 48-pixel intensity and range images for each laser pulse. An experiment to test the property of this lidar is carried out in the laboratory; the intensity images and range images are gained by image remapping, and the range sampling is 0.21 m. Field test imagery demonstrated the capability of the flash lidar system to image a building 705 m away.     

Zeta function and regularized determinant on a disc and on a cone

We give formulas for the analytic extension of the zeta function of the induced Laplacian L on a disc and on a cone. This allows the explicit computation of the value of the zeta function and of its derivative at the origin, and hence we get a formula for the regularized determinant of L.     

受曲面约束弹性细杆的平衡问题

作为DNA等一类生物大分子的力学模型，弹性细杆的非线性力学再次受到关注，形成一个力学与分子生物学的交叉学科.除了不受外界约束的自由弹性细杆外，受曲面约束的弹性细杆静力学具有重要的应用背景.在分析约束、约束方程和约束力的基础上建立了受曲面约束的圆截面弹性细杆的平衡微分方程，即曲面上的Kirchhoff方程，它是以截面主矢和截面姿态坐标以及中心线的Descartes坐标为变量的微分/代数方程.作为应用，讨论了约束是圆柱面的情形.此时平衡的无量纲方程仅含的物理参数是截面对形心的抗扭刚度和对主轴的抗弯刚度的比值，与几何参数无关.由此导出方程的螺旋杆特解.数值计算表明，对弹性细杆中心线的几何形状有显著影响的是截面主矢和姿态坐标及其导数的起始值，而不是物理参数. 关键词： 弹性细杆 DNA超螺旋 曲面约束 螺旋杆     

How a liquid becomes a glass both on cooling and on heating

The onset of structural arrest and glass formation in a concentrated suspension of silica nanoparticles in a water-lutidine binary mixture near its consolute point is studied by exploiting the near-critical fluid degrees of freedom to control the strength of an attraction between particles and multispeckle x-ray photon correlation spectroscopy to determine the particles' collective dynamics. This model system undergoes a glass transition both on cooling and on heating, and the intermediate liquid realizes unusual logarithmic relaxations. How vitrification occurs for the two different glass transitions is characterized in detail and comparisons are drawn to recent theoretical predictions for glass formation in systems with attractive interactions.     

Instantons on a line

Witten's multi-instanton solutions are shown explicitly to be gauge equivalent to fields obtained using the ansatz developed by Corrigan, Fairlie, 't Hooft and Wilczek.     

Dimers on a Simple-Quartic Net with a Vacancy

A seminal milestone in lattice statistics is the exact solution of the enumeration of dimers on a simple-quartic net obtained by Fisher, Kasteleyn, and Temperley (FKT) in 1961. An outstanding related and yet unsolved problem is the enumeration of dimers on a net with vacant sites. Here we consider this vacant-site problem with a single vacancy occurring at certain specific sites on the boundary of a simple-quartic net. First, using a bijection between dimer and spanning tree configurations due to Temperley, Kenyon, Propp, and Wilson, we establish that the dimer generating function is independent of the location of the vacancy, and deduce a closed-form expression for the generating function. We next carry out finite-size analyses of this solution as well as that of the FKT solution. Our analyses lead to a logarithmic correction term in the large-size expansion for the vacancy problem with free boundary conditions. A concrete example exhibiting this difference is given. We also find the central charge c=–2 in the language of conformal field theory for the vacancy problem, as versus the value c=1 when there is no vacancy.     

Pressures for a One-Component Plasma on a Pseudosphere

The classical (i.e., non-quantum) equilibrium statistical mechanics of a two-dimensional one-component plasma (a system of charged point-particles embedded in a neutralizing background) living on a pseudosphere (an infinite surface of constant negative curvature) is considered. In the case of a flat space, it is known that, for a one-component plasma, there are several reasonable definitions of the pressure, and that some of them are not equivalent to each other. In the present paper, this problem is revisited in the case of a pseudosphere. General relations between the different pressures are given. At one special temperature, the model is exactly solvable in the grand canonical ensemble. The grand potential and the one-body density are calculated in a disk, and the thermodynamic limit is investigated. The general relations between the different pressures are checked on the solvable model.     

Subdiffusion of a sticky particle on a surface

Conventional diffusion (ΔR2(t))=2Dt gives way to subdiffusion (ΔR2(t))～t(μ), 0<μ<1 when the waiting time distribution φ(τ) is nonintegrable. We have studied a model system, colloidal particles functionalized with DNA "sticky ends" diffusing on a complementary coated surface. We observe a crossover from subdiffusive to conventional behavior for (ΔR2(t)) and φ(τ) as temperature is increased near the particle-surface melting temperature consistent with a simple Gaussian distribution of sticky ends. Our results suggest that any system with randomness in its binding energy should exhibit subdiffusive behavior as it unbinds. This will strongly affect the kinetics of self-assembly.     

Quasi-wetting on a sphere

Wetting phenomena on a sphere of radius R are studied in the context of the Sullivan model. Neither a first nor a continuous transition is found for finite R. Only in the strict limit of R→∞ a second-order transition appears. For temperatures T higher than the wetting temperature in a flat geometry, T^∞_w, the thickness l of the enhanced density layer, which forms on the surface of the sphere, is for large R proportional to In R.     

Gravity on a multifractal

Despite their diversity, many of the most prominent candidate theories of quantum gravity share the property to be effectively lower-dimensional at small scales. In particular, dimension two plays a fundamental role in the finiteness of these models of Nature. Thus motivated, we entertain the idea that spacetime is a multifractal with integer dimension 4 at large scales, while it is two-dimensional in the ultraviolet. Consequences for particle physics, gravity and cosmology are discussed.     

Spreading of a drop on a contaminated substrate

Most wetting or spreading problems are treated with surface and interfacial free energies taken as constants for the system in question. We consider here the case where a two-dimensional drop (ribbon) is deposited on a solid substrate bearing a very fine layer of a contaminant which modifies the effective drop/solid interfacial free energy. As the contaminant diffuses into the drop, the interfacial free energy, and thus the capillary balance, evolve. This has strange effects on wetting behaviour, including causing a wetting `overshoot'. Possible applications are briefly discussed.     

Strings on a plane

Some features for a model of strings moving in 2+1$2+1$ spacetime dimensions are discussed that suggest applications to the quantum Hall effect. These features include edge-state configurations and anyons.     

Quantising on a Category

We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded as objects in a category whose arrows are structure-preserving maps. This motivates investigating the general problem of quantising a system whose configuration space (or history-theory analogue) is the set of objects Ob(Q) in a category Q. We develop a scheme based on constructing an analogue of the group that is used in the canonical quantisation of a system whose configuration space is a manifold Q G/H, where G and H are Lie groups. In particular, we choose as the analogue of G the monoid of arrow fields on Q. Physically, this means that an arrow between two objects in the category is viewed as an analogue of momentum. After finding the category quantisation monoid, we show how suitable representations can be constructed using a bundle (or, more precisely, presheaf) of Hilbert spaces over Ob(Q). For the example of a category of finite sets, we construct an explicit representation structure of this type.     

Criterion for the existence of a continuous embedding of a weighted Sobolev class on a closed interval and on a semiaxis

A criterion for the existence of a continuous embedding of a weighted Sobolev class in a weighted L _p space is obtained, i.e., the existence of an index n for which the Kolmogorov n-diameter is finite. For the case in which a continuous embedding exists, the reduced Sobolev class is constructed together with a continuous operator of a natural embedding of the class in a weighted L _p -space.