Entire Cake Research Articles

Potential of Near-Infrared Chemical Imaging as Process Analytical Technology Tool for Continuous Freeze-Drying.

Near-infrared chemical imaging (NIR-CI) is an emerging tool for process monitoring because it combines the chemical selectivity of vibrational spectroscopy with spatial information. Whereas traditional near-infrared spectroscopy is an attractive technique for water content determination and solid-state investigation of lyophilized products, chemical imaging opens up possibilities for assessing the homogeneity of these critical quality attributes (CQAs) throughout the entire product. In this contribution, we aim to evaluate NIR-CI as a process analytical technology (PAT) tool for at-line inspection of continuously freeze-dried pharmaceutical unit doses based on spin freezing. The chemical images of freeze-dried mannitol samples were resolved via multivariate curve resolution, allowing us to visualize the distribution of mannitol solid forms throughout the entire cake. Second, a mannitol-sucrose formulation was lyophilized with variable drying times for inducing changes in water content. Analyzing the corresponding chemical images via principal component analysis, vial-to-vial variations as well as within-vial inhomogeneity in water content could be detected. Furthermore, a partial least-squares regression model was constructed for quantifying the water content in each pixel of the chemical images. It was hence concluded that NIR-CI is inherently a most promising PAT tool for continuously monitoring freeze-dried samples. Although some practicalities are still to be solved, this analytical technique could be applied in-line for CQA evaluation and for detecting the drying end point.

Counting Blanks in Polygonal Arrangements

Inside a two-dimensional region (``cake''), there are $m$ nonoverlapping tiles of a certain kind (``toppings''). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same “certain kind,” such that the entire cake is covered. How many blanks must we add? We study this question in several cases: (1) The cake and toppings are general polygons. (2) The cake and toppings are convex figures. (3) The cake and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear polygon and the toppings are axis-parallel rectangles. In all four cases, we provide tight bounds on the number of blanks.

Non‐ionic soft materials influence on filtration resistance and cake dry matter content

Filtration of organic slurries is important in many industries but challenging because the hydraulic resistance is high due to gel materials in the slurries. Particles with solid polystyrene (PS) core and varying amount of poly(N‐isopropylacrylamide) (PNIPAM) gel surface were synthesized. At low amount of gel, the gel deformed and partly filled the cake void increasing the resistance. This was successfully fitted using a semi‐theoretical model for deformable particles. At high amount of gel, the gel deformed filling the entire cake void and the resistance was dominated by the gel. During consolidation, the primary retardation time increased three orders of magnitude with gel thickness as expected as primary consolidation were dominated by the dissipation of pore water. The secondary retardation time also increased but not as pronounced as primary retardation time. Secondary consolidation was due to local compression of the gel and therefore less dependent on gel thickness. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2241–2247, 2017

Waste Makes Haste

We consider the classic problem of envy-free division of a heterogeneous good (“cake”) among several agents. It is known that, when the allotted pieces must be connected, the problem cannot be solved by a finite algorithm for three or more agents. The impossibility result, however, assumes that the entire cake must be allocated. In this article, we replace the entire-allocation requirement with a weaker partial-proportionality requirement: the piece given to each agent must be worth for it at least a certain positive fraction of the entire cake value. We prove that this version of the problem is solvable in bounded time even when the pieces must be connected. We present simple, bounded-time envy-free cake-cutting algorithms for (1) giving each of n agents a connected piece with a positive value; (2) giving each of three agents a connected piece worth at least 1/3; (3) giving each of four agents a connected piece worth at least 1/7; (4) giving each of four agents a disconnected piece worth at least 1/4; and (5) giving each of n agents a disconnected piece worth at least (1 − ϵ)/ n for any positive ϵ.

Toss one’s cake, and eat it too: partial divisions can improve social welfare in cake cutting

We consider the problem of fairly dividing a heterogeneous good (a.k.a. “cake”) between a number of players with different tastes. In this setting, it is known that fairness requirements may result in a suboptimal division from the social welfare standpoint. Here we show that, in some cases, leaving some of the cake unallocated, and fairly dividing only the remainder of the cake may be socially preferable to any fair division of the entire cake. We study this phenomenon, providing asymptotically-tight bounds on the social improvement achievable by such partial divisions.

Degrees of Freedom of Two-Hop Wireless Networks: Everyone Gets the Entire Cake

We show that fully connected two-hop wireless networks with K sources, K relays, and K destinations have K degrees of freedom both in the case of time-varying channel coefficients and constant channel coefficients (in which case the result holds for almost all values of constant channel coefficients). Our main contribution is a new achievability scheme which we call Aligned Network Diagonalization. This scheme allows the data streams transmitted by the sources to undergo a diagonal linear transformation from the sources to the destinations, thus being received free of interference by their intended destination. In addition, we extend our scheme to multihop networks with fully connected hops, and multihop networks with MIMO nodes, for which the degrees of freedom are also fully characterized.

Cake Fouling Mechanism and Analysis of Synthetic Coke Wastewater Treatment by Membrane Bioreactor

Cake fouling mechanism was studied for membrane bioreactor (MBR) treatment of synthetic coke wastewater. Cake fouling characteristics of the aerobic activated sludge from MBR was investigated. The experimental results demonstrated that the cake governing equation fit the entire cake microfiltration (MF) process while cake fouling model was applicable to simulate the decrease in permeability and was used to predict the cake fouling development for both PVDF and PP MF membranes. Based on four-step development progresses, cake formation mechanism had been depicted with the increasing of TMP and the reduction of the cake porosity ratio. In addition, the comparison experiments under different operation modes were performed to further analyze the cake governing mechanism for MBR filtration.

