Reverse Partition Research Articles

Light-induced targeting enables proteomics on endogenous condensates.

Endogenous condensates with transient constituents are notoriously difficult to study with common biological assays like mass spectrometry and other proteomics profiling. Here, we report a method for light-induced targeting of endogenous condensates (LiTEC) in living cells. LiTEC combines the identification of molecular zip codes that target the endogenous condensates with optogenetics to enable controlled and reversible partitioning of an arbitrary cargo, such as enzymes commonly used in proteomics, into the condensate in a blue light-dependent manner. We demonstrate a proof of concept by combining LiTEC with proximity-based biotinylation (BioID) and uncover putative components of transcriptional condensates in mouse embryonic stem cells. Our approach opens the road to genome-wide functional studies of endogenous condensates.

Modeling Novel Aqueous Particle and Cloud Chemistry Processes of Biomass Burning Phenols and Their Potential to Form Secondary Organic Aerosols.

Phenols emitted from biomass burning contribute significantly to secondary organic aerosol (SOA) formation through the partitioning of semivolatile products formed from gas-phase chemistry and multiphase chemistry in aerosol liquid water and clouds. The aqueous-phase SOA (aqSOA) formed via hydroxyl radical (•OH), singlet molecular oxygen (1O2*), and triplet excited states of organic compounds (3C*), which oxidize dissolved phenols in the aqueous phase, might play a significant role in the evolution of organic aerosol (OA). However, a quantitative and predictive understanding of aqSOA has been challenging. Here, we develop a stand-alone box model to investigate the formation of SOA from gas-phase •OH chemistry and aqSOA formed by the dissolution of phenols followed by their aqueous-phase reactions with •OH, 1O2*, and 3C* in cloud droplets and aerosol liquid water. We investigate four phenolic compounds, i.e., phenol, guaiacol, syringol, and guaiacyl acetone (GA), which represent some of the key potential sources of aqSOA from biomass burning in clouds. For the same initial precursor organic gas that dissolves in aerosol/cloud liquid water and subsequently reacts with aqueous phase oxidants, we predict that the aqSOA formation potential (defined as aqSOA formed per unit dissolved organic gas concentration) of these phenols is higher than that of isoprene-epoxydiol (IEPOX), a well-known aqSOA precursor. Cloud droplets can dissolve a broader range of soluble phenols compared to aqueous aerosols, since the liquid water contents of aerosols are orders of magnitude smaller than cloud droplets. Our simulations suggest that highly soluble and reactive multifunctional phenols like GA would predominantly undergo cloud chemistry within cloud layers, while gas-phase chemistry is likely to be more important for less soluble phenols. But in the absence of clouds, the condensation of low-volatility products from gas-phase oxidation followed by their reversible partitioning to organic aerosols dominates SOA formation, while the SOA formed through aqueous aerosol chemistry increases with relative humidity (RH), approaching 40% of the sum of gas and aqueous aerosol chemistry at 95% RH for GA. Our model developments of biomass-burning phenols and their aqueous chemistry can be readily implemented in regional and global atmospheric chemistry models to investigate the aqueous aerosol and cloud chemistry of biomass-burning organic gases in the atmosphere.

Minuscule reverse plane partitions via quiver representations

Minuscule reverse plane partitions via quiver representations

Effect of Ru on Deformation Mechanism and Microstructure Evolution of Single-Crystal Superalloys under Medium-Temperature and High-Stress Creep.

In this work, the effect of the Ru element on the γ'-phase evolution and deformation mechanism in the fourth-generation Ni-based single-crystal superalloy was investigated. Results show that the Ru element alters the distribution coefficient of other elements in the alloy to produce reverse partitioning behavior, which leads to a difference in microstructure between 0Ru and 3Ru. The addition of Ru triggered the incubation period before the beginning of the primary creep stage, which depends on the creep temperature and stress during creep deformation. TEM results revealed that Ru addition inhibits the slip system {111}<112> at medium-temperature (760-1050 °C) and high-stress (270-810 MPa) creep, which brings a considerably low creep rate and high creep life to the Ru-containing alloy.

