Three-dimensional water impact at normal incidence to a blunt structure

The three-dimensional (3D) water impact onto a blunt structure with a spreading rectangular contact region is studied. The structure is mounted on a flat rigid plane with the impermeable curved surface of the structure perpendicular to the plane. Before impact, the water region is a rectangular domain of finite thickness bounded from below by the rigid plane and above by the flat free surface. The front free surface of the water region is vertical, representing the front of an advancing steep wave. The water region is initially advancing towards the structure at a constant uniform speed. We are concerned with the slamming loads acting on the surface of the structure during the initial stage of water impact. Air, gravity and surface tension are neglected. The problem is analysed by using some ideas of pressure-impulse theory, but including the time-dependence of the wetted area of the structure. The flow caused by the impact is 3D and incompressible. The distribution of the pressure-impulse (the time-integral of pressure) over the surface of the structure is analysed and compared with the distributions provided by strip theories. The total impulse exerted on the structure during the impact stage is evaluated and compared with numerical and experimental predictions. An example calculation is presented of water impact onto a vertical rigid cylinder. Three-dimensional effects on the slamming loads are of main concern in this study

Interaction imaging with amplitude-dependence force spectroscopy

Knowledge of surface forces is the key to understanding a large number of processes in fields ranging from physics to material science and biology. The most common method to study surfaces is dynamic atomic force microscopy (AFM). Dynamic AFM has been enormously successful in imaging surface topography, even to atomic resolution, but the force between the AFM tip and the surface remains unknown during imaging. Here, we present a new approach that combines high accuracy force measurements and high resolution scanning. The method, called amplitude-dependence force spectroscopy (ADFS) is based on the amplitude-dependence of the cantilever's response near resonance and allows for separate determination of both conservative and dissipative tip-surface interactions. We use ADFS to quantitatively study and map the nano-mechanical interaction between the AFM tip and heterogeneous polymer surfaces. ADFS is compatible with commercial atomic force microscopes and we anticipate its wide-spread use in taking AFM toward quantitative microscopy

Characterization of Films with Thickness Less than 10 nm by Sensitivity-Enhanced Atomic Force Acoustic Microscopy

We present a method for characterizing ultrathin films using sensitivity-enhanced atomic force acoustic microscopy, where a concentrated-mass cantilever having a flat tip was used as a sensitive oscillator. Evaluation was aimed at 6-nm-thick and 10-nm-thick diamond-like carbon (DLC) films deposited, using different methods, on a hard disk for the effective Young's modulus defined as E/(1 - ν2), where E is the Young's modulus, and ν is the Poisson's ratio. The resonant frequency of the cantilever was affected not only by the film's elasticity but also by the substrate even at an indentation depth of about 0.6 nm. The substrate effect was removed by employing a theoretical formula on the indentation of a layered half-space, together with a hard disk without DLC coating. The moduli of the 6-nm-thick and 10-nm-thick DLC films were 392 and 345 GPa, respectively. The error analysis showed the standard deviation less than 5% in the moduli

Morphology and Nanomechanics of Sensory Neurons Growth Cones following Peripheral Nerve Injury

A prior peripheral nerve injury in vivo, promotes a rapid elongated mode of sensory neurons neurite regrowth in vitro. This in vitro model of conditioned axotomy allows analysis of the cellular and molecular mechanisms leading to an improved neurite re-growth. Our differential interference contrast microscopy and immunocytochemistry results show that conditioned axotomy, induced by sciatic nerve injury, did not increase somatic size of adult lumbar sensory neurons from mice dorsal root ganglia sensory neurons but promoted the appearance of larger neurites and growth cones. Using atomic force microscopy on live neurons, we investigated whether membrane mechanical properties of growth cones of axotomized neurons were modified following sciatic nerve injury. Our data revealed that neurons having a regenerative growth were characterized by softer growth cones, compared to control neurons. The increase of the growth cone membrane elasticity suggests a modification in the ratio and the inner framework of the main structural proteins

A Criterion for Brittle Failure of Rocks Using the Theory of Critical Distances

This paper presents a new analytical criterion for brittle failure of rocks and heavily overconsolidated soils. Griffith’s model of a randomly oriented defect under a biaxial stress state is used to keep the criterion simple. The Griffith’s criterion is improved because the maximum tensile strength is not evaluated at the boundary of the defect but at a certain distance from the boundary, known as the critical distance. This fracture criterion is known as the Point Method, and is part of the Theory of Critical Distances, which is utilized in fracture mechanics. The proposed failure criterion has two parameters: the inherent tensile strength, ó0, and the ratio of the half-length of the initial crack/flaw to the critical distance, a/L. These parameters are difficult to measure but they may be correlated with the uniaxial compressive and tensile strengths, óc and ót. The proposed criterion is able to reproduce the common range of strength ratios for rocks and heavily overconsolidated soils (óc/ót=3-50) and the influence of several microstructural rock properties, such as texture and porosity. Good agreement with laboratory tests reported in the literature is found for tensile and low confining stresses.The work presented was initiated during a research project on “Structural integrity assessments of notch-type defects", for the Spanish Ministry of Science and Innovation (Ref.: MAT2010-15721)

Bacterial Surface Appendages Strongly Impact Nanomechanical and Electrokinetic Properties of Escherichia coli Cells Subjected to Osmotic Stress

The physicochemical properties and dynamics of bacterial envelope, play a major role in bacterial activity. In this study, the morphological, nanomechanical and electrohydrodynamic properties of Escherichia coli K-12 mutant cells were thoroughly investigated as a function of bulk medium ionic strength using atomic force microscopy (AFM) and electrokinetics (electrophoresis). Bacteria were differing according to genetic alterations controlling the production of different surface appendages (short and rigid Ag43 adhesins, longer and more flexible type 1 fimbriae and F pilus). From the analysis of the spatially resolved force curves, it is shown that cells elasticity and turgor pressure are not only depending on bulk salt concentration but also on the presence/absence and nature of surface appendage. In 1 mM KNO3, cells without appendages or cells surrounded by Ag43 exhibit large Young moduli and turgor pressures (∼700–900 kPa and ∼100–300 kPa respectively). Under similar ionic strength condition, a dramatic ∼50% to ∼70% decrease of these nanomechanical parameters was evidenced for cells with appendages. Qualitatively, such dependence of nanomechanical behavior on surface organization remains when increasing medium salt content to 100 mM, even though, quantitatively, differences are marked to a much smaller extent. Additionally, for a given surface appendage, the magnitude of the nanomechanical parameters decreases significantly when increasing bulk salt concentration. This effect is ascribed to a bacterial exoosmotic water loss resulting in a combined contraction of bacterial cytoplasm together with an electrostatically-driven shrinkage of the surface appendages. The former process is demonstrated upon AFM analysis, while the latter, inaccessible upon AFM imaging, is inferred from electrophoretic data interpreted according to advanced soft particle electrokinetic theory. Altogether, AFM and electrokinetic results clearly demonstrate the intimate relationship between structure/flexibility and charge of bacterial envelope and propensity of bacterium and surface appendages to contract under hypertonic conditions

On some generalizations of the properties of the multidimensional generalized Erdélyi-Kober operators and their applications

In this paper we investigate the composition of a multidimensional generalized Erdélyi-Kober operator with differential operators of high order. In particular, with powers of the differential Bessel operator. Applications of proved properties to solving the Cauchy problem for a multidimensional polycaloric equation with a Bessel operator are show