Majority rip-off in referendum voting

Many democracies complement a parliamentarian system with elements of direct democracy, where the electorate decides on single issues by majority voting. A well-known paradox states that in a sequence of referenda one can get from an arbitrary original income distribution to one in which one player gets almost all the cake. In this paper we design a three-player game modelling the sequential modification mechanism. The strategic analysis reveals that the paradox survives even with rational strategic voters and though the right to propose is allocated to each player once: the last player receives almost the entire cake. The result can be extended to the three-party n-voter case and is for some cases similar when we consider a random rather than fixed sequence of proposers.

Dynamic analysis of cake properties in microfiltration of soft colloids

The properties of cakes formed using soft colloids in “dead-end” microfiltration were studied. The empirical power functions were used to relate the local cake properties. However, the cake compressibility factors are functions of time due to the retardation effect of cake compression. A dynamic analysis method is proposed to estimate the cake properties during soft colloid microfiltration. The results show that the entire filtration course can be divided into three stages. At the beginning of filtration, the deposition and rearrangement of the colloidal particles on the membrane surface cause the overall filtration resistance to increase. The average porosity and average specific filtration resistance of the cake vary slightly during this period of filtration. In the second stage, a rapid increase in filtration resistance and a decrease in cake porosity due to cake compression and colloid deformation can be found. A compact skin layer begins to be formed next to the filter membrane in this stage. The skin thickness is about 10–20% of the entire cake but this layer exhibits about 90% of the overall filtration resistance. The average cake porosity increases gradually in the third stage due to the loose packing in the newly formed cake. This trend can be reflected in the d t/d v versus v filtration curves and is demonstrated by the experimental data. The structure of the cake formed in each stage was observed using scanning electronic microscopy (SEM).

Yeast cake layers as secondary membranes in dead-end microfiltration of bovine serum albumin

Dead-end filtration of bovine serum albumin was performed in a phosphate buffer through a yeast cake layer deposited on an asymmetric, polysulfone microfiltration membrane having a nominal pore size of 0.2 μm. Yeast cake layers of varying thicknesses were preformed in two ways - by gravity settling prior to the onset of filtration and by vacuum filtration. The role of the cake layer of rejected cells as a secondary membrane for reducing protein transmission and affecting permeate flux was studied. The steady-state flux was found to be higher in the presence of a thin cake layer than in the absence of a cake layer. This is thought to result from the yeast cake serving as a filter-aid to remove membrane foulants from the protein solution. Due to the micro-channeling effects, higher fluxes were observed for filtration through a cake layer preformed by vacuum filtration, as compared to the corresponding values for a cake layer of equal dry mass preformed by gravity settling. The protein transmission studies revealed three types of fouling - membrane fouling due to the internal pore deposition of protein, protein adsorption through the entire cake depth, and surface filtration leading to protein rejection at the cake surface.

Effect of mud penetration on borehole skin properties

Clay particles in drilling muds can form a filter cake (skin) on the walls of the well and migrate into the adjacent formation. In general, filter cakes are formed when a liquid phase containing solid particles is forced through a pervious surface which allows liquid transport, while retaining solid particles. Following a literature survey, the governing equations for the concentration of suspended solid particles in the pore fluid, cake permeability, and solid velocity are obtained by considering the mass balance equations for the fluid phase and suspended and captured solid particles. The capture mechanism is represented by a kinetic equation with rate constants for particle trapping and cake erosion. Numerical solutions for the cake permeability, cake resistance, solid particle velocity (cake compression rate), and concentration of suspended particles are obtained by utilizing experimentally available porosity and pressure variations along the dimensionless cake thickness. The results compared for a simplified experimental case, show excellent match. A sensitivity analysis shows that cake permeability and cake resistance are more sensitive to the rate constant of cake erosion than they are to the rate constant of particle capture. It was also determined that the permeability has larger values along the entire cake thickness when the rate constant of particle capture is zero in comparison to values obtained with a nonzero rate constant. Cake permeability is small when the rate constant of cake erosion is large.

Experimental and Theoretical Studies of Constant Pressure Filtration of Dense Slurries

For studying the correlation between filtration and permeation, the newly derived rigorous analytical method which i ncludes the expressions for the flow rate distribution qz/q1, through the entire cake and for the true average specific resistance ar was used. The predicted filtration characteristics are compared favorably with actual constant pressure filtration results of dense slurries of various clays.i) The value of correction factor J, defined by Eq. 13 depends mainly on slurry concentration s but slightly on filtration pressure p. The numerical values of J drop into the neighborhood of 0.9 for dense slurries as shown in Fig. 4. As far as compressible thick slurries are concerned, it has become clear that the conventional theory should be modified.ii) On both sides of theoretical analysis and experimental studies, it is clear that the average specific resistance of filter-cake should be a function of both p and s. The maximum specific resistance of a cake is supposed to be encountered at the washing stage of the cake.iii) The ratio of wet cake mass to dry cake mass is also a function of both p and s. The ratio depends mainly on p and slightly on S.iv) The modern filtration theory is expected to be able to cover various practical aspects of filtration behaviors.