Dimensionless scaling of heat-release-induced planar shock waves in near-critical CO2

We performed highly resolved one-dimensional fully compressible Navier-Stokes simulations of heat-release-induced compression waves in near-critical CO2. The computational setup, inspired by the experimental setup of Miura et al., Phys. Rev. E, 2006, is composed of a closed inviscid (one-dimensional) duct with adiabatic hard ends filled with CO2 at three supercritical pressures. The corresponding initial temperature values are taken along the pseudo-boiling line. Thermodynamic and transport properties of CO2 in near-critical conditions are modeled via the Peng-Robinson equation of state and Chung's Method. A heat source is applied at a distance from one end, with heat release intensities spanning the range 10^3-10^11 W/m^2, generating isentropic compression waves for values < 10^9 W/m^2. For higher heat-release rates such compressions are coalescent with distinct shock-like features (e.g. non-isentropicity and propagation Mach numbers measurably greater than unity) and a non-uniform post-shock state is present due to the strong thermodynamic nonlinearities. The resulting compression wave intensities have been collapsed via the thermal expansion coefficient, highly variable in near-critical fluids, used as one of the scaling parameters for the reference energy. The proposed scaling applies to isentropic thermoacoustic waves as well as shock waves up to shock strength 2. Long-term time integration reveals resonance behavior of the compression waves, raising the mean pressure and temperature at every resonance cycle. When the heat injection is halted, expansion waves are generated, which counteract the compression waves leaving conduction as the only thermal relaxation process. In the long term evolution, the decay in amplitude of the resonating waves observed in the experiments is qualitatively reproduced by using isothermal boundary conditions.Comment: As submitted to AIAA SciTech 2017, available at http://arc.aiaa.org/doi/pdf/10.2514/6.2017-008

Thermo-acoustic wave propagation and reflection near the liquid-gas critical point

We study the thermo-acoustic wave propagation and reflection near the liquid-gas critical point. Specifically, we perform a numerical investigation of the acoustic responses in a near-critical fluid to thermal perturbations based on the same setup of a recent ultrasensitive interferometry measurement in CO2 [Y. Miura et al. Phys. Rev. E 74, 010101(R) (2006)]. The numerical results agree well with the experimental data. New features regarding the reflection pattern of thermo-acoustic waves near the critical point under pulse perturbations are revealed by the proper inclusion of the critically diverging bulk viscosity.Comment: 14 pages, 4 figures, Accepted by PRE (Rapid Communication

Thermoacoustic effects in supercritical fluids near the critical point: Resonance, piston effect, and acoustic emission and reflection

We present a general theory of thermoacoustic phenomena in supercritical fluids near the critical point in a one-dimensional cell. We take into account the effects of the heat conduction in the boundary walls and the bulk viscosity near the critical point. We introduce a coefficient $Z(\omega)$ characterizing reflection of sound with frequency $\omega$ at the boundary. As applications, we examine the acoustic eigenmodes in the cell, the response to time-dependent perturbations, sound emission and reflection at the boundary. Resonance and rapid adiabatic changes are noteworthy. In these processes, the role of the thermal diffusion layers is enhanced near the critical point because of the strong critical divergence of the thermal expansion.Comment: 15 pages, 7 figure

Doubly connected minimal surfaces and extremal harmonic mappings

The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.Comment: 35 pages, 2 figures. Minor edits, references adde

Elliptic Phases: A Study of the Nonlinear Elasticity of Twist-Grain Boundaries

We develop an explicit and tractable representation of a twist-grain-boundary phase of a smectic A liquid crystal. This allows us to calculate the interaction energy between grain boundaries and the relative contributions from the bending and compression deformations. We discuss the special stability of the 90 degree grain boundaries and discuss the relation of this structure to the Schwarz D surface.Comment: 4 pages, 2 figure

Mappings of least Dirichlet energy and their Hopf differentials

The paper is concerned with mappings between planar domains having least Dirichlet energy. The existence and uniqueness (up to a conformal change of variables in the domain) of the energy-minimal mappings is established within the class $\bar{\mathscr H}_2(X, Y)$ of strong limits of homeomorphisms in the Sobolev space $W^{1,2}(X, Y)$, a result of considerable interest in the mathematical models of Nonlinear Elasticity. The inner variation leads to the Hopf differential $h_z \bar{h_{\bar{z}}} dz \otimes dz$ and its trajectories. For a pair of doubly connected domains, in which $X$ has finite conformal modulus, we establish the following principle: A mapping $h \in \bar{\mathscr H}_2(X, Y)$ is energy-minimal if and only if its Hopf-differential is analytic in $X$ and real along the boundary of $X$. In general, the energy-minimal mappings may not be injective, in which case one observes the occurrence of cracks in $X$. Nevertheless, cracks are triggered only by the points in the boundary of $Y$ where $Y$ fails to be convex. The general law of formation of cracks reads as follows: Cracks propagate along vertical trajectories of the Hopf differential from the boundary of $X$ toward the interior of $X$ where they eventually terminate before making a crosscut.Comment: 51 pages, 4 figure

Does meiotic drive alter male mate preference?

