Energy conservation during remeshing in the analysis of dynamic fracture

The analysis of (dynamic) fracture often requires multiple changes to the discretisation during crack propagation. The state vector from the previous time step must then be transferred to provide the initial values of the next time step. A novel methodology based on a least‐squares fit is proposed for this mapping. The energy balance is taken as a constraint in the mapping, which results in a complete energy preservation. Apart from capturing the physics better, this also has advantages for numerical stability. To further improve the accuracy, Powell‐Sabin B‐splines, which are based on triangles, have been used for the discretisation. Since urn:x-wiley:nme:media:nme6142:nme6142-math-0001 continuity of the displacement field holds at crack tips for Powell‐Sabin B‐splines, the stresses at and around crack tips are captured much more accurately than when using elements with a standard Lagrangian interpolation, or with NURBS and T‐splines. The versatility and accuracy of the approach to simulate dynamic crack propagation are assessed in two case studies, featuring mode‐I and mixed‐mode crack propagation

Integral form of mixed-mode crack opening in the phase field method

Phase-field modelling of cracks has gained popularity in the fracturing analysis recently. Originally developed for brittle fracture, the method has now been extended to cohesive fracture. In the latter case, the crack opening displacement is an essential variable, due to the dependence on it of the interface tractions. But also in brittle fracture, the crack opening displacement is crucial in certain applications, for instance for transport of fluids in the cracks. Herein, we derive the complete formulation for mixed-mode crack opening within the framework of the phase-field model, given for brittle as well as for cohesive fracture. The crack opening displacement is associated with a line integral that is perpendicular to the crack. Different factors and matrices apply in the integration for both fracture models and crack directions. These derivations have been validated analytically through an edge-cracked problem and numerically through curved crack scenarios

Computation of the crack opening displacement in the phase-field model

The phase-field model treats discrete cracks in a smeared sense by a regularisation technique. It holds attractive properties: there is no need to consider cracks as geometric discontinuities, and it avoids remeshing around crack tips. The method has been employed in the analysis of brittle and cohesive fracture problems. In the brittle fracture model, a Griffith-like energy functional is used in the simulation, while in the cohesive fracture model, the fracturing problem exploits a displacement jump governed energy functional. Obviously, the displacement jump is crucial in the cohesive fracture model and in certain other applications, e.g. for hydraulic fracturing. In the current study, the approximated form of the crack opening displacement is derived for the brittle and cohesive fracture models. In both models, the crack opening displacement is associated with a line integral normal to the crack, but different factors in front of the integral apply. The derived integrals are verified analytically in a one-dimensional setting and numerically in multi-dimensional set-ups, featuring straight and curved cracks

On the flow-level stability of data networks without congestion control: the case of linear networks and upstream trees

In this paper, flow models of networks without congestion control are considered. Users generate data transfers according to some Poisson processes and transmit corresponding packet at a fixed rate equal to their access rate until the entire document is received at the destination; some erasure codes are used to make the transmission robust to packet losses. We study the stability of the stochastic process representing the number of active flows in two particular cases: linear networks and upstream trees. For the case of linear networks, we notably use fluid limits and an interesting phenomenon of "time scale separation" occurs. Bounds on the stability region of linear networks are given. For the case of upstream trees, underlying monotonic properties are used. Finally, the asymptotic stability of those processes is analyzed when the access rate of the users decreases to 0. An appropriate scaling is introduced and used to prove that the stability region of those networks is asymptotically maximized

Separating the effects of 24-hour urinary chloride and sodium excretion on blood pressure and risk of hypertension:Results from PREVEND

OBJECTIVE:Research into dietary factors associated with hypertension has focused on the sodium component of salt. However, chloride has distinct physiological effects that may surpass the effect of sodium on blood pressure. This study aims to separate the specific effects of chloride and sodium intake on blood pressure. METHODS:We studied 5673 participants from the Prevention of Renal and Vascular End-Stage Disease(PREVEND) study. Urinary chloride(uCl) and sodium(uNa) were measured in two 24-hour collections. We used generalized-linear-regression to evaluate the relation of uCl and uNa with baseline blood pressure and Cox-proportional-hazards-analysis to assess the association with hypertension. Multicollinearity was assessed with Ridge regression. RESULTS:Baseline 24-hour uCl was 135±39mmol and uNa was 144±54mmol. The correlation between uCl and uNa was high (Pearson's r = 0.96). UCl and uNa had similar non-significant positive and linear associations with blood pressure. In 3515 normotensive patients, 1021 patients developed hypertension during a median follow-up of 7.4 years. UCl and uNa had a comparable but non-significant J-shaped effect on the risk of hypertension. Adding both uCl and uNa to the same model produced instability, demonstrated by Ridge coefficients that converged or changed sign. The single index of uNa minus uCl showed a non-significant higher risk of hypertension of 2% per 10mmol/24-hour difference (HR1.02, 95%CI 0.98-1.06). CONCLUSION:UCl and uNa had similar positive but non-significant associations with blood pressure and risk of hypertension and their effects could not be disentangled. Hence, the alleged adverse effects of high salt intake could be due to sodium, chloride or both. This encourages further study into the effect of chloride in order to complement dietary recommendations currently focused on sodium alone

Coding Efficiency of Fly Motion Processing Is Set by Firing Rate, Not Firing Precision