New insights into the microstructural stability based on the element segregation behavior at γ/γ′ interface in Ni-based single crystal superalloys with Ru addition

A new insight into the microstructural stability was proposed in Ni-based single crystal superalloys with Ru addition, and the element segregation behavior at γ/γ′ interface was investigated by three-dimensional atom probe technology (3D-APT). After standard heat treatment, it was found that Ru addition barely altered the element partitioning coefficient between γ matrix and γ′ phase, and no element-segregation layer was observed at γ/γ′ interface. During the heat exposure at 1100 °C, Ru addition obviously promoted the rafting of the γ′ precipitates and inhibited the precipitation of topological close-packed (TCP) phases. It was more important that an element-segregation layer containing Re, Co, and Cr was formed in the γ matrix close to the γ/γ′ interface due to an “uphill diffusion” effect, and its concentration was obviously reduced after Ru addition. Finally, the microstructural stability based on the element segregation behavior at γ/γ′ interface was discussed. This element-segregation layer increased the γ/γ′ interfacial energy by increasing the absolute value of the lattice misfit of γ/γ′ interface to promote the rafting of the γ′ precipitates after Ru addition. On the other hand, the decrease of the segregation concentration of Re, Co, and Cr elements as TCP phase-forming elements near the γ/γ′ interface due to a “reverse partitioning” effect inhibits the precipitation of TCP phases in Ni-based single crystal superalloys after Ru addition.

Quantitative characterization of membrane-protein reversible association using FCS

Functionally meaningful reversible protein-membrane interactions mediate many biological events. Fluorescence correlation spectroscopy (FCS) is increasingly used to quantitatively study the non-reversible binding of proteins to membranes using lipid vesicles in solution. However, the lack of a complete description of the phase and statistical equilibria in the case of reversible protein-membrane partitioning has hampered the application of FCS to quantify the partition coefficient (Kx). In this work, we further extend the theory that describes membrane-protein partitioning to account for spontaneous protein-membrane dissociation and reassociation to the same or a different lipid vesicle. We derive the probability distribution of proteins on lipid vesicles for reversible binding and demonstrate that FCS is a suitable technique for accurate Kx quantification of membrane-protein reversible association. We also establish the limits to Kx determination by FCS studying the Cramer-Rao bound on the variance of the retrieved parameters. We validate the mathematical formulation against reaction-diffusion simulations to study phase and statistical equilibria and compare the Kx obtained from a computational FCS titration experiment with the experimental ground truth. Finally, we demonstrate the application of our methodology studying the association of anti-HIV broadly neutralizing antibody (10E8-3R) to the membrane.

Hematocrit skewness along sequential bifurcations within a microfluidic network induces significant changes in downstream red blood cell partitioning.

There has been a wealth of research conducted regarding the partitioning of red blood cells (RBCs) at bifurcations within the microvasculature. In previous studies, partitioning has been characterized as either regular partitioning, in which the higher flow rate daughter channel receives a proportionally larger percentage of RBCs, or reverse partitioning, in which the opposite occurs. While there are many examples of network studies in silico, most in vitro work has been conducted using single bifurcation. When microfluidic networks have been used, the channel dimensions are typically greater than 20 μm, ignoring conditions where RBCs are highly confined. This paper presents a study of RBC partitioning in a network of sequential bifurcations with channel dimensions less than 8 μm in hydraulic diameter. The study investigated the effect of the volumetric flow rate ratio (Q*) at each bifurcation, solution hematocrit, and channel length on the erythrocyte flux ratio (N*), a measure of RBC partitioning. We report significant differences in partitioning between upstream and downstream bifurcations even when the flow rate ratio remains the same. Skewness analysis, a measure of cell distribution across the width of a vessel, strongly suggests that immediately following the first bifurcation most RBCs are skewed toward the inner channel wall, leading to preferential RBC perfusion into one daughter channel at the subsequent bifurcation even at higher downstream flow rate ratios. The skewness of RBC distribution following the first bifurcation can either manifest as enhanced regular partitioning or reverse partitioning at the succeeding branch.

