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In previous papers it was shown that in a quasi-spherical Szekeres (QSS) metric, impulses of gamma radiation can arise that have several properties in common with the observed gamma-ray bursts. This happens when the bang-time function $t_B(r)$ has a gate-shaped hump around the origin of the QSS region. The gamma rays arise along two preferred directions of the QSS geometry (coincident with dipole extrema when axially symmetric, otherwise unrelated). In these directions, the rays of the relic radiation are blueshifted rather than redshifted. The blueshift is generated in a thin region between the Big Bang (BB) and the extremum-redshift hypersurface (ERH). But the Szekeres models can describe the real Universe only forward in time from the last-scattering hypersurface (LSH) because the matter in them has zero pressure. The ERH is tangent to the BB at the origin, so in a neighbourhood thereof the ERH lies earlier than the LSH and no blueshift is generated in the physical region. The question thus arose whether the BB and ERH can be ``unglued'' if the QSS region has no origin, but the areal radius function $\Phi$ has a local maximum or minimum somewhere. In the present paper it is demonstrated that this is indeed the case. If the hump in $t_B(r)$ is centered around the minimum of $\Phi$, then the BB and ERH in general do not coincide there and a stronger blueshift is generated on rays passing nearby. It follows that a lower and narrower hump on the BB set can generate sufficient blueshift to move the initial frequencies of the relic radiation to the gamma range. These facts are demonstrated by numerical calculations in an explicit example of a QSS region., Comment: 35 pages, 9 figures. Literature on GRBs updated, conclusions section extended, small editorial corrections. This text matches the published one. Length spuriously increased because of APPB page display

In this work the esterification of diethyl tartrate was studied. The research was focused on the enhancement of reversible reaction yield, which is accomplished by dewatering of the reaction mixture. The removal of water shifts the equilibrium towards the main product. Pervaporation was applied for this purpose, and results were compared to distillation. The advantages and limitations of both processes are discussed. The experimental part consists of dewatering of mixture after the reaction had reached the equilibrium, and was subsequently fed to the test rig equipped with a single zeolite membrane purchased from Pervatech B.V. Results show a significant conversion increase as a result of water removal by pervaporation. Compared to distillation no addition of organics is necessary to efficiently remove water above the azeotrope. Nevertheless, some limitations and issues which call for optimisation are pointed out. A simple numerical model is proposed to support design and sizing of the pervaporation system. Various modes of integrated system operation are also briefly discussed.

The removal of emulsified water from diesel fuels often encounters serious problems, which lead to operation failure and breakthrough of water into the fuel injection equipment. This can cause a severe damage of common rail systems. Here, a novel design of diesel filter shows significant improvements in terms of dirt holding capacity, water separation and thus the life-time of the engine.

In this work the coalescence performance of the melt-blown structures applied for removal of emulsified water from the diesel fuel is studied. Fibrous polyester media (polybutylene terephthalate, PBT) were fabricated in-house using the melt-blow technique. Postproduction treatment towards the fiber modification involving hydrolysis of the surface with sodium hydroxide or exposure to a low temperature plasma was applied. Different properties of polymer surface were obtained for each modification method, which was verified by the capillary rise test with oil and water. The applied treatment had a significant impact on the coalescence performance comparing to the unmodified PBT structure. In contrary to numerous experimental studies the hydrophilic polyester media obtained by hydrolysis performed much worse than plasma treated filters. It was also shown that the combination of water wettable and non-wettable fibers respectively on the inlet and outlet can significantly improve the separation efficiency. However, in such case the pressure drop is significantly increased as the water captured and collected within the inlet layer is not effectively transported to the outlet. This confirmed that the wettability of fiber surface is not an independent parameter which affects the process. The filter material should be carefully selected with regards to both structural and surface properties of adjacent layers to form a reasonable saturation of the coalescence layer for the high efficiency and also enable the transport of collected liquid to the outlet. Both the structural and surface properties have a pronounced impact on the coalescence efficiency and detachment of droplets from the porous structure on the outlet.

Separation of emulsified water from a low sulfur diesel fuel using coalescence filtration was studied in this work. Multilayer coalescence elements were manufactured in-house using the meltblow technique with or without an electric field applied directly to jets of molten polypropylene. The results were compared with coalescence elements made of fiberglass. Hydrophobic media are usually not recommended for coalescence filters applied in dewatering applications. However, experimental results presented in this work show that a properly designed and prepared nanofibrous structure performs with good separation efficiency, while maintaining the pressure drop on a relatively low level.

