Levitation conditions for condensing droplets over heated liquid surfaces

We report experimental studies of levitation of microdroplets over evaporating liquid layer and show that all data for levitation height as a function of droplet size represented in nondimensional form collapses onto a single curve obtained from mathematical modeling.

Minimizing intersection points of curves under virtual homotopy

A flat virtual link is a finite collection of oriented closed curves [Formula: see text] on an oriented surface [Formula: see text] considered up to virtual homotopy, i.e., a composition of elementary stabilizations, destabilizations, and homotopies. Specializing to a pair of curves [Formula: see text], we show that the minimal number of intersection points of curves in the virtual homotopy class of [Formula: see text] equals to the number of terms of a generalization of the Anderson–Mattes–Reshetikhin Poisson bracket. Furthermore, considering a single curve, we show that the minimal number of self-intersections of a curve in its virtual homotopy class can be counted by a generalization of the Cahn cobracket.

AN ARITHMETIC PURE-JUMP MULTI-CURVE INTEREST RATE MODEL

We propose a multi-curve model involving interest rates and spreads which are modeled by arithmetic martingale processes being larger than some arbitrarily chosen constant. Under our mean-reverting pure-jump approach, we derive tractable martingale representations for the OIS rate, the spread, as well as the LIBOR rate, and provide analytical caplet price formulae. In a second part, we introduce an extended jump-diffusion version of our model and investigate hedging and the computation of Greeks under this new specification. As a by-product, we infer the related arithmetic pure-jump single-curve model. We finally consider the modeling of future information in multi-curve interest rate markets by enlarged filtrations and deduce the related OIS and LIBOR rate representations as well as the corresponding information premium.

EKSPLORASI MATERIAL GLULAM PADA PERANCANGAN SHELTER MENGGUNAKAN SALURAN KREATIVITAS FOCUS ON MATERIAL

Setiap material memiliki karakteristik yang dapat dieksplorasi dan digunakan sebagai saluran kreativitas dalam merancang bangunan. Proses eksplorasi material tersebut harus dapat mendukung efisiensi penggunaan sumber daya dalam keseluruhan daur hidup (life cycle) bangunan, mulai dari pemilihan material, desain, konstruksi, pemeliharaan, hingga pembongkaran. Glued Laminated Timber (Glulam) merupakan salah satu material alternatif dari bahan dasar kayu yang dapat diperbaharui dan memiliki low embodied energy. Dengan menggunakan saluran kreativitas focus on material, karakteristik dari glulam digunakan sebagai pendekatan merancang bangunan. Tipe bangunan yang digunakan sebagai obyek eksplorasi adalah bangunan sederhana non-ruang, yaitu shelter (naungan). Proses rancang menggunakan Cyclical Design Process yang terdiri dari tahap analisis, sintesis, dan evaluasi yang dilakukan berulang-ulang hingga mendapat rancangan paling yang optimal. Tahap analisis data dari glulam, shelter, dan focus on material dilakukan untuk menghasilkan kriteria desain yang akan digunakan untuk menghasilkan beberapa alternatif rancangan pada tahap sintesis. Beberapa alternatif rancangan tersebut kemudian di evaluasi pada tahap evaluasi untuk mendapatkan rancangan yang paling sesuai. Hasil yang diperoleh adalah rancangan skematik bangunan shelter dengan bentuk single curve dan double curve yang tersusun dari konfigurasi monomaterial elemen-elemen glulam berukuran 60x60 cm menggunakan sambungan takik.

Universality in the viscous-to-inertial coalescence of liquid droplets

We present a theory on the coalescence of 2 spherical liquid droplets that are initially stationary. The evolution of the radius of a liquid neck formed upon coalescence was formulated as an initial value problem and then solved to yield an exact solution without free parameters, with its 2 asymptotic approximations reproducing the well-known scaling relations in the inertially limited viscous and inertial regimes. The viscous-to-inertial crossover observed in previous research is also recovered by the theory, rendering the collapse of data of different viscosities onto a single curve.

The controlled vertical impact of an inclined flat plate on a quiescent water surface

The generation of spray during the vertical impact of a flat plate (length $L=1.22~\text{m}$, width $B=0.38~\text{m}$) on a quiescent water surface is studied experimentally. The plate is held in an orientation tilted up from horizontal by angles $\unicode[STIX]{x1D6FD}$ ranging from $10^{\circ }$ to $25^{\circ }$ about one of its long edges, which is positioned close to a vertical wall. The plate motion, which is driven by a servo motor system, is set to maintain a constant speed, $W_{0}$, until the trailing (upper) long edge of the plate passes the still water level (SWL) and then to decelerate to a stop. The impact Froude numbers $\mathit{Fr}$ ($=W_{0}/\sqrt{gB}$, where $g$ is the gravitational acceleration) range from 0.21 to 0.63. The evolution of the water surface underneath the plate and outboard of its trailing edge is measured with a cinematic laser induced fluorescence technique. As the plate’s leading (low) edge passes the SWL, the local water surface rises and develops into a thin spray sheet that travels along the plate’s lower surface toward the trailing edge. The horizontal speed of the under-plate spray tip is approximately $2.25W_{0}/\tan \unicode[STIX]{x1D6FD}$, as high as $15~\text{m}~\text{s}^{-1}$. In agreement with published similarity theory for the flow during the vertical water entry of a wedge, the under-plate surface profiles scaled by $W_{0}t$ nearly collapse on a single curve for each $\unicode[STIX]{x1D6FD}$. As the under-plate spray passes the plate’s trailing edge, it develops into the leading portion (called herein the Type I spray) of the outboard spray system. As the trailing edge of the plate passes through the local water surface, a crater develops and a large nearly vertical spray sheet (called the Type II spray) is generated from the outer edge (called the outboard spray root) of the crater. The characteristic horizontal length scale of the crater is found to expand in time following a power law with an exponent of approximately 0.77 for all conditions. A short time after its formation, the outboard spray root becomes the crest of a gravity wave whose propagation speed is of the order of $1~\text{m}~\text{s}^{-1}$ for all $\unicode[STIX]{x1D6FD}$ and $\mathit{Fr}$. The dimensionless envelope of the Type II spray profiles collapse to a single curve at high $\mathit{Fr}$ for each $\unicode[STIX]{x1D6FD}$. The connecting spray sheet between the Type I and Type II sprays tends to break up at small $\unicode[STIX]{x1D6FD}$ and large $\mathit{Fr}$.