Effect of repeated sorption–desorption on irreversible and reversible absorption of hydrophobic perfluoroalkyl acids to freshwater sediment

Understanding the factors governing irreversible and reversible sorption is essential to predict the influence of sediment on contaminant fate and transport in surface waters. This study used sediment of an urban water body to demonstrate irreversible accumulation and reversible absorption of perfluoroalkyl acids (perfluorooctane sulfonate (PFOS), perfluorononanoic (PFNA) and perfluorodecanoic acid (PFDA)) during two sorption–desorption (S–D) cycles. Absorption and desorption isotherms were consistent with sorption to irreversibly absorbing glassy sediment organic carbon (SOC) and liquid–liquid like partitioning to rubbery SOC. The observed absorption isotherms and the desorption isotherms were adequately fitted linear models. Irreversible absorption showed signs of saturation and the reversible partitioning diminished during the 2nd S–D cycle causing the composite sorption capacity to decrease. Results suggest that under the conditions tested, surface water sediment can act as sink for the studied PFAAs. Rubbery SOC can potentially release or absorb contaminants, thus acting as a concentration buffer. S–D cycling can cause irreversible absorption concentration to increase even when exposure occurs at lower concentrations (i.e. 5 μ g / L ). log K O C values of sediment that underwent S–D cycling overlaps with the range of field date, suggesting that the sediment of surface water may have experienced some degree of S–D cycling. • History of absorption–desorption affect the fate of PFAAs in aquatic environment. • Sorption of PFAAs is consistent with two-domain absorption assumption. • Surface water sediment can act as sink for PFAAs. • Rubbery sediment organic carbon can act as a concentration buffer.

Simultaneous determination of nereistoxin insecticides in foods of animal origins by combining pH-dependent reversible partitioning with hydrophilic interaction chromatography-mass spectrometry

Although nereistoxin insecticides (NIs) are banned for animal husbandry operations, they are still used because of their high insecticidal activities. Therefore, a reliable residue analysis method for the simultaneous detection of cartap, bensultap, thiocyclam, and nereistoxin in foods of animal origins, including beef, pork, chicken, milk, and eggs, was developed using hydrophilic interaction liquid chromatography–mass spectrometry (HILIC–LC–MS/MS). The NIs were extracted with an acidic cysteine and formate buffer solution and hydrolyzed to nereistoxin. The molarity and pH of the buffer were optimized at 20 mM and 3, respectively, to keep the pH of the extracts at 4–5. pH-dependent acid–base partitioning coupled with salting-out-assisted liquid–liquid extraction using acetonitrile was performed for purification and for the direct introduction of the extracts to LC. The optimal pH values were 5 and 9 for the acid–base partitioning. Nereistoxin quantitation was achieved with consistent column retention (RSD < 0.6%) and a high degree of separation (N > 106). The matrix-dependent method limit of quantitation was 2 μg nereistoxin/kg, and the calibration curve showed good linearity (R2 > 0.998). The recovery efficiencies were in the range of 89.2–109.9% with relative standard deviations less than 10%, and matrix effects did not exceed ± 10%, which satisfied the criteria outlined in the European SANTE/12682/2019 guidelines.