Oil droplet coalescence and the separation of emulsions are industrially relevant processes. In this article, Dr Andrzej Krasinski of Warsaw University of Technology discusses his studies into the separation of oil-in-water emulsions by forced flow through meltblown polypropylene (PP) fibrous media. The research focuses on the structural design of the inlet layer and examines the effects of the fibre size, bed depth and flowrate.

This paper is a follow-up on two previous ones, in which properties of blueshifted rays were investigated in Lema\^{\i}tre - Tolman (L-T) and quasispherical Szekeres (QSS) spacetimes. In the present paper, an axially symmetric QSS deformation is superposed on such an L-T background that was proved, in the first paper, to mimic several properties of gamma-ray bursts. The present model makes $z$ closer to $-1$ than in the background L-T spacetime, and, as implied by the second paper, strong blueshifts exist in it only along two opposite directions. The QSS region is matched into a Friedmann background. The Big Bang (BB) function $t_B(r)$, which is constant in the Friedmann region, has a gate-shaped hump in the QSS region. Since a QSS island generates stronger blueshifts than an L-T island, the BB hump can be made lower - then it is further removed from the observer and implies a smaller observed angular radius of the source. Consequently, more sources can be fitted into the sky - all these facts are confirmed by numerical computations. Null geodesics reaching present observers from different directions relative to the BB hump are numerically calculated. Patterns of redshift across the image of the source and along the rays are displayed., Comment: 17 pages, 12 figures. Most references to gamma-ray bursts removed at the insistence of the referee, with the implications unchanged. Title changed. Old Fig. 2 removed. Tables I, III and IV recalculated, and Figs. 4, 5, and 7 - 10 redrawn to correct a numerical error; this did not influence any conclusions. The current text matches the published version

In this study, the process of membrane cleaning by supercritical fluid extraction was investigated. Polypropylene microfiltration membranes, contaminated with oils, were treated in a batch process with a supercritical fluid (SCF). As extractant, pure supercritical carbon dioxide or supercritical carbon dioxide with admixtures of methanol, ethanol and isopropanol were used. Single-stage and multi-stage extraction was carried out and process efficiency was determined. The obtained results showed that addition of organic solvents significantly enhances the cleaning performance, which increases with increase of organic solvent concentration and decreases with increasing temperature. All three solvents showed a comparable effect of efficiency enhancement. The results confirmed that supercritical fluid extraction can be applied for polypropylene membrane cleaning.

In Lema\^��tre -- Tolman (L--T) models, light rays emitted \textit{radially} at the Big Bang (BB) at such radial coordinates $r$ where the bang-time function $t_B(r)$ has $\dril {t_B} r \neq 0$ reach every observer with \textit{infinite blueshift}, $z = -1$. Consequently, there exist rays, emitted soon after the BB, that will reach later observers with finite blueshift ($-1 < z < 0$). But in spacetimes without symmetry there are no radial directions. The question thus arises whether blueshifts can exist at all in the Szekeres models that contain L--T as a limit, but in general have no symmetry. The aim of the present paper is to show that strong blueshifts can be generated in quasi-spherical Szekeres (QSS) models. It is shown that in an axially symmetric QSS model, infinite blueshift can appear only on axial rays, which intersect every space orthogonal to the dust flow on the symmetry axis. In an exemplary QSS model it is numerically shown that if such a ray is emitted from the Big Bang where $\dril {t_B} r \neq 0$, then indeed observers see it with $z \approx -1$. Rays emitted shortly after the BB and running close to the symmetry axis will reach the observers with a strong blueshift, too. Then, in a toy QSS model that has no symmetry, it was shown by numerical calculations that two null lines exist such that rays in their vicinity have redshift profiles similar to those in a vicinity of the axial rays in the axially symmetric case. This indicates that rays generating infinite blueshifts exist in general QSS spacetimes and are concentrated around two directions., 20 pages, 19 figures. All references to gamma-ray bursts removed at the insistence of the referees; otherwise this version is the same as version 1. The text matches the one published in Phys. Rev. D

