Potassium (K) is known for alleviating the negative effects of abiotic stresses on plants. To explore functions K in controlling reactive oxygen species (ROS), antioxidant activities, and osmoregulation sesame under drought stress, a pot experiment was conducted with three levels (0, 60, 120 kg ha-1, recorded as K0, K1, K2, respectively) exposed to well-watered (WW, 75% ± 5% soil relative water content) drought-stressed (DS, 50% conditions. The results showed that DS stimulated production...

Universality is a fundamental concept in modern physics. For the $q$-state Potts model, critical exponents are merely determined by order-parameter symmetry $S_q$, spatial dimensionality and interaction range, independent of microscopic details. In simplest mean-field treatment--i.e., model on complete graph (CG), phase transition further established to be percolation universality for range $0 < q <2$. By simulating CG random-cluster representation, we numerically demonstrate such...

Recently, we argued [Chin. Phys. Lett. 39, 080502 (2022)0256-307X10.1088/0256-307X/39/8/080502] that the Ising model simultaneously exhibits two upper critical dimensions (d_{c}=4,d_{p}=6) in Fortuin-Kasteleyn (FK) random-cluster representation. In this paper, perform a systematic study of FK on hypercubic lattices with spatial d from 5 to 7, and complete graph. We provide detailed data analysis behaviors variety quantities at near points. Our results clearly show many exhibit distinct...

The adverse effects of climate change on crop production are constraining breeders to develop high-quality environmentally stable varieties. Hence, efforts being made identify key genes that could be targeted for enhancing tolerance environmental stresses. ERF transcription factors play an important role in various abiotic stresses plants. However, the roles family still largely unknown sesame, "queen" oilseed crops.In total, 114 sesame (SiERFs) were identified and characterized. 96.49%...

Sesame production is severely affected by unexpected drought stress during flowering stage. However, little known about dynamic drought-responsive mechanisms anthesis in sesame, and no particular attention was given to black the most common ingredient East Asia traditional medicine. Herein, we investigated of two contrasting sesame cultivars (Jinhuangma, JHM, Poyanghei, PYH) anthesis. Compared PYH, JHM plants showed higher tolerance through maintenance biological membrane properties, high...

Little attention is paid to the mitigating effect of different potassium (K) levels on sesame (Sesamum indicum L.) growth performance in response drought stress (DS). A pot experiment was performed under DS conditions along with four K (0, 60, 120 and 180 kg ha−1, denoted as DK0, DK1, DK2 DK3 respectively), ha−1 K2O application normal watering set control (CK). Results showed that plant height, specific leaf weight, water content, chlorophyll crop rate biomass were significantly decreased by...

We address a long-standing debate regarding the finite-size scaling (FSS) of Ising model in high dimensions, by introducing random-length random walk model, which we then study rigorously. prove that this exhibits same universal FSS behavior previously conjectured for self-avoiding and on finite boxes high-dimensional lattices. Our results show mean length controls corresponding Green's function. numerically demonstrate universality our rigorous findings extensive Monte Carlo simulations...

The two-dimensional q-state clock model for q≥5 undergoes two Berezinskii-Kosterlitz-Thouless (BKT) phase transitions as temperature decreases. Here we report an extensive worm-type simulation of the square-lattice q=5-9 in a pair flow representations, from high- and low-temperature expansions, respectively. By finite-size scaling analysis susceptibilitylike quantities, determine critical points with precision improving over existing results. Due to dual each point region is observed...

Besides its original spin representation, the Ising model is known to have Fortuin-Kasteleyn (FK) bond and loop representations, of which former was recently shown exhibit two upper critical dimensions $({d}_{c}=4,{d}_{p}=6)$. Using a lifted worm algorithm, we determine coupling as ${K}_{c}=0.077\phantom{\rule{0.16em}{0ex}}708\phantom{\rule{0.16em}{0ex}}91(4)$ for $d=7$, significantly improves over previous results, then study geometric properties clusters on tori spatial $d=5$ 7. We show...

The upper critical dimension of the Ising model is known to be d c = 4, above which behavior regarded trivial. We hereby argue from extensive simulations that, in random-cluster representation, simultaneously exhibits two dimensions at ( p 6), and clusters for ≥ , except largest one, are governed by exponents percolation universality. predict a rich variety geometric properties then provide strong evidence 4 7 on complete graphs. Our findings significantly advance understanding model,...

