An advection-robust Hybrid High-Order method for the Oseen problem

In this work, we study advection-robust Hybrid High-Order discretizations of the Oseen equations. For a given integer $k\ge 0$, the discrete velocity unknowns are vector-valued polynomials of total degree $\le k$ on mesh elements and faces, while the pressure unknowns are discontinuous polynomials of total degree $\le k$ on the mesh. From the discrete unknowns, three relevant quantities are reconstructed inside each element: a velocity of total degree $\le(k+1)$, a discrete advective derivative, and a discrete divergence. These reconstructions are used to formulate the discretizations of the viscous, advective, and velocity-pressure coupling terms, respectively. Well-posedness is ensured through appropriate high-order stabilization terms. We prove energy error estimates that are advection-robust for the velocity, and show that each mesh element $T$ of diameter $h_T$ contributes to the discretization error with an $\mathcal{O}(h_T^{k+1})$-term in the diffusion-dominated regime, an $\mathcal{O}(h_T^{k+\frac12})$-term in the advection-dominated regime, and scales with intermediate powers of $h_T$ in between. Numerical results complete the exposition

A 58-year-old Man with Abdominal Pain; Acute Appendicitis due to an Appendicolith

Case presentation: A 58-year-old man presented to the emergency department with abdominal pain, nausea and loss of appetite for the last 8 hours. He reported diffuse pain that had been localized to the right lower quadrant (RLQ). Physical examination revealed muscular defense and tenderness in the RLQ. Computed tomography (CT) of the abdomen and pelvis confirmed luminal distension with a thickened enhancing wall with an appendicolith. Learning points: Appendicitis may be developed by an appendicolith, a calcified deposit within the appendix. It may be an incidental finding on an abdominal radiograph, ultrasound (US) examination or CT. It appears as echogenic focus and casts an acoustic shadow on US examination and manifests as a calcified mass on plain radiograph or CT. The incidence of appendicolith is higher among patients with a retrocaecal appendix. In our patient, a clinical diagnosis of acute appendicitis was made and the patient was immediately transferred to the operating room and an appendectomy was performed

A 27-years-old Man with Abdominal Pain; Lead Toxicity

Case presentation: A 27-year-old man came to our emergency department with chief complaints of abdominal pain, nausea and vomiting, colicky pain in all area of abdomen without any radiation and generalized myalgia. In his background, he had no previous medical problem. In his social history he had worked in an automobile battery-reclaiming factory for 5 years. During his physical examination, his appearance was pale with perioral priority, ill and agitated but not toxic with a blood pressure of 127/85 mmHg and a pulse of 80 beats/min, respiratory rate of 14 breaths/min and oral temperature of 37.3 °C, mild generalized abdominal tenderness without rebound. No obvious signs of sensory and motor neuropathy were found. In the head and neck examination, we found lead-lined teeth. Learning points: The most common cause of chronic metal poisoning is lead. Exposure occurs through inhalation or ingestion. Both inorganic and organic forms of lead that exist naturally produce clinical toxicity. Gastrointestinal manifestations occur more frequently with acute rather than with chronic poisoning, and concurrent hemolysis may cause the colicky abdominal pains. Patients may have complained of a metallic taste and, with long-term exposure, have bluish-gray gingival lead lines. In addition, constitutional symptoms, including arthralgia, generalized weakness, and weight loss raises the possibility of lead toxicity

Hybrid Simulator for Space Docking and Robotic Proximity Operations

In this work, we present a hybrid simulator for space docking and robotic proximity operations methodology. This methodology also allows for the emulation of a target robot operating in a complex environment by using an actual robot. The emulation scheme aims to replicate the dynamic behavior of the target robot interacting with the environment, without dealing with a complex calculation of the contact dynamics. This method forms a basis for the task verification of a flexible space robot. The actual emulating robot is structurally rigid, while the target robot can represent any class of robots, e.g., flexible, redundant, or space robots. Although the emulating robot is not dynamically equivalent to the target robot, the dynamical similarity can be achieved by using a control law developed herein. The effect of disturbances and actuator dynamics on the fidelity and the contact stability of the robot emulation is thoroughly analyzed

Optimal Control of Legged-Robots Subject to Friction Cone Constraints

A hierarchical control architecture is presented for energy-efficient control of legged robots subject to variety of linear/nonlinear inequality constraints such as Coulomb friction cones, switching unilateral contacts, actuator saturation limits, and yet minimizing the power losses in the joint actuators. The control formulation can incorporate the nonlinear friction cone constraints into the control without recourse to the common linear approximation of the constraints or introduction of slack variables. A performance metric is introduced that allows trading-off the multiple constraints when otherwise finding an optimal solution is not feasible. Moreover, the projection-based controller does not require the minimal-order dynamics model and hence allows switching contacts that is particularly appealing for legged robots. The fundamental properties of constrained inertia matrix derived are similar to those of general inertia matrix of the system and subsequently these properties are greatly exploited for control design purposes. The problem of task space control with minimum (point-wise) power dissipation subject to all physical constraints is transcribed into a quadratically constrained quadratic programming (QCQP) that can be solved by barrier methods