It is shown that the basic observed properties of the gamma-ray bursts (GRBs) are accounted for if one assumes that the GRBs arise by blueshifting the emission radiation of hydrogen and helium generated during the last scattering epoch. The blueshift generator for a single GRB is a region with a nonconstant bang-time function $t_B(r)$ (described by a Lema\^{\i}tre -- Tolman (L--T) exact solution of Einstein's equations) matched into a homogeneous and isotropic (Friedmann) background. Blueshift visible to the present observer arises \textit{only on those rays that are emitted radially in an L--T region}. The paper presents three L--T models with different Big Bang profiles, adapted for the highest and the lowest end of the GRB frequency range. The models account for: (1) The observed frequency range of the GRBs; (2) Their limited duration; (3) The afterglows; (4) Their hypothetical collimation into narrow jets; (5) The large distances to their sources; (6) The multitude of the observed GRBs. Properties (2), (3) and (6) are accounted for only qualitatively. With a small correction of the parameters of the model, the implied perturbations of the CMB radiation will be consistent with those actually caused by the GRBs. A complete model of the Universe would consist of many L--T regions with different $t_B(r)$ profiles, matched into the same Friedmann background. This paper is meant to be an initial exploration of the possibilities offered by models of this kind; the actual fitting of all parameters to observational results requires fine-tuning of several interconnected variables and is left for a separate study., Comment: 23 pages, 18 figures. Typos corrected, title and two sentences in the abstract modified, bibliography updated. The present text matches the published version

The maximally extended Reissner--Nordstr\"om (RN) manifold with $e^2 < m^2$ begs for attaching a material source to it that would preserve the infinite chain of asymptotically flat regions and evolve through the wormhole between the RN singularities. So far, the attempts were discouraging. Here we try one more possible source -- a solution found by Ruban in 1972 that is a charged generalisation of an inhomogeneous Kantowski--Sachs-type dust solution. It can be matched to the RN solution, and the matching surface must stay all the time between the two RN event horizons. However, shell crossings do not allow even half a cycle of oscillation between the maximal and the minimal size., Comment: journal reference added

In this article we present a model of formation of a galaxy with a black hole in the center. It is based on the Lema\^{\i}tre--Tolman solution and is a refinement of an earlier model. The most important improvement is the choice of the interior geometry of the black hole allowing for the formation of Gyrs old black holes. Other refinements are the use of an arbitrary Friedmann model as the background (unperturbed) initial state and the adaptation of the model to an arbitrary density profile of the galaxy. Our main interest was the M87 galaxy (NGC 4486), which hosts a supermassive black hole of mass $3.2\cdot 10^{9}M_{\odot}$. It is shown that for this particular galaxy, within the framework of our model and for the initial state being a perturbation of the $\Lambda$CDM model, the age of the black hole can be up to 12.7 Gyrs. The dependence of the model on the chosen parameters at the time of last scattering was also studied. The maximal age of the black hole as a function of the $\Omega_m$ and $\Omega_\Lambda$ parameters for the M87 galaxy can be 3.717 or 12.708 Gyr., Comment: 24 pages, 10 figures, 3 tables

By Niky KamranPart1ofCarter’s“Blackholeequilibriumstates”givesamasterlyaccountbyoneoftheleading researchers in classical general relativity of the analytic and geometric prop-ertiesoftheKerrsolutions.Thesesolutionsincludenotonlythetwoparameterfamilyof Kerr solutions of the Einstein vacuum equations, but also the Kerr–Newman andKerr–de Sitter solutions, which are the generalizations of the vacuum Kerr solutionsto the cases in which either a non-singular electromagnetic field or a cosmologicalconstant is present. The derivation of the Kerr solution and its generalizations givenbyCarter inSection 5ofthepaper isanchored around therequirement that themetricshouldbestationaryandaxisymmetric,andthatboththeHamilton–Jacobiequationfor

Theoretical aspects of shear flows of aggregated nanosuspensions are presented and applied to formulate appropriate models. Technological context of this work is related to formulation of stable suspensions of nanoparticles of specific rheological properties by breaking‐up nanoparticle clusters in high shear devices. Accordingly the population balance modeling is applied with kinetics including effects of aggregation, breakage and restructuring of aggregates; effects of suspension rheology on the flow are included as well. Rheological model includes the effect of clustering of primary nanoparticles. Population balances are solved using QMOM that is linked to the CFD code. Results of numerical simulations are presented for laminar and turbulent flows. Part of the 1st International Conference on Industrial Processes for Nano and Micro Products, London, 2007.

The seminal paper by Kasner (Am. J. Math. 43, 217–221, 1921) is reprinted here, together with an editorial comment on its lasting scientific relevance, and a biography of the author.

