Response of bubbles to diagnotic ultrasound:a unifying theoretical approach

The scattering of ultrasound from bubbles of $\sim 1~\mu$m radius, such as used in contrast enhancers for ultrasound diagnostics, is studied. We show that sound scattering and ``active'' emission of sound from oscillating bubbles are not contradictory, but are just two different aspects derived from the same physics. Treating the bubble as a nonlinear oscillator, we arrive at general formulas for scattering and absorption cross-sections. We show that several well-known formulas are recovered in the linear limit of this ansatz. In the case of strongly nonlinear oscillations, however, the cross-sections can be larger than those for linear response by several orders of magnitude. The major part of the incident sound energy is then converted into emitted sound, unlike what happens in the linear case, where the absorption cross-sections exceed the scattering cross-sections

Response maxima in modulated turbulence

Isotropic and homogeneous turbulence driven by an energy input modulated in time is studied within a variable range mean-field theory. The response of the system, observed in the second order moment of the large-scale velocity difference D(L,t)=>~Re(t)^2$, is calculated for varying modulation frequencies w and weak modulation amplitudes. For low frequencies the system follows the modulation of the driving with almost constant amplitude, whereas for higher driving frequencies the amplitude of the response decreases on average 1/w. In addition, at certain frequencies the amplitude of the response either almost vanishes or is strongly enhanced. These frequencies are connected with the frequency scale of the energy cascade and multiples thereof.Comment: 11 pages, 6 figure

Morphology Development in Model Polyethylene via Two-Dimensional Correlation Analysis

Two-dimensional (2D) correlation analysis is applied to synchrotron X-ray scattering data to characterize morphological regimes during nonisothermal crystallization of a model ethylene copolymer (hydrogenated polybutadiene, HPBD). The 2D correlation patterns highlight relationships among multiple characteristics of structure evolution, particularly the extent to which separate features change simultaneously versus sequentially. By visualizing these relationships during cooling, evidence is obtained for two separate physical processes occurring in what is known as “irreversible crystallization” in random ethylene copolymers. Initial growth of primarily lamellae into unconstrained melt (“primary-irreversible crystallization”) is distinguished from subsequent secondary lamellae formation in the constrained, noncrystalline regions between the primary lamellae (“secondary-irreversible crystallization”). At successively lower temperatures (“reversible crystallization”), growth of the crystalline reflections is found to occur simultaneously with the change in shape of the amorphous halo, which is inconsistent with the formation of an additional phase. Rather, the synchronous character supports the view that growth of frustrated crystals distorts the adjacent noncrystalline material. Furthermore, heterocorrelation analysis of small-angle and wideangle X-ray scattering data from the reversible crystallization regime reveals that the size of new crystals is consistent with fringedmicellar structures (~9 nm). Thus, 2D correlation analysis provides new insights into morphology development in polymeric systems

Scaling relations in large-Prandtl-number natural thermal convection

In this study we follow Grossmann and Lohse, Phys. Rev. Lett. 86 (2001), who derived various scalings regimes for the dependence of the Nusselt number $Nu$ and the Reynolds number $Re$ on the Rayleigh number $Ra$ and the Prandtl number $Pr$. We focus on theoretical arguments as well as on numerical simulations for the case of large-$Pr$ natural thermal convection. Based on an analysis of self-similarity of the boundary layer equations, we derive that in this case the limiting large-$Pr$ boundary-layer dominated regime is I$_\infty^<$, introduced and defined in [1], with the scaling relations $Nu\sim Pr^0\,Ra^{1/3}$ and $Re\sim Pr^{-1}\,Ra^{2/3}$. Our direct numerical simulations for $Ra$ from $10^4$ to $10^9$ and $Pr$ from 0.1 to 200 show that the regime I$_\infty^<$ is almost indistinguishable from the regime III$_\infty$, where the kinetic dissipation is bulk-dominated. With increasing $Ra$, the scaling relations undergo a transition to those in IV$_u$ of reference [1], where the thermal dissipation is determined by its bulk contribution