To comprehend the principles underlying sensory information processing, it is important to understand how the nervous system deals with various sources of perturbation. Here, we analyze how the representation of motion information in the fly's nervous system changes with temperature and luminance. Although these two environmental variables have a considerable impact on the fly's nervous system, they do not impede the fly to behave suitably over a wide range of conditions. We recorded responses from a motion-sensitive neuron, the H1-cell, to a time-varying stimulus at many different combinations of temperature and luminance. We found that the mean firing rate, but not firing precision, changes with temperature, while both were affected by mean luminance. Because we also found that information rate and coding efficiency are mainly set by the mean firing rate, our results suggest that, in the face of environmental perturbations, the coding efficiency is improved by an increase in the mean firing rate, rather than by an increased firing precision

YaxAB, a Yersinia enterocolitica Pore-Forming Toxin Regulated by RovA

ABSTRACT The transcriptional regulator RovA positively regulates transcription of the Yersinia enterocolitica virulence gene inv . Invasin, encoded by inv , is important for establishment of Y. enterocolitica infection. However, a rovA mutant is more attenuated for virulence than an inv mutant, implying that RovA regulates additional virulence genes. When the Y. enterocolitica RovA regulon was defined by microarray analysis, YE1984 and YE1985 were among the genes identified as being upregulated by RovA. Since these genes are homologous to Xenorhabdus nematophila cytotoxin genes xaxA and xaxB , we named them yaxA and yaxB , respectively. In this work, we demonstrate the effects of YaxAB on the course of infection in the murine model. While a yaxAB mutant (Δ yaxAB ) is capable of colonizing mice at the same level as the wild type, it slightly delays the course of infection and results in differing pathology in the spleen. Further, we found that yaxAB encode a probable cytotoxin capable of lysing mammalian cells, that both YaxA and YaxB are required for cytotoxic activity, and that the two proteins associate. YaxAB-mediated cell death occurs via osmotic lysis through the formation of distinct membrane pores. In silico tertiary structural analysis identified predicted structural homology between YaxA and proteins in pore-forming toxin complexes from Bacillus cereus (HBL-B) and Escherichia coli (HlyE). Thus, it appears that YaxAB function as virulence factors by inducing cell lysis through the formation of pores in the host cell membrane. This characterization of YaxAB supports the hypothesis that RovA regulates expression of multiple virulence factors in Y. enterocolitica

Extrauterine listeriosis in the gravid mouse influences embryonic growth and development

Gravid mice and other rodents inoculated with Listeria monocytogenes typically fail to clear an intrauterine infection and either succumb or expel their intrauterine contents. We took advantage of this property to investigate the effects of an extrauterine infection on parameters of pregnancy success. Pregnant mice were selected for our study if they showed no clinical signs of listeriosis following oral inoculation at 7.5 gestational days (gd), and had no detectable intrauterine colony forming units (cfu) at near term (18.5 gd). The range of oral doses employed was 10(6)-10(8) cfu per mouse for two listerial serotype strains (4nonb and 1/2a). At all doses, inoculation resulted in a decrease in average near-term (18.5 gd) fetal weight per litter compared to sham inoculated controls. Additionally, embryonic death (indicated by intrauterine resorptions) was exhibited by some inoculated mice but was absent in all sham inoculated animals. In parallel experiments designed to detect possible loss of placental function, gravid uteruses were examined histopathologically and microbiologically 96 h after oral inoculation. Placental lesions were associated with high (> 10(6)), but not low (< 10(2)) or absent intrauterine cfu. In vitro, mouse embryonic trophoblasts were indistinguishable from mouse enterocytes in terms of their sensitivity to listerial exposure. A model consistent with our observations is one in which products (host or bacterial) generated during an acute infection enter embryos transplacentally and influences embryonic survival and slows normal growth in utero

Generalized Interpolation Material Point Approach to High Melting Explosive with Cavities Under Shock

Criterion for contacting is critically important for the Generalized Interpolation Material Point(GIMP) method. We present an improved criterion by adding a switching function. With the method dynamical response of high melting explosive(HMX) with cavities under shock is investigated. The physical model used in the present work is an elastic-to-plastic and thermal-dynamical model with Mie-Gr\"uneissen equation of state. We mainly concern the influence of various parameters, including the impacting velocity $v$, cavity size $R$, etc, to the dynamical and thermodynamical behaviors of the material. For the colliding of two bodies with a cavity in each, a secondary impacting is observed. Correspondingly, the separation distance $D$ of the two bodies has a maximum value $D_{\max}$ in between the initial and second impacts. When the initial impacting velocity $v$ is not large enough, the cavity collapses in a nearly symmetric fashion, the maximum separation distance $D_{\max}$ increases with $v$. When the initial shock wave is strong enough to collapse the cavity asymmetrically along the shock direction, the variation of $D_{\max}$ with $v$ does not show monotonic behavior. Our numerical results show clear indication that the existence of cavities in explosive helps the creation of ``hot spots''.Comment: Figs.2,4,7,11 in JPG format; Accepted for publication in J. Phys. D: Applied Physic

Asymptotic Expansions for the Sojourn Time Distribution in the M/G/1M/G/1-PS Queue

We consider the $M/G/1$ queue with a processor sharing server. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, as well as the unconditional distribution, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. Our results demonstrate the possible tail behaviors of the unconditional distribution, which was previously known in the cases $G=M$ and $G=D$ (where it is purely exponential). We assume that the service density decays at least exponentially fast. We use various methods for the asymptotic expansion of integrals, such as the Laplace and saddle point methods.Comment: 45 page