We present a Monte Carlo study of the Fortuin-Kasteleyn (FK) clusters Ising model on square (2D) and simple-cubic (3D) lattices. The wrapping probability, dimensionless quantity characterizing topology FK torus, is found to suffer from smaller finite-size corrections than well-known Binder ratio, yields high-precision critical coupling as $K_c(3\rm D)=0.221\,654\,631(8)$. then geometric properties at criticality. It demonstrated that distribution largest-cluster size $C_1$ follows...

We present an extensive Markov chain Monte Carlo study of the finite-size scaling behavior Fortuin-Kasteleyn Ising model on five-dimensional hypercubic lattices with periodic boundary conditions. observe that physical quantities, which include contribution largest cluster, exhibit complete graph asymptotics. However, for quantities where cluster is removed, we mainly controlled by Gaussian fixed point. Our results therefore suggest both predictions, i.e., and point asymptotics, are needed to...

Core Ideas Defoliants enhanced seed cotton yield by increasing opening boll number. N application promoted weight per boll. 150 kg ha −1 and thidiazuron+ethephon of 900+3000 g ai was suggested. Appropriate nitrogen levels combined with safe rates harvest aids can provide timely efficient harvesting in the wheat–cotton double cropping system Yangtze River Valley Cotton Belt. Three (0+0, 450+1500, thidiazuron+ethephon) under four (0, 75, 150, 225 ) were established to study interactive effects...

In this article, a worm algorithm is used to study the problem of Ising model on complete graph. The approach shows connections between different representations and leads better understanding its scaling properties critical behavior.

The n-vector spin model, which includes the self-avoiding walk (SAW) as a special case for n→0 limit, has an upper critical dimensionality at four spatial dimensions (4D). We simulate SAW on 4D hypercubic lattices with periodic boundary conditions by irreversible Berretti-Sokal algorithm up to linear size L=768. From unwrapped end-to-end distance, we obtain fugacity z_{c}=0.147622380(2), improving over existing result z_{c}=0.1476223(1) 50 times. Such precisely estimated point enables us...

We present a Monte Carlo study of the backbone and shortest-path exponents two-dimensional Q-state Potts model in Fortuin-Kasteleyn bond representation. first use cluster algorithms to simulate critical on square lattice obtain d_{B}=1.7320(3) 1.794(2) for Q=2,3, respectively. However, large Q, suffers from serious slowing down slowly converging finite-size corrections. To overcome these difficulties, we consider O(n) loop honeycomb densely packed phase, which is regarded correspond with...

Cottonseed produces oil for human consumption and protein meals ruminant feed, carbohydrate metabolism takes responsibility seed biosynthesis. Here, 6-BA GA3 were evaluated by or foliar application its effect on physiological productive parameters of cottonseed in two-year field experiment. Results showed that significantly enhanced yield because increased boll number index. Boll was the dominant driver increment priming with 6-BA, increase greater than GA3, resulting higher (18.8–20.1%)...

The Fortuin-Kasteleyn (FK) random cluster model, which can be exactly mapped from the $q$-state Potts spin is a correlated bond percolation model. By extensive Monte Carlo simulations, we study FK representation of critical Ising model ($q=2$) on finite complete graph, i.e. mean-field We provide strong numerical evidence that configuration space for $q=2$ contains an asymptotically vanishing sector in quantities exhibit same finite-size scaling as uncorrelated ($q=1$) graph. Moreover,...

In the presence of attraction, jamming transition packings frictionless particles corresponds to rigidity percolation. When range attraction is long, distribution size rigid clusters, $P(s)$, continuous and shows a power-law decay. For systems with short-range attractions, however, $P(s)$ appears discontinuous. There decay for small cluster sizes, followed by low probability gap peak near system size. We find that this appearing ``discontinuity'' does not mean fact, it signifies coexistence...

Field-theoretical calculations predict that, at the upper critical dimension $d_c=4$, finite-size scaling (FSS) behaviors of Ising model would be modified by multiplicative logarithmic corrections with thermal and magnetic correction exponents $(\hat{y}_t, \hat{y}_h)=(1/6,1/4)$. Using high-efficient cluster algorithms lifted worm algorithm, we present a systematic study FSS four-dimensional in Fortuin-Kasteleyn (FK) bond loop representations. Our numerical results reveal various geometric...