Non-Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Benard convection in glycerol

We numerically analyze Non-Oberbeck-Boussinesq (NOB) effects in two-dimensional Rayleigh-Benard flow in glycerol, which shows a dramatic change in the viscosity with temperature. The results are presented both as functions of the Rayleigh number (Ra) up to $10^8$ (for fixed temperature difference between the top and bottom plates) and as functions of "non-Oberbeck-Boussinesqness'' or "NOBness'' ($\Delta$) up to 50 K (for fixed Ra). For this large NOBness the center temperature $T_c$ is more than 5 K larger than the arithmetic mean temperature $T_m$ between top and bottom plate and only weakly depends on Ra. To physically account for the NOB deviations of the Nusselt numbers from its Oberbeck-Boussinesq values, we apply the decomposition of $Nu_{NOB}/Nu_{OB}$ into the product of two effects, namely first the change in the sum of the top and bottom thermal BL thicknesses, and second the shift of the center temperature $T_c$ as compared to $T_m$. While for water the origin of the $Nu$ deviation is totally dominated by the second effect (cf. Ahlers et al., J. Fluid Mech. 569, pp. 409 (2006)) for glycerol the first effect is dominating, in spite of the large increase of $T_c$ as compared to $T_m$.Comment: 6 pages, 7 figure

Resolving Structure in Human Brain Organization: Identifying Mesoscale Organization in Weighted Network Representations

Human brain anatomy and function display a combination of modular and hierarchical organization, suggesting the importance of both cohesive structures and variable resolutions in the facilitation of healthy cognitive processes. However, tools to simultaneously probe these features of brain architecture require further development. We propose and apply a set of methods to extract cohesive structures in network representations of brain connectivity using multi-resolution techniques. We employ a combination of soft thresholding, windowed thresholding, and resolution in community detection, that enable us to identify and isolate structures associated with different weights. One such mesoscale structure is bipartivity, which quantifies the extent to which the brain is divided into two partitions with high connectivity between partitions and low connectivity within partitions. A second, complementary mesoscale structure is modularity, which quantifies the extent to which the brain is divided into multiple communities with strong connectivity within each community and weak connectivity between communities. Our methods lead to multi-resolution curves of these network diagnostics over a range of spatial, geometric, and structural scales. For statistical comparison, we contrast our results with those obtained for several benchmark null models. Our work demonstrates that multi-resolution diagnostic curves capture complex organizational profiles in weighted graphs. We apply these methods to the identification of resolution-specific characteristics of healthy weighted graph architecture and altered connectivity profiles in psychiatric disease.Comment: Comments welcom

R116C mutation of cationic trypsinogen in a Turkish family with recurrent pancreatitis illustrates genetic microheterogeneity of hereditary pancreatitis

Hereditary pancreatitis is due to heterozygosity for gain-of-function mutations in the cationic trypsinogen gene which result in increased levels of active trypsin within pancreatic acinar cells and autodigestion of the pancreas. The number of disease-causing defects is generally considered to be low. To gain further insight into the molecular basis of this disorder, DNA sequence analysis of all five exons was performed in 109 unrelated patients with idiopathic chronic pancreatitis in order to determine the variability of the underlying mutations. Two German females and one German male were carriers of the most common N291 and R122H mutations (trypsinogen numbering system). In a Turkish proband, an arginine (CGT) to cysteine (TGT) substitution at amino acid position 116 was identified. Family screening demonstrated that the patient had inherited the mutation from his asymptomatic father and that he had transmitted it to both of his children, his daughter being symptomatic since the age of 3 years. In addition, a German male was found to be a heterozygote for a D100H (GAC-->CAC) amino acid replacement. Our data provide evidence for genetic heterogeneity of hereditary pancreatitis. The growing number of cationic trypsinogen mutations is expected to change current mutation screening practices for this disease