Tumor growth with a necrotic core as an obstacle problem in pressure

Motivated by the incompressible limit of a cell density model, we propose a free boundary tumor growth model where the pressure satisfies an obstacle problem on an evolving domain $\Omega(t)$, and the coincidence set $\Lambda(t)$ captures the emerging necrotic core. We contribute to the analytical characterization of the solution structure in the following two aspects. By deriving a semi-analytical solution and studying its dynamical behavior, we obtain quantitative transitional properties of the solution separating phases in the development of necrotic cores and establish its long time limit with the traveling wave solutions. Also, we prove the existence of traveling wave solutions incorporating non-zero outer densities outside the tumor bulk, provided that the size of the outer density is below a threshold

AT2019 avd: A tidal disruption event with a two-phase evolution

Tidal disruption events (TDEs) can uncover the quiescent super-massive black holes (SMBHs) at the center of galaxies and also offer a promising method to study them. After the disruption of a star by a SMBH, the highly elliptical orbit of the debris stream will be gradually circularized due to the self-crossing, and then the circularized debris will form an accretion disk. The recent TDE candidate AT 2019avd has double peaks in its optical light curve, and the X-ray emerges near the second peak. The durations of the peaks are about 400 and 600 days, respectively, and the separation between them is ~ 700 days. We fit and analyse its spectral energy distribution (SED) in optical/UV, mid-infrared, and X-ray bands. We find that this source can be interpreted as the circularization process in the first phase plus the delayed accretion process in the second phase. Under this two-phase scenario, we use the succession of self-crossing circularization model to fit the first peak, and the delayed accretion model to fit the second peak. The fitting results are consistent with the partial disruption of a 0.9 M_sun star by a 7 * 10^6 M_sun SMBH with the penetration factor \beta ~ 0.6. Furthermore, we find the large-amplitude (by factors up to ~ 5) X-ray variability in AT 2019avd can be interpreted as the rigid-body precession of the misaligned disk due to the Lense-Thirring effect of a spinning SMBH, with the disk precession period of 10 - 25 days.Comment: 14 pages, 11 figures, 4 tables, Submitted to Ap

Combined cloud:a mixture of voluntary cloud and reserved instance marketplace

Voluntary cloud is a new paradigm of cloud computing.It provides an alternative selection along with some well-provisioned clouds.However,for the uncertain time span that participants share their computing resources in voluntary cloud,there are some challenging issues,i.e.,fluctuation,under-capacity and low-benefit.In this paper,an architecture is first proposed based on Bittorrent protocol.In this architecture,resources could be reserved or requested from Reserved Instance Marketplace and could be accessed with a lower price in a short circle.Actually,these resources could replenish the inadequate resource pool and relieve the fluctuation and under-capacity issue in voluntary cloud.Then,the fault rate of each node is used to evaluate the uncertainty of its sharing time.By leveraging a linear prediction model,it is enabled by a distribution function which is used for evaluating the computing capacity of the system.Moreover,the cost optimization problem is investigated and a computational method is presented to solve the low-benefit issue in voluntary cloud.At last,the system performance is validated by two sets of simulations.And the experimental results show the effectiveness of our computational method for resource reservation optimization

Exact analytical solution to ultrasonic interfacial reflection enabling optimal oil film thickness measurement

The ultrasonic reflection from a lubricated interface has been widely analyzed to measure fluid film thickness, with different algorithms being applied to overcome measurement accuracy and resolution issues. Existing algorithms use either the amplitude or the phase angle of the ultrasonic interfacial reflection. In this paper, a new algorithm (named the “exact model – complex”) that simultaneously utilizes both the amplitude and the phase of the complex ultrasonic reflection coefficient is proposed and mathematically derived. General procedures for theoretical analysis in terms of measurement accuracy and uncertainty are proposed and applied to the new algorithm, the beneficial features of which (as compared to other existing algorithms) can be summarized as: 1) a direct calculation, instead of an iterative approximation, 2) guaranteed maximum measurement accuracy, and 3) acceptable measurement uncertainty. None of the existing methods have showed this combination of benefits. Moreover, two groups of raw data from previous experimental studies are utilized to further validate the practical feasibility of the new algorithm. Overall, the proposed “exact model – complex” algorithm fully exploits the potential of ultrasonic reflection for oil film thickness measurement, with an accurate and a convenient calculation suited to practical implementation

Male Populus cathayana than female shows higher photosynthesis and less cellular injury through ABA-induced manganese transporting inhibition under high manganese condition

High Mn poisoned male and female Populus cathayana. The toxicity could be alleviated by exogenous ABA application. Intriguingly, ABA granted higher resistance to males than to females under high Mn stress because ABA could induce more blocking of Mn translocation to leaf in males than in females. Abscisic acid (ABA) is involved in plants' adaptive responses to various environmental stresses. However, little is known about the sex-related detoxification of ABA in plants under excess manganese (Mn) conditions. To reveal potentially different ABA detoxification mechanisms between Populus cathayana males and females against excess Mn exposure, photosynthesis performance, Mn2+ concentrations and morphologic changes were investigated. High Mn stress led to a more severe chloroplast destruction and, thus, greater reduction in the photosynthesis of P. cathayana females when compared to males. Under high Mn conditions, Mn reallocated mainly to leaves in females, while in males, it was distributed equally to roots and leaves. With the application of ABA, photosynthesis was restored more in males and more integrated grana in males than in females. It should be noted that Mn concentrations in males were lower in leaves and higher in roots and stems than those in females when treated with the combination of Mn and ABA. Conclusively, due to the reduction of root-shoot Mn transportation induced by ABA in P. cathayana males, males experienced less physiological injuries than do females, which suggest that males possess greater ABA-inducible resistance to Mn stress than do females.Peer reviewe

Self‐Sacrificial Template‐Directed Synthesis of Metal–Organic Framework‐Derived Porous Carbon for Energy‐Storage Devices

Metal–organic framework (MOF)‐derived carbon materials exhibit large surface areas, but dominant micropore characteristics and uncontrollable dimensions. Herein, we propose a self‐sacrificial template‐directed synthesis method to engineer the porous structure and dimensions of MOF‐derived carbon materials. A porous zinc oxide (ZnO) nanosheet solid is selected as the self‐sacrificial template and two‐dimensional (2D) nanostructure‐directing agent to prepare 2D ZIF‐8‐derived carbon nanosheets (ZCNs). The as‐prepared ZCN materials exhibit a large surface area with hierarchical porosity. These intriguing features render ZCN materials advanced electrode materials for electrochemical energy‐storage devices, demonstrating large ion‐accessible surface area and high ion‐/electron‐transport rates. This self‐sacrificial template‐directed synthesis method offers new avenues for rational engineering of the porous structure and dimensions of MOF‐derived porous carbon materials, thus exploiting their full potential for electrochemical energy‐storage devices.On the surface: A self‐sacrificial template‐directed synthesis method is proposed to engineer the porosity and dimensions of MOF‐derived carbon materials. By using a porous nanosheet solid as the self‐sacrificial template and two‐dimensional (2D) nanostructure‐directing agent, 2D ZIF‐8‐derived carbon nanosheets are prepared, which exhibit a large ion‐accessible surface area and rapid ion transport as the electrode materials for electrochemical energy‐storage devices.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137193/1/celc201500536-sup-0001-misc_information.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137193/2/celc201500536.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137193/3/celc201500536_am.pd