Finite element modeling of transient ultrasonic waves in linear viscoelastic media

Linear viscoelasticity offers a minimal framework within which to construct a causal model for wave propagation in absorptive media. Viscoelastic media are often described as media with memory, that is, the present state of stress is dependent on the present strain and the complete time history of strain weighted by time convolution with an appropriate time-dependent stress relaxation modulus. An axisymmetric, displacement based finite element method for modeling pulsed ultrasonic waves in linear, homogeneous viscoelastic media is developed that does not require storage of the complete time history of displacement at every node. This is accomplished by modeling the stress relaxation moduli as discrete or continuous spectra of decaying exponentials. The viscoelastic finite element method serves as a test bed for studying three inverse methods for recovering time dependent longitudinal moduli from pulsed ultrasonic waves transmitted through a slab of viscoelastic material with properties known a priori. Specifically, two existing inverse methods called propagator methods, denoted here as the two-slab method and slab-substitution method, are modeled and compared to show relative advantages and disadvantages of both. Both methods require attenuation and wave speed as a function of frequency derived from transmitted wave data for inversion and recovery of modulus data. Several different variables such as measurement location and source radius are varied to discern those variables that have greatest influence on accuracy of reconstructed moduli. It is found that an increase in source aperture radius causes the greatest improvement in modulus accuracy. Another novel inverse method known as wave splitting is applied to numerical data generated by the finite element test bed. Wave splitting requires a time-dependent transmission kernel for recovery of a viscoelastic modulus rather than frequency-dependent attenuation and wave speed. It is shown that in principle wave splitting can recover the material modulus with a data derived from a simulated ultrasonic experiment, but it is not as robust as the other two frequency-domain inverse methods studied. Its main drawback is that transmission kernel data required for inversion must be known for the same thickness of viscoelastic slab implying that pulses with relatively high center frequencies must be propagated through slabs whose thickness is only appropriate for low frequency measurement. Material attenuation quickly reduces transmitted waves at high frequencies to unacceptable low levels when propagated through thick slabs appropriate for pulses centered at lower frequencies. In general, the finite element method has been utilized as an effective tool for comparing alternative inverse methods

Extensive regulation of metabolism and growth during the cell division cycle

Yeast cells grown in culture can spontaneously synchronize their respiration, metabolism, gene expression and cell division. Such metabolic oscillations in synchronized cultures reflect single-cell oscillations, but the relationship between the oscillations in single cells and synchronized cultures is poorly understood. To understand this relationship and the coordination between metabolism and cell division, we collected and analyzed DNA-content, gene-expression and physiological data, at hundreds of time-points, from cultures metabolically-synchronized at different growth rates, carbon sources and biomass densities. The data enabled us to extend and generalize an ensemble-average-over-phases (EAP) model that connects the population-average gene-expression of asynchronous cultures to the gene-expression dynamics in the single-cells comprising the cultures. The extended model explains the carbon-source specific growth-rate responses of hundreds of genes. Our data demonstrate that for a given growth rate, the frequency of metabolic cycling in synchronized cultures increases with the biomass density. This observation underscores the difference between metabolic cycling in synchronized cultures and in single cells and suggests entraining of the single-cell cycle by a quorum-sensing mechanism. Constant levels of residual glucose during the metabolic cycling of synchronized cultures indicate that storage carbohydrates are required to fuel not only the G1/S transition of the division cycle but also the metabolic cycle. Despite the large variation in profiled conditions and in the time-scale of their dynamics, most genes preserve invariant dynamics of coordination with each other and with the rate of oxygen consumption. Similarly, the G1/S transition always occurs at the beginning, middle or end of the high oxygen consumption phases, analogous to observations in human and drosophila cells.Comment: 34 pages, 7 figure

Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity

Molecular transport in living systems regulates numerous processes underlying biological function. Although many cellular components exhibit anomalous diffusion, only recently has the subdiffusive motion been associated with nonergodic behavior. These findings have stimulated new questions for their implications in statistical mechanics and cell biology. Is nonergodicity a common strategy shared by living systems? Which physical mechanisms generate it? What are its implications for biological function? Here, we use single particle tracking to demonstrate that the motion of DC-SIGN, a receptor with unique pathogen recognition capabilities, reveals nonergodic subdiffusion on living cell membranes. In contrast to previous studies, this behavior is incompatible with transient immobilization and therefore it can not be interpreted according to continuous time random walk theory. We show that the receptor undergoes changes of diffusivity, consistent with the current view of the cell membrane as a highly dynamic and diverse environment. Simulations based on a model of ordinary random walk in complex media quantitatively reproduce all our observations, pointing toward diffusion heterogeneity as the cause of DC-SIGN behavior. By studying different receptor mutants, we further correlate receptor motion to its molecular structure, thus establishing a strong link between nonergodicity and biological function. These results underscore the role of disorder in cell membranes and its connection with function regulation. Due to its generality, our approach offers a framework to interpret anomalous transport in other complex media where dynamic heterogeneity might play a major role, such as those found, e.g., in soft condensed matter, geology and ecology.Comment: 27 pages, 5 figure

Discontinuities in regularised media

Discontinuous interpolation of the problem fields in non-local and rate-dependent media is considered. The necessity of discontinuities in the analysis of failure processes and some of the requirements for the introduction of discontinuities in regularised media are discussed. The regularisation properties of a novel rate-dependent elastoplastic damage continuum model are presented

The impact of copper, nitrate and carbon status on the emission of nitrous oxide by two species of bacteria with biochemically distinct denitrification pathways

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