Male mate preferences have been demonstrated across a range of species, including the Malaysian stalk-eyed fly, Teleopsis dalmanni. This species is subject to sex-ratio (SR), an X-linked male meiotic driver, which causes the dysfunction of Y-sperm and the production of all-female broods. While there has been work considering female avoidance of meiotic drive males, the mating decisions of drive-bearing males have not been considered previously. Drive males may be less able to bear the cost of choice as SR is associated with a low-frequency inversion that causes reduced organismal fitness. Drive males may also experience weaker selection for preference maintenance if they are avoided by females. Using binary choice trials, across two experiments, we confirmed male preference for large (fecund) females but found no evidence that the strength of male preference differs between drive and standard males. We showed that large eyespan males displayed strong preference for large females, whereas small eyespan males showed no preference. Taken together, these results suggest that, even though meiotic drive is associated with lower genetic quality, it does not directly interfere with male mate preference among available females. However, as drive males tend to have smaller eyespan (albeit only ~5% on average), this will to a minor extent weaken their strength of preference

Does meiotic drive alter male mate preference?

Male mate preferences have been demonstrated across a range of species, including the Malaysian stalk-eyed fly, Teleopsis dalmanni. This species is subject to sex-ratio (SR), an X-linked male meiotic driver, which causes the dysfunction of Y-sperm and the production of all-female broods. While there has been work considering female avoidance of meiotic drive males, the mating decisions of drive-bearing males have not been considered previously. Drive males may be less able to bear the cost of choice as SR is associated with a low-frequency inversion that causes reduced organismal fitness. Drive males may also experience weaker selection for preference maintenance if they are avoided by females. Using binary choice trials, across two experiments, we confirmed male preference for large (fecund) females but found no evidence that the strength of male preference differs between drive and standard males. We showed that large eyespan males displayed strong preference for large females, whereas small eyespan males showed no preference. Taken together, these results suggest that, even though meiotic drive is associated with lower genetic quality, it does not directly interfere with male mate preference among available females. However, as drive males tend to have smaller eyespan (albeit only ~5% on average), this will to a minor extent weaken their strength of preference

Simulating the Mammalian Blastocyst - Molecular and Mechanical Interactions Pattern the Embryo

Mammalian embryogenesis is a dynamic process involving gene expression and mechanical forces between proliferating cells. The exact nature of these interactions, which determine the lineage patterning of the trophectoderm and endoderm tissues occurring in a highly regulated manner at precise periods during the embryonic development, is an area of debate. We have developed a computational modeling framework for studying this process, by which the combined effects of mechanical and genetic interactions are analyzed within the context of proliferating cells. At a purely mechanical level, we demonstrate that the perpendicular alignment of the animal-vegetal (a-v) and embryonic-abembryonic (eb-ab) axes is a result of minimizing the total elastic conformational energy of the entire collection of cells, which are constrained by the zona pellucida. The coupling of gene expression with the mechanics of cell movement is important for formation of both the trophectoderm and the endoderm. In studying the formation of the trophectoderm, we contrast and compare quantitatively two hypotheses: (1) The position determines gene expression, and (2) the gene expression determines the position. Our model, which couples gene expression with mechanics, suggests that differential adhesion between different cell types is a critical determinant in the robust endoderm formation. In addition to differential adhesion, two different testable hypotheses emerge when considering endoderm formation: (1) A directional force acts on certain cells and moves them into forming the endoderm layer, which separates the blastocoel and the cells of the inner cell mass (ICM). In this case the blastocoel simply acts as a static boundary. (2) The blastocoel dynamically applies pressure upon the cells in contact with it, such that cell segregation in the presence of differential adhesion leads to the endoderm formation. To our knowledge, this is the first attempt to combine cell-based spatial mechanical simulations with genetic networks to explain mammalian embryogenesis. Such a framework provides the means to test hypotheses in a controlled in silico environment