Non-optimality of conical parts for Newton’s problem of minimal resistance in the class of convex bodies and the limiting case of infinite height

We consider Newton’s problem of minimal resistance, in particular we address the problem arising in the limit if the height goes to infinity. We establish existence of solutions and lack radial symmetry of solutions. Moreover, we show that certain conical parts contained in the boundary of a convex body inhibit the optimality in the classical Newton’s problem with finite height. This result is applied to certain bodies considered in the literature, which are conjectured to be optimal for the classical Newton’s problem, and we show that they are not.

THEORETICAL DESCRIPTION OF THE PROCESS OF HEATING THE GAS-AIR MIXTURE IN THE BODY OF THE BURNER WITH A THERMAL DIVIDER

The main thermal processes occurring during the operation of a gas burner device for household use are considered. One of the important functions performed by the gas burner device is the preparation of fuel for subsequent combustion. The efficiency and quality of the combustion process directly depends on the temperature of the gas-air mixture. Since an increase in the temperature of the mixture contributes to the intensification of the combustion process, when designing gas burner devices, it is useful to determine the temperature of the gas-air mixture inside the burner body. We have proposed a solution that makes it possible to increase the efficiency of the gas burner device by intensifying the preheating from the thermal divider to the gas-air mixture inside the body of the gas burner. It has been established that the placement of the thermal divider in the central part on the inner side of the cover allows one to reduce the stagnant zone area when the flow of the gas-air mixture moves, and the conical shape of the thermal divider provides minimal resistance to the movement of the gas-air mixture flow inside the gas burner, in addition, the side surface of the thermal divider additionally increases the area heat transfer. An expression is obtained for calculating the average temperature of the gas-air mixture at the outlet from the firing holes of the gas burner.

On a Non-Newtonian Calculus of Variations

The calculus of variations is a field of mathematical analysis born in 1687 with Newton’s problem of minimal resistance, which is concerned with the maxima or minima of integral functionals. Finding the solution of such problems leads to solving the associated Euler–Lagrange equations. The subject has found many applications over the centuries, e.g., in physics, economics, engineering and biology. Up to this moment, however, the theory of the calculus of variations has been confined to Newton’s approach to calculus. As in many applications negative values of admissible functions are not physically plausible, we propose here to develop an alternative calculus of variations based on the non-Newtonian approach first introduced by Grossman and Katz in the period between 1967 and 1970, which provides a calculus defined, from the very beginning, for positive real numbers only, and it is based on a (non-Newtonian) derivative that permits one to compare relative changes between a dependent positive variable and an independent variable that is also positive. In this way, the non-Newtonian calculus of variations we introduce here provides a natural framework for problems involving functions with positive images. Our main result is a first-order optimality condition of Euler–Lagrange type. The new calculus of variations complements the standard one in a nontrivial/multiplicative way, guaranteeing that the solution remains in the physically admissible positive range. An illustrative example is given.

Carbon/Silicone Nanocomposite-Enabled Soft Pressure Sensors with a Liquid-Filled Cell Structure Design for Low Pressure Measurement

In the fields of humanoid robots, soft robotics, and wearable electronics, the development of artificial skins entails pressure sensors that are low in modulus, high in sensitivity, and minimal in hysteresis. However, few sensors in the literature can meet all the three requirements, especially in the low pressure range (<10 kPa). This article presents a design for such pressure sensors. The bioinspired liquid-filled cell-type structural design endows the sensor with appropriate softness (Young’s modulus < 230 kPa) and high sensitivity (highest at 0.7 kPa−1) to compression forces below 0.65 N (6.8 kPa). The low-end detection limit is ~0.0012 N (13 Pa), only triple the mass of a bee. Minimal resistance hysteresis of the pressure sensor is 7.7%. The low hysteresis is attributed to the study on the carbon/silicone nanocomposite, which reveals the effect of heat treatment on its mechanical and electromechanical hysteresis. Pressure measurement range and sensitivity of the sensor can be tuned by changing the structure and strain gauge parameters. This concept of sensor design, when combined with microfluidics technology, is expected to enable soft, stretchable, and highly precise touch-sensitive artificial skins.

Intraluminal catheter plasty. an alternative technique to remove tethered abdominal surgical drains

Objective: Retained surgical drains can lead to significant complications including gastrointestinal fistulae, abscess formation and intestinal obstruction. Today, there is little in the literature describing the role of Interventional Radiology (IR) in assisting the removal of surgical drains. We describe the use of the well-established intraluminal catheter plasty technique, previously used for the removal of adhered central venous catheters, in order to remove a tethered abdominal drain. Methods and materials: A 67-year-old female was referred to the IR department for the removal of a 24 Fr Robinson’s intra abdominal surgical drain that could not be removed by conventional methods, as there was a concern that it was kinked internally. Both fluoroscopy and cone beam CT was performed which identified the drain to be sited within the pelvis with no kinks. A first attempt to remove the drain over a 0.035 stiff wire was unsuccessful due to resistance and patient discomfort. We suspected that this was due to adhesions surrounding the drain. Consequently, a 9 x 40mm angioplasty balloon was used over the wire with serial dilatations along the drain to disrupt the adhesions. Several areas of waisting were identified. The drain was gently withdrawn over the wire with minimal resistance. Ex-vivo inspection of the drain showed no evidence of structural damage and fluoroscopic imaging confirmed no retained fragments. Conclusion: We describe a safe and effective novel technique of intraluminal catheter plasty used to remove a tethered surgical drain following failed conventional methods.

The coronary microcirculation in sepsis: not of micro-importance

[No abstract - showing first paragraph]The coronary arterial system consists of a continuous network of functionally distinct vessels of decreasing size. The epicardial arteries (>500 μm) have primarily a conductance function and, therefore, physiologically offer minimal resistance to flow. The microcirculation, including pre-arterioles (100 to 500 μm) and arterioles (<100 μm), on the other hand, is the main active determinant of resistance within the coronary tree, responsible for the metabolic regulation of regional blood flow to the myocardium.

Fulminant Guillain Barre syndrome with recurrent lung collapse

Fulminant Guillain-Barré syndrome (GBS) is a rapidly progressive form of polyneuropathy in which patients demonstrate eventual flaccid quadriplegia and an absence of brainstem function. Most patients present initially with a mild upper respiratory or gastrointestinal illness and have non-diagnostic cerebral imaging studies. Here we report the case of child aged 7 who was admitted initially with complaints of weakness of lower limbs lasting for 4-5 hours. He had difficulty in standing and walking, associated with pain in both lower limbs. Flaccid weakness rapidly progressed over 12 hours to involve both upper limbs along with difficulty in swallowing and nasal regurgitation of feeds. He was intubated and mechanically ventilated for respiratory failure. Over the period of time, after confirmation with all the test reports and symptoms, other differential diagnoses were ruled out and fulminant GBS was considered and hence plasmapheresis was started. Over the period of 3 months his muscle power slowly improved. During discharge, he was able to lift limbs against minimal resistance, turn sideways on bed, sit up with minimal support and likewise stand with support.