On the Okounkov-Olshanski formula for standard tableaux of skew shapes

The classical hook length formula counts the number of standard tableaux of straight shapes. In 1996, Okounkov and Olshanski found a positive formula for the number of standard Young tableaux of a skew shape. We prove various properties of this formula, including three determinantal formulas for the number of nonzero terms, an equivalence between the Okounkov-Olshanski formula and another skew tableaux formula involving Knutson-Tao puzzles, and two $q$-analogues for reverse plane partitions, which complement work by Stanley and Chen for semistandard tableaux. We also give several reformulations of the formula, including two in terms of the excited diagrams appearing in a more recent skew tableaux formula by Naruse. Lastly, for thick zigzag shapes we show that the number of nonzero terms is given by a determinant of the Genocchi numbers and improve on known upper bounds by Morales-Pak-Panova on the number of standard tableaux of these shapes.Mathematics Subject Classifications: 05A15, 05A15, 05A19, 05A05

Jacobi–Trudi formulas for flagged refined dual stable Grothendieck polynomials

Recently Galashin, Grinberg, and Liu introduced the refined dual stable Grothendieck polynomials, which are symmetric functions in $x=(x_1,x_2,\dots)$ with additional parameters $t=(t_1,t_2,\dots)$. The refined dual stable Grothendieck polynomials are defined as a generating function for reverse plane partitions of a given shape. They interpolate between Schur functions and dual stable Grothendieck polynomials introduced by Lam and Pylyavskyy in 2007. Flagged refined dual stable Grothendieck polynomials are a more refined version of refined dual stable Grothendieck polynomials, where lower and upper bounds are given for the entries of each row or column. In this paper Jacobi--Trudi-type formulas for flagged refined dual stable Grothendieck polynomials are proved using plethystic substitution. This resolves a conjecture of Grinberg and generalizes a result by Iwao and Amanov--Yeliussizov.

Electron Spin Echo Envelope Modulation Spectroscopy Reveals How Adenosylcobalamin-Dependent Lysine 5,6-Aminomutase Positions the Radical Pair Intermediates and Modulates Their Stabilities for Efficient Catalysis

Electron spin echo envelope modulation (ESEEM) spectroscopy reveals several interactions that serve to weaken the Co–C5′ bond, through stabilization of the cleaved state, thereby facilitating the 5′-deoxyadenosyl (5′-dAdo•) radical formation in unlabeled and 15N-labeled lysine 5,6-aminomutase. In the first place, we show that the CoII–His133β interaction enhances the spin delocalization from CoII to the α-axial ligand, reducing the 5′-dAdo•–CoII recombination probability in situ and allowing nascent 5′-dAdo• to migrate toward the substrate. Next, using [5′-2H]-deoxyadenosylcobalamin, we show that the C5′ methyl group of 5′-dAdoH is at closest contact with the substrate radical. In the case of 5′-dAdo•, this would allow the 5′-methylene radical to be rapidly quenched by H-transfer from the substrate. Finally, we show that the spin density is transferred noncovalently from the substrate radical to the adenine N7 of 5′-dAdoH. In the one-radical substrate–5′-dAdo•–product H-exchange triad, which is central in the mechanism of action of B12 enzymes, such transfer would promote the forward H-transfer reaction by dynamically lowering the free energy of the substrate radical, thereby facilitating its formation and quenching of 5′-dAdo•. In the reverse H-transfer reaction following the 1,2-rearrangement, the reversibility of the noncovalent spin transfer allows the product radical to restore full radical character to reform 5′-dAdo• and a diamagnetic product. The role of dynamical and reversible spin partitioning as a mechanism for modulating the radical stability is likely common in B12 enzymes. This study leads to a better comprehension about how an enzyme controls the reaction trajectory of 5′-dAdo• exquisitely with specificity. The ESEEM results support the positioning of the interacting partners in the catalytic form of lysine 5,6-aminomutase obtained by modeling.

Approximation algorithm for rearrangement distances considering repeated genes and intergenic regions

The rearrangement distance is a method to compare genomes of different species. Such distance is the number of rearrangement events necessary to transform one genome into another. Two commonly studied events are the transposition, which exchanges two consecutive blocks of the genome, and the reversal, which reverts a block of the genome. When dealing with such problems, seminal works represented genomes as sequences of genes without repetition. More realistic models started to consider gene repetition or the presence of intergenic regions, sequences of nucleotides between genes and in the extremities of the genome. This work explores the transposition and reversal events applied in a genome representation considering both gene repetition and intergenic regions. We define two problems called Minimum Common Intergenic String Partition and Reverse Minimum Common Intergenic String Partition. Using a relation with these two problems, we show a Theta left( k right)-approximation for the Intergenic Transposition Distance, the Intergenic Reversal Distance, and the Intergenic Reversal and Transposition Distance problems, where k is the maximum number of copies of a gene in the genomes. Our practical experiments on simulated genomes show that the use of partitions improves the estimates for the distances.

