Parametric Study of Hypoplasticity Constitutive Model for Granular Media via the Discrete Element Method

Granular media, as a general definition, includes a large class of materials, such as cereal grains; pharmaceutical tablets and capsules; geomaterials, such as sand; and the masses of rock and ice in planetary rings. Alternatively, a granular material could consist of highly fractured rock masses regarded as cracked elastic solids. In all cases, a very important property of granular media is their ability to yield, that is, exhibit irreversible deformation properties. Because the granular elastic modulus ‘G’ is the key relevant stress parameter, there is an interesting and nagging question as to the microscopic origins of the stress scales assumed in various empiricisms associated with critical-state soil mechanics and Hypoplasticity. This question may reflect a philosophical divide, separating those concerned with the relation of constitutive equations to micromechanics, from those whose primary concern is correlation of data from laboratory and field tests.The goal of this research is to first understand how hypoplastic constitutive equation works to account for the granular material behavior. From the original Hypoplastic constitutive equation which was introduced by Kolymbas, Lade-Duncan, Mohr-Coulomb and Matsuoka-Nakai yield surfaces (which are regarded as the significant approach for yield prediction in elastoplasticity theory) are generated. Then, with the Discrete Element Method (DEM) true-triaxial test results, the parametric study is processed by the developed inverse hypoplastic constitutive equation. The results show the concept of inverting the hypoplastic constitutive model is capable of generating the actual and effective non-dimensional material parameters. Due to the input of the improved stress and strain obtained from the true-triaxial test, the improved method is shown to be improved from original experimental data. Also, the Hypoplastic method performs as effective as the other previous method such as elastoplastic

Impartial digraphs

We prove a conjecture of Fox, Huang, and Lee that characterizes directed graphs that have constant density in all tournaments: they are disjoint unions of trees that are each constructed in a certain recursive way.Comment: 15 page

MicroRNA-like RNAs from the same miRNA precursors play a role in cassava chilling responses

Abstract MicroRNAs (miRNAs) are known to play important roles in various cellular processes and stress responses. MiRNAs can be identified by analyzing reads from high-throughput deep sequencing. The reads realigned to miRNA precursors besides canonical miRNAs were initially considered as sequencing noise and ignored from further analysis. Here we reported a small-RNA species of phased and half-phased miRNA-like RNAs different from canonical miRNAs from cassava miRNA precursors detected under four distinct chilling conditions. They can form abundant multiple small RNAs arranged along precursors in a tandem and phased or half-phased fashion. Some of these miRNA-like RNAs were experimentally confirmed by re-amplification and re-sequencing, and have a similar qRT-PCR detection ratio as their cognate canonical miRNAs. The target genes of those phased and half-phased miRNA-like RNAs function in process of cell growth metabolism and play roles in protein kinase. Half-phased miR171d.3 was confirmed to have cleavage activities on its target gene P-glycoprotein 11, a broad substrate efflux pump across cellular membranes, which is thought to provide protection for tropical cassava during sharp temperature decease. Our results showed that the RNAs from miRNA precursors are miRNA-like small RNAs that are viable negative gene regulators and may have potential functions in cassava chilling responses

Enhanced Prediction of Three-dimensional Finite Iced Wing Separated Flow Near Stall

Icing on three-dimensional wings causes severe flow separation near stall. Standard improved delayed detached eddy simulation (IDDES) is unable to correctly predict the separating reattaching flow due to its inability to accurately resolve the Kelvin-Helmholtz instability. In this study, a shear layer adapted subgrid length scale is applied to enhance the IDDES prediction of the flow around a finite NACA (National Advisory Committee for Aeronautics) 0012 wing with leading edge horn ice. It is found that applying the new length scale contributes to a more accurate prediction of the separated shear layer (SSL). The reattachment occurs earlier as one moves towards either end of the wing due to the downwash effect of the wing tip vortex or the influence of end-wall flow. Consequently, the computed surface pressure distributions agree well with the experimental measurements. In contrast, standard IDDES severely elongates surface pressure plateaus. For instantaneous flow, the new length scale helps correctly resolve the rollup and subsequent pairing of vortical structures due to its small values in the initial SSL. The computed Strouhal numbers of vortical motions are approximately 0.2 in the initial SSL based on the vorticity thickness and 0.1 around the reattachment based on the separation bubble length. Both frequencies increase when moving towards the wing tip due to the downwash effect of the tip vortex. In comparison, the excessive eddy viscosity levels from the standard IDDES severely delay the rollup of spanwise structures and give rise to "overcoherent" structures

Gr\"obner-Shirshov bases and linear bases for free multi-operated algebras over algebras with applications to differential Rota-Baxter algebras and integro-differential algebras

Quite much recent studies has been attracted to the operated algebra since it unifies various notions such as the differential algebra and the Rota-Baxter algebra. An $\Omega$-operated algebra is a an (associative) algebra equipped with a set $\Omega$ of linear operators which might satisfy certain operator identities such as the Leibniz rule. A free $\Omega$-operated algebra $B$ can be generated on an algebra $A$ similar to a free algebra generated on a set. If $A$ has a Gr\"{o}bner-Shirshov basis $G$ and if the linear operators $\Omega$ satisfy a set $\Phi$ of operator identities, it is natural to ask when the union $G\cup \Phi$ is a Gr\"{o}bner-Shirshov basis of $B$. A previous work answers this question affirmatively under a mild condition, and thereby obtains a canonical linear basis of $B$. In this paper, we answer this question in the general case of multiple linear operators. As applications we get operated Gr\"{o}bner-Shirshov bases for free differential Rota-Baxter algebras and free integro-differential algebras over algebras as well as their linear bases. One of the key technical difficulties is to introduce new monomial orders for the case of two operators, which might be of independent interest.Comment: 27 page

Seasonal Variations in Circumpolar Deep Water Intrusions Into The Ross Sea Continental Shelf

Intrusions of the warm and nutrient-rich Circumpolar Deep Water (CDW) across the Ross Sea shelf break play an important role in providing heat for ice shelf basal melting and setting the physical environment for biochemical processes. Several mechanisms driving CDW intrusions into the Ross Sea were proposed such as mesoscale eddies, tidal rectification, and interactions between Antarctic Slope Current (ASC) and topographic features. The seasonal variations in the poleward transport of CDW are investigated using ERA-Interim wind data and a Ross Sea circulation model based on the Regional Ocean Modeling System (ROMS) between September 1999 and September 2014. The analyses focus on the currents along the shelf break and deep troughs on the Ross Sea shelf and discuss the wind-driven Ekman pumping in both shelf and adjacent open ocean regions. The results reveal that the poleward intrusions generally move up onto the continental shelf along the eastern flanks of deep troughs. Seasonal variations of the ocean surface stress torque exerted by wind and sea ice in the offshelf area are correlated with CDW intrusions. The maxima of CDW intrusions usually occur in austral summer. There is a significant temporal correlation on the seasonal time scale between the onshelf intrusions in deep troughs in the western Ross Sea shelf and poleward Sverdrup transports in the adjacent offshelf open ocean driven by Ekman pumping. The analysis of ocean surface stress fields also indicates that the vorticity fluxes through Ekman pumping are in favor of southward and northward transports in the eastern and western parts of the Ross Sea, respectively. The relationships between currents, CDW intrusions and ocean surface stress fields imply the importance of air-sea interactions and potential climate change to the environment in the Ross Sea