After introducing the Szekeres and Lema\^{\i}tre--Tolman cosmological models, the real-time cosmology program is briefly mentioned. Then, a few widespread misconceptions about the cosmological models are pointed out and corrected. Investigation of null geodesic equations in the Szekeres models shows that observers in favourable positions would see galaxies drift across the sky at a rate of up to $10^{-6}$ arc seconds per year. Such a drift would be possible to measure using devices that are under construction; the required time of monitoring would be $\approx10$ years. This effect is zero in the FLRW models, so it provides a measure of inhomogeneity of the Universe. In the Szekeres models, the condition for zero drift is zero shear. But in the shearfree normal models, the condition for zero drift is that, in the comoving coordinates, the time dependence of the metric completely factors out., Comment: 8 pages, 5 figures, based on the talk delivered at the Marcel Grossman Meeting 13 in Stockholm, 2012. Sections and references permuted, one figure added, title changed, style corrections in text; actual content not changed. Changes done in response to referee's opinion

In the Lema\^{\i}tre -- Tolman (L--T) models that have nonconstant bang-time function $t_B(r)$, light emitted close to those points of the Big Bang where $\dril {t_B} r \neq 0$ is blueshifted at the receiver position. The blueshifted rays are expected to perturb the temperature of the cosmic microwave background (CMB) radiation along the lines of sight of the present central observer. It is shown here that, in a general L--T model, the $t_B(r)$ can be chosen so that the blueshift-generating region is hidden before the recombination time, where the L--T model does not apply. The rest of the paper is devoted to investigating blueshifts in one specific L--T model, called L--T$(t_B)$ -- the one that duplicates the luminosity distance vs. redshift relation of the $\Lambda$CDM model using nonconstant $t_B(r)$ alone. The location of the blueshift-generating region in the L--T$(t_B)$ spacetime is determined. Profiles of redshift/blueshift along several rays intersecting the past light cone of the present central observer are calculated. The L--T$(t_B)$ model matched to Friedmann is considered, and profiles of redshift/blueshift in such a composite model are calculated. The requirement of invisibility of blueshifts makes the L--T$(t_B)$ model astrophysically unacceptable if it should apply back to the recombination time, but does not "rule out" a general L--T model -- it only puts limits on $\dril {t_B} r$., Comment: 13 pages, 12 figures; axis labels added in all figures, new paragraph added after (2.16), Ref. 22 updated; no substantial changes

Precipitation of a solid product from aqueous ionic solutions, including mixing, fast chemical reaction, nucleation, growth and agglomeration of crystals is considered. This work concentrates on the phenomenon of particle agglomeration which dominates the precipitation process at high supersaturation. Modeling of particle collision includes effects of bulk fluid motion, Brownian diffusion and colloidal forces for particles of equal and unequal size. The concept of probability of agglomeration based on multifractal formalism is introduced and applied. A simplified version of the model is linked to CFD and results of computations are compared with experimental data for barium sulfate precipitation.

The historical development of the Bianchi classification of homogeneous cosmological models is described with special emphasis on the contributions by Schucking and Behr.

This is a continuation of the paper published in {\it Phys. Rev.} {\bf D89}, 023520 (2014). It is investigated here how the luminosity distance -- redshift relation $D_L(z)$ of the $\Lambda$CDM model is duplicated in the Lema\^itre -- Tolman (L--T) model with $\Lambda = 0$, constant bang-time function $t_B$ and the energy function $E(r)$ mimicking accelerated expansion on the observer's past light cone ($r$ is a uniquely defined comoving radial coordinate). Numerical experiments show that $E > 0$ necessarily. The functions $z(r)$ and $E(r)$ are numerically calculated from the initial point at the observer's position; then backward from the initial point at the apparent horizon (AH). Reconciling the results of the two calculations allows one to determine the values of $E/r^2$ at $r = 0$ and at the AH. The problems connected with continuing the calculation through the AH are discussed in detail and solved. Then $z(r)$ and $E(r)$ are continued beyond the AH, up to the numerical crash that signals the contact of the light cone with the Big Bang. Similarly, the light cone of the L--T model is calculated by proceeding from the two initial points, and compared with the $\Lambda$CDM light cone. The model constructed here contains shell crossings, but they can be removed by matching the L--T region to a Friedmann background, without causing any conflict with the type Ia supernovae observations. The mechanism of imitating the accelerated expansion by the $E(r)$ function is explained in a descriptive way.