Reverse partitioning of Al from κ-carbide to the γ-matrix upon Ni addition and its strengthening effect in Fe–Mn–Al–C lightweight steel

The effect of the addition of Ni to Fe–30Mn–10Al–0.9C–0.5Si–1.5Mo (wt.%) cast lightweight steel was investigated with a focus on the precipitation behavior of (Fe,Mn)3AlC κ-carbide. The addition of 3 wt.% Ni (3Ni steel) resulted in continuous hardening of the steel during aging heat treatment at 550 °C for 100 h whereas the addition of 1.5 wt.% Ni (1.5Ni steel) led to peak hardening at 550 °C for 20 h. The size of κ-carbides after aging heat treatment for 100 h was smaller in 3Ni steel compared with 1.5Ni steel, despite its higher hardness and progressed hardening. Atom probe tomography of the aged 3Ni steel revealed that Al atoms were preferentially enriched in the γ-matrix with clustering of Ni atoms observed, resulting in the relative depletion of Al in κ-carbide. This is the first report of reverse partitioning of Al from κ-carbide to the γ-matrix through Ni addition, indicating that the affinity of C–Al is lower than that of Ni–Al. The substitution of Mn to the Al site of the κ-carbide lattice is energetically favorable when Ni–Al bonding actively occurs in the γ-matrix, as determined by first-principles calculations. This is clearly evidenced by the Mn enrichment of κ-carbide in the 3Ni steel. The amount of Ni–Al clustering resulting from the reverse partitioning of Al to the γ-matrix during the precipitation of κ-carbide could be increased according to the growth of κ-carbide. Therefore, we found that the addition of Ni led to simultaneous cooperative precipitation- and solid solution-strengthening after aging, contributing to continuous hardening by effectively suppressing the movement of dislocations.

Variation of the partition coefficient of phase-partitioning compounds between hydrocarbon and aqueous phases: an experimental study

Many non-ionic chemical compounds will form real solutions in equilibrium between two immiscible phases in contact. The partition coefficient (K) is defined as the quotient between the equilibrium concentration of the substance in the hydrocarbon and the aqueous phase. The reversible partition of a compound between hydrocarbon and aqueous phases is the basis of the partitioning inter-well tracer test (PITT). PITTs are of high interest for the characterization of oil reservoirs, in hydrogeology for assessment of the contamination of soils by non-aqueous phase liquids (NAPLs), and in process technology. The K value of substance is influenced by the actual chemical and physical conditions of the system where it will be used as phase-partitioning tracer. Thus, it is important to evaluate the extent of variation that the K value can exhibit under different relevant conditions.In the present document, we report the methodology and findings from the experimental determination of the K values of 4-methoxybenzyl alcohol, 3,4-dimethoxybenzyl alcohol, 4-chlorobenzyl alcohol, 2,6-dichlorobenzyl alcohol, pyridine, 2,3-dimethylpyrazine and 2,6-dimethylpyrazine between different hydrocarbon and aqueous phases. These 7 compounds were previously identified as interesting PITT tracer candidates. Individual K-values were determined under different temperatures, compositions of the hydrocarbon phase (synthetic mixtures of toluene, isooctane, and 1-octanol and 5 real crude oils), and different ionic strengths (I) and ionic compositions of the aqueous phase. The reversibility of the partitioning phenomena was also evaluated. The composition of the hydrocarbon phase and the ionic strength of the water phase were found to influence the K values of all seven compounds. Results suggest that the substitution of monovalent ions with divalent ions in the aqueous phase, keeping the ionic strength constant, does not influence the K values. Temperature effects on the K-values are always visible for 3,4-dimethoxybenzyl alcohol, 2,6-dichlorobenzyl alcohol, pyridine, 2,3-dimethylpyrazine and 2,6-dimethylpyrazine. Dependent on the hydrocarbon phase composition, temperature also influences the K-values for 4-methoxybenzyl alcohol and 4-chlorobenzyl alcohol.

