Heat equation on the hypergraph containing vertices with given data

This paper is concerned with the Cauchy problem of a multivalued ordinary differential equation governed by the hypergraph Laplacian, which describes the diffusion of ``heat'' or ``particles'' on the vertices of hypergraph. We consider the case where the heat on several vertices are manipulated internally by the observer, namely, are fixed by some given functions. This situation can be reduced to a nonlinear evolution equation associated with a time-dependent subdifferential operator, whose solvability has been investigated in numerous previous researches. In this paper, however, we give an alternative proof of the solvability in order to avoid some complicated calculations arising from the chain rule for the time-dependent subdifferential. As for results which cannot be assured by the known abstract theory, we also discuss the continuous dependence of solution on the given data and the time-global behavior of solution.Comment: 19 pages, 3 figure

Design of Hemispherical Radio Frequency (RF) Capacitive-type Electrode Free of Edge Effects for Treatment of Intracavitary Tumors

A new hemispherical electrode to heat oral cavity cancer is proposed. The electrode does not produce a hot spot around its edge, a feature that usually arises when using radio frequency (RF) capacitive-type heating. The hemispherical electrode was designed by computer simulation using a 3-D finite element method. To assess its practicality and effectiveness, we built a prototype hemispherical electrode and evaluated its heating characteristics by phantom experiments. The heating effects on the phantom were measured by thermography. The concave phantom surface in contact with the hemispherical electrode showed a uniform increase in temperature, with no obvious edge effect. The proposed electrode allows non-invasive RF capacitive-type heating for intracavity tumors that was not previously considered possible, and should contribute to the multidisciplinary treatment of intracavity tumors

Spinal epidural oxygen partial pressure and evoked spinal cord potential in relation to the severity of spinal ischemia during cross-clamping of the thoracic aorta.

Experiments were undertaken to determine the relationship between evoked spinal cord potential (ESP) and the partial pressure of oxygen in tissue in the epidural space (E-pO2) during aortic clamping. Eighteen adult mongrel dogs were studied as follows. In group I (n = 6), the descending thoracic aorta was clamped partially at the proximal site for 15 min to maintain the distal arterial pressure at 60, 40, and 20 mmHg consecutively at 15 min intervals. In group II (n = 6), the descending thoracic aorta was clamped proximally for 30 min. In group III (n = 6), the descending thoracic aorta was cross-clamped at proximal and distal sites for 30 min. Postoperative complete paraplegia was observed in 4 of 6 dogs in group III, but none in group II. The change in ESP with aorta cross-clamping was very mild in groups I and II. Transient increases and decreases in the ESP amplitude were observed in group III. The decrease of E-pO2 correlated well with the distal arterial pressure, and a rapid return to baseline of the E-pO2 was observed after declamping. The E-pO2 changed in response to spinal ischemia more rapidly than did ESP in all groups. The critical level of E-pO2 was 50 mmHg or a 40% decrease from baseline. Because the ESP reflects spinal function and the E-pO2 reflects spinal blood pressure, we propose that combined recording of ESP and E-pO2 would improve spinal monitoring during thoracic aortic surgery.</p

Studies on Silage-Making (XXV) : The Changes in Lignin Content and Dry Matter Digestibility During Growth Stages of Forage Crops

サイレージ材料の刈取適期を栄養的な面から検討するために,イタリアンライグラス,レッドクローバー,トウモロコシおよびローズグラスの生育にともなうリグニン含量ならびに乾物の人工消化率を調査し,両者の関係についても解析した. 乾物中のリグニン含量は,生育の進行とともにイタリアンライグラス,レッドクローバー,ローズグラスで増加し,トウモロコシで減少する傾向があり,乾物の消化率は,生育の進行とともにトウモロコシで上昇し,イタリアンライグラス,レッドクローバー,ローズグラスで下降する傾向があった. 乾物中のリグニン含量と乾物の消化率との間に,レッドクローバー以外の草種において有意な負の相関が認められた. 全試料について両因子の関係を調査した結果,r=-0.822(P<0.001)の相関があり,リグニン含量(X)から乾物消化率(Y)を推定する回帰式はY=99.61-3.60Xであった

Studies on Silage-Making (XXIV) : Effects of Acrylic Acid and Sodium Acrylate as Additives