The Lema\^{\i}tre -- Tolman model with $\Lambda = 0$ and constant bang time that imitates the luminosity distance -- redshift relation of the $\Lambda$CDM model using the energy function $E$ alone contains shell crossings. In this paper, the location in spacetime and the consequences of existence of the shell-crossing set (SCS) are investigated. The SCS would come into view of the central observer only at $t \approx 1064 T$ to the future from now, where $T$ is the present age of the Universe, but would not leave any recognizable trace in her observations. Light rays emitted near to the SCS are blueshifted at the initial points, but the blueshift is finite, and is overcompensated by later-induced redshifts if the observer is sufficiently far. The local blueshifts cause that $z$ along a light ray is not a monotonic function of the comoving radial coordinate $r$. As a consequence, the angular diameter distance $D_A$ and the luminosity distance $D_L$ from the central observer fail to be functions of $z$; the relations $D_A(z)$ and $D_L(z)$ are multiple-valued in a vicinity of the SCS. The following quantities are calculated and displayed: (1) The distribution of mass density on a few characteristic hypersurfaces of constant time; some of them intersect the SCS. (2) The distribution of density along the past light cone of the present central observer. (3) A few light cones intersecting the SCS at characteristic instants. (4) The redshift profiles along several light cones. (5) The extremum-redshift hypersurface. (6) The $D_A(z)$ and $D_L(z)$ relations. (7) The last scattering time and its comparison with the $\Lambda$CDM last scattering epoch., Comment: 13 pages, 13 figures. New secs. X and XI added, secs. I, II, V, IX and the old XI(now XIII) re-edited to accommodate the new material, Figs. 3, 8 and old 11 (now 10) redrawn, old Fig. 10 removed. The extensions were inspired by the referee. New text matches that accepted for Phys. Rev. D

It is shown how certain observations interpreted in the background of the Friedmann model with $\mathrm{\ensuremath{\Lambda}}l0=k$ (the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model) can be reinterpreted using the $\mathrm{\ensuremath{\Lambda}}=0$ Lema\^{\i}tre-Tolman (L-T) model so as to do away with the ``dark energy.'' The purpose of this paper is to clarify the underlying geometrical relations by doing the calculations as much as possible analytically or by very simple numerical programs. In the first part of the paper (fictitious) observations of the distribution of expansion velocity along the past light cone of the observer are considered. It is shown that the whole past light cone of the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ observer can be reproduced in the L-T model with $\mathrm{\ensuremath{\Lambda}}=0=E$. This is a geometric exercise that has the advantage of being free of numerical complications. In the second part, the luminosity distance-redshift relation of the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model is duplicated using the L-T model with $\ensuremath{-}k=2E/{r}^{2}=\text{constant}\text{ }g0$. The value of $k$ and the function ${t}_{B}(r)$ are determined by the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ parameters. General properties of this L-T model are described. Difficulties of carrying the numerical calculations through the apparent horizon are presented in detail and mostly solved. The second model is a counterexample to the general belief that an L-T model mimicking $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ must contain a void around the center---it has a peak of density at $R=0$.

For a rotating dust with a 3-dimensional symmetry group all possible metric forms can be classified and, within each class, explicitly written out. This is made possible by the formalism of Plebanski based on the Darboux theorem. In the resulting coordinates, the Killing vector fields (if any exist) assume a special form. Each Killing vector field may be either spanned on the fields of velocity and rotation or linearly independent of them. By considering all such cases one arrives at the classification. With respect to the structures of the groups, this is just the Bianchi classification, but with all possible orientations of the orbits taken into account. In this paper, which is part 1 of a 3-part series, all solutions are considered for which two Killing fields are spanned on velocity and rotation. The solutions of Lanczos and Godel are identified as special cases, and their new invariant definitions are provided. In addition, a new invariant definition is given of the Ozsvath class III solution.

The flow of the Golden Oldies through the pages of the GRG Journal has slowed down in recent years, but the series is still alive and the new Editorial Board is going to continue running it. We decided to formalise the rules by which the Oldies are managed. The Editor of the series will now be assisted by the Advisory Board whose decisions will be binding for him/her and for the Editor in chief. Currently, the Editor of the series is the undersigned, and the Advisory Board consists of

The Gibbs–Duhem equation dU+pdV=TdS imposes restrictions on the perfect fluid solutions of Einstein equations that have a one-dimensional symmetry group or no symmetry at all. In this paper, we investigate the restrictions imposed on the Stephani Universe and on the two classes of models found by Szafron. Upon the Stephani Universe and the β≠0 class of Szafron symmetries are forced. We find the most general subcases of the β=0 model of Szafron that are consistent with the Gibbs–Duhem equation and have no symmetry.