Investigation of red blood cell partitioning in an in vitro microvascular bifurcation.

There is a long history of research examining red blood cell (RBC) partitioning in microvasculature bifurcations. These studies commonly report results describing partitioning that exists as either regular partitioning, which occurs when the RBC flux ratio is greater than the bulk fluid flowrate ratio, or reverse partitioning when the RBC flux ratio is less than or equal to that of the bulk fluid flowrate. This paper presents a study of RBC partitioning in a single bifurcating microchannel with dimensions of 6 to 16μm, investigating the effects of hematocrit, channel width, daughter channel flowrate ratio, and bifurcation angle. The erythrocyte flux ratio, N*, manifests itself as either regular or reverse partitioning, and time-dependent partitioning is much more dynamic, occurring as both regular and reverse partitioning. We report a significant reduction in the well-known sigmoidal variation of the erythrocyte flux ratio (N*) versus the volumetric flowrate ratio (Q*), partitioning behavior with increasing hematocrit in microchannels when the channel dimensions are comparable with cell size. RBCs "lingering" or jamming at the bifurcation were also observed and quantified in vitro. Results from trajectory analyses suggest that the RBC position in the feeder channel strongly affects both partitioning and lingering frequency of RBCs, with both being significantly reduced when RBCs flow on streamlines near the edge of the channel as opposed to the center of the channel. Furthermore, our experiments suggest that even at low Reynolds number, partitioning is affected by the bifurcation angle by increasing cell-cell interactions. The presented results provide further insight into RBC partitioning as well as perfusion throughout the microvasculature.

Formation and sink of glyoxal and methylglyoxal in a polluted subtropical environment: observation-based photochemical analysis and impact evaluation

Abstract. The dicarbonyls glyoxal (Gly) and methylglyoxal (Mgly) have been recognized as important precursors of secondary organic aerosols (SOAs) through the atmospheric heterogeneous process. In this study, field measurement was conducted at a receptor site in the Pearl River Delta (PRD) region in southern China, and an observation-based photochemical box model was subsequently applied to investigate the production and evolution of Gly and Mgly as well as their contributions to SOA formation. The model was coupled with a detailed gas-phase oxidation mechanism of volatile organic compounds (VOCs) (i.e., Master Chemical Mechanism, MCM, v3.2), heterogeneous processes of Gly and Mgly (i.e., reversible partitioning in aqueous phase, irreversible volume reactions and irreversible surface uptake processes), and the gas–particle partitioning of oxidation products. The results suggested that without considering the heterogeneous processes of Gly and Mgly on aerosol surfaces, the model would overpredict the mixing ratios of Gly and Mgly by factors of 3.3 and 3.5 compared to the observed levels. The agreement between observation and simulation improved significantly when the irreversible uptake and the reversible partitioning were incorporated into the model, which in total both contributed ∼ 62 % to the destruction of Gly and Mgly during daytime. Further analysis of the photochemical budget of Gly and Mgly showed that the oxidation of aromatics by the OH radical was the major pathway producing Gly and Mgly, followed by degradation of alkynes and alkenes. Furthermore, based on the improved model mechanism, the contributions of VOC oxidation to SOA formed from gas–particle partitioning (SOAgp) and from heterogeneous processes of Gly and Mgly (SOAhet) were also quantified. It was found that o-xylene was the most significant contributor to SOAgp formation (∼ 29 %), while m,p-xylene and toluene made dominant contributions to SOAhet formation. Overall, the heterogeneous processes of Gly and Mgly can explain ∼ 21 % of SOA mass in the PRD region. The results of this study demonstrated the important roles of heterogeneous processes of Gly and Mgly in SOA formation and highlighted the need for a better understanding of the evolution of intermediate oxidation products.