高水分ならびに低水分のイタリアンライグラスを埋蔵材料に用い,実験用プラスチックミニサイロおよび実験用スチール製気密サイロを供用して,アクリル酸ならびにアクリル酸ナトリウムのサイレージヘの添加試験をおこない,サイロ内のサイレージ発酵および開封後サイレージの好気的変敗に対する影響について調査した. 本研究結果の要約は次のようである. 1)本研究の実験の範囲においては,これら添加剤添加による,いわゆる発酵的品質の改善効果は確認できなかったが,添加によって発酵が総体的に抑えられ,タンパク質の分解抑制などによる埋蔵中の養分分解損失の減少の可能性が示された. 2)開封後サイレージの変化についての調査より,これらの添加により,温度上昇の抑制遅延,カビ発生増殖の抑制ならびにタンパク質分解の低減など,変敗の遅延もしくは抑制の効果が認められた. 3)添加効果ならびに取り扱いの簡便性や安全性などの点から,アクリル酸ナトリウムはアクリル酸またはプロピオン酸ナトリウムより,サイレージ添加剤として優れているものと思われた

Load carrying behavior of concrete reinforced with bundled BFRP bars by using DIC

Recently, basalt fiber-reinforced polymer (BFRP) has gained attention in the construction industry because of its worldwide availability and eco-friendly nature. Different from conventional steel bars, BFRP bar do not corrode being an ideal reinforcing material in structures surrounding magnetic fields and marine environments, given its chemical stability. This study investigated the load carrying behavior of concrete beams reinforced with conventional deformed steel bars and seven-bundled BFRP bars through four-point flexural test. For each case, two beams were pre-pared; one beam was designed with a low reinforcement ratio and another with a high rein-forcement ratio in order to obtain a load carrying capacity of around 330-368 kN and 483-519 kN, respectively. Deflection, crack width evolution, and strain behavior of each beam were comparatively analyzed using a digital image correlation (DIC) based technique. The DIC analysis results showed that the neutral axis of bundled BFRP reinforced cases move to the upper end in an early loading stage, with larger cracks width, and the deflection is larger in BFRP cases than in those of steel-reinforced beams with the respective reinforcement ratio. However, the four-point flexural test results revealed that bundled BFRP bars can be used as an alternative to conventional steel bars. The load carrying capacities were obtained similarly to designed values, around 364 and 551 kN for low and high reinforcement ratio cases, respectively

Simple Model Representations of Transport in a Complex Fracture and Their Effects on Long-Term Predictions

A complex fracture model for fluid flow and tracer transport was previously developed that incorporates many of the important physical effects of a realistic fracture, including advection through a heterogeneous fracture plane, partitioning of flow into multiple subfractures in the third dimension, and diffusion and sorption into fracture-filling gouge, small altered rock matrix blocks within the fracture zone, and the unaltered semi-infinite rock matrix on both sides of the fracture zone (Tsang and Doughty, 2003). It is common, however, to represent the complex fracture by much simpler models consisting of a single fracture, with a uniform or heterogeneous transmissivity distribution over its plane and bounded on both sides by a homogeneous semi-infinite matrix. Simple-model properties are often inferred from the analysis of short-term (one to a few days) site characterization (SC) tracer-test data. The question addressed in this paper is: How reliable is the temporal upscaling of these simplified models? Are they adequate are for long-term calculations that cover thousands of years? In this study, a particle-tracking approach is used to calculate tracer-test breakthrough curves (BTCs) in a complex fracture model, incorporating all the features described above, for both a short-term SC tracer test and a 10,000-year calculation. The results are considered the 'real-world'. Next, two simple fracture models, one uniform and the other heterogeneous, are introduced. Properties for these simple models are taken either from laboratory data or found by calibration to the short-term SC tracer-test BTCs obtained with the complex fracture model. Then the simple models are used to simulate tracer transport at the long-term time scale. Results show that for the short-term SC tracer test, the BTCs calculated using simple models with laboratory-measured parameters differ significantly from the BTCs obtained with the complex fracture model. By adjusting model properties, the simple models can be calibrated to reproduce the peak arrival time and height of the complex-fracture-model BTCs, but the overall match remains quite poor. Using simple models with short-term SC-calibrated parameters for long-term calculations causes order-of-magnitude errors in tracer BTCs: peak arrival time is 10-100 times too late, and peak height is 50-300 times too small. On the other hand, using simple models with laboratory-measured properties of unfractured rock samples for 10,000-year calculations results in peak arrivals and heights up to a factor of 50 too early and large, respectively. The actual magnitudes of the errors made by using the simple models depend on the parameter values assumed for the complex fracture model, but in general, simple models are not expected to provide reliable long-term predictions. The paper concludes with some suggestions on how to improve long-term prediction calculations