Local vs. Global Blood Flow Modulation in Artificial Microvascular Networks: Effects on Red Blood Cell Distribution and Partitioning.

Our understanding of cerebral blood flow (CBF) regulation during functional activation is still limited. Alongside with the accepted role of smooth muscle cells in controlling the arteriolar diameter, a new hypothesis has been recently formulated suggesting that CBF may be modulated by capillary diameter changes mediated by pericytes. In this study, we developed in vitro microvascular network models featuring a valve enabling the dilation of a specific micro-channel. This allowed us to investigate the non-uniform red blood cell (RBC) partitioning at microvascular bifurcations (phase separation) and the hematocrit distribution at rest and for two scenarios modeling capillary and arteriolar dilation. RBC partitioning showed similar phase separation behavior during baseline and activation. Results indicated that the RBCs at diverging bifurcations generally enter the high-flow branch (classical partitioning). Inverse behavior (reverse partitioning) was observed for skewed hematocrit profiles in the parent vessel of bifurcations, especially for high RBC velocity (i.e., arteriolar activation). Moreover, results revealed that a local capillary dilation, as it may be mediated in vivo by pericytes, led to a localized increase of RBC flow and a heterogeneous hematocrit redistribution within the whole network. In case of a global increase of the blood flow, as it may be achieved by dilating an arteriole, a homogeneous increase of RBC flow was observed in the whole network and the RBCs were concentrated along preferential pathways. In conclusion, overall increase of RBC flow could be obtained by arteriolar and capillary dilation, but only capillary dilation was found to alter the perfusion locally and heterogeneously.

Role of Ru on the Microstructural Evolution During Long-Term Aging of Ni-Based Single Crystal Superalloys

Two experimental alloys containing different contents of Ru were investigated to study the effect of Ru on the microstructural evolution during long-term thermal exposure. The increase in Ru promoted the formation of cubical, tiny, and even γ′ phase after full heat treatment. Moreover, the samples after full heat treatment were exposed at 1100 °C for different time. Based on the classical model by Lifshitz, Slyozov, and Wagner, the coarsening of γ′ phase of the alloy containing 2.5 and 3.5 wt.% Ru during the long-term aging was controlled by the interface reaction and diffusion, respectively. The γ/γ′ lattice misfit was more negative with the increment of Ru addition, which induced the formation of stable rafted γ′ phase in the alloy containing 3.5 wt.% Ru at the initiation of long-term aging. Besides, the increase in Ru reduced the diffusion coefficient, which could restrain the γ′ phase coarsening. The lower γ/γ′ lattice misfit of the alloy containing 2.5 wt.% Ru promoted the interface reaction, which induced the rapid coarsening of γ′ phase. Therefore, the increase in Ru improved the microstructural stability of the alloys. On the other hand, the raise of Ru induced “reverse partitioning” behavior, which was effective in suppressing the emergence of the topologically close-packed phase (TCP phase). The TCP phase occasionally occurred in the alloy containing 2.5 wt.% Ru, which was attributed to the high temperature and the supersaturation of the γ matrix. Moreover, the TCP phase was determined as μ phase, which had a high concentration of Co, Re, Mo, and W. A sketch map describing the evolution of the TCP phase was also constructed.

Refined dual stable Grothendieck polynomials and generalized Bender-Knuth involutions

The dual stable Grothendieck polynomials are a deformation of the Schur functions, originating in the study of the K-theory of the Grassmannian. We generalize these polynomials by introducing a countable family of additional parameters such that the generalization still defines symmetric functions. We outline two self-contained proofs of this fact, one of which constructs a family of involutions on the set of reverse plane partitions generalizing the Bender-Knuth involutions on semistandard tableaux, whereas the other classifies the structure of reverse plane partitions with entries 1 and 2.