Parameter Ρ2 Research Articles

Bloom dynamics under the effects of periodic driving forces

Phytoplankton bloom received considerable attention for many decades. Different approaches have been used to explain the bloom phenomena. In this paper, we study a Nutrient–Phytoplankton–Zooplankton (NPZ) model consisting of a periodic driving force in the growth rate of phytoplankton due to solar radiation and analyse the dynamics of the corresponding autonomous and non-autonomous systems in different parametric regions. Then we introduce a novel aspect to extend the model by incorporating another periodic driving force into the growth term of the phytoplankton due to sea surface temperature (SST), a key point of innovation. Temperature dependency of the maximum growth rate (μmax) of the phytoplankton is modelled by the well-known Q10 formulation: μmax=μ0∗(Q10)T/10, where μ0 is maximum growth at 0oC. Stability conditions for all three equilibrium points are expressed in terms of the new parameter ρ2, which appears due to the incorporation of periodic driving forces. System dynamics is explored through a detailed bifurcation analysis, both mathematically and numerically, with respect to the light and temperature dependent phytoplankton growth response. Bloom phenomenon is explained by the saddle point bloom mechanism even when the co-existing equilibrium point does not exist for some values of ρ2. Solar radiation and SST are modelled using sinusoidal functions constructed from satellite data. Our results of the proposed model describe the initiation of the phytoplankton bloom better than an existing model for the region 25–35° W, 40–45° N of the North Atlantic Ocean. An improvement of 14 days (approximately) is observed in the bloom initiation time. The rate of change method (ROC) is applied to predict the bloom initiation.

Expected polynomial-time randomized algorithm for graph coloring problem

Given a graph G=(V,E) with n=|V| vertices, the graph coloring problem is defined as Find a color vectorC=(c(v)), where c(v)∈{1,2,…,n} denotes the color of vertex v∈V, such that no monochromatic edge exists in G and the span, the total number of distinct colors in C, is minimized. Since the problem is NP-complete, a greedy coloring is commonly used for solving it. Greedy coloring visits the vertices of G following an order S, and while visiting a vertex v, it puts the minimum color absent in all neighbors of v. We show that the orders producing span ≤k, where k≤n is a positive integer, can be partitioned into disjoint subsets of equivalent orders. Next, we propose a selective search (SS) algorithm, which takes ρ as an input parameter, selects ≥ρ orders each from a different set of equivalent orders with high probability, applies greedy coloring on them, and returns the color vector with minimum span. We analytically show that SS performs better than greedy coloring with high probability by evaluating the same number of orders. We propose an incremental search heuristic (ISH), which ρ1 times execute SS with parameter ρ2 and returns the color vector with minimum span. A parallel version of ISH called PISH is also proposed, executing ρ1 SS calls in parallel. We show that ISH hits an optimum coloring for a graph G=(V,E) with χ(G)(Δ(G)+1)≤ne in expected O(|V|+|E|) time and space complexities. We have evaluated ISH and PISH on 136 challenging benchmarks and shown that they significantly outperform 10 existing state-of-the-art algorithms. Finally, we validated our theoretical findings by evaluating ISH and greedy coloring on random graphs.

Classical and Quantum Mixed-Type Lemon Billiards without Stickiness

The boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius with the distance 2B between their centers, as introduced by Heller and Tomsovic in Phys. Today 46 38 (1993). This paper is a continuation of our recent paper on classical and quantum ergodic lemon billiard (B = 0:5) with strong stickiness effects published in Phys. Rev. E 103 012204 (2021). Here we study the classical and quantum lemon billiards, for the cases B = 0:42; 0:55; 0:6, which are mixed-type billiards without stickiness regions and thus serve as ideal examples of systems with simple divided phase space. The classical phase portraits show the structure of one large chaotic sea with uniform chaoticity (no stickiness regions) surrounding a large regular island with almost no further substructure, being entirely covered by invariant tori. The boundary between the chaotic sea and the regular island is smooth, except for a few points. The classical transport time is estimated to be very short (just a few collisions), therefore the localization of the chaotic eigenstates is rather weak. The quantum states are characterized by the following universal properties of mixed-type systems without stickiness in the chaotic regions: (i) Using the Poincare-Husimi (PH) functions the eigenstates are separated to the regular ones and chaotic ones. The regular eigenenergies obey the Poissonian statistics, while the chaotic ones exhibit the Brody distribution with various values of the level repulsion exponent β, its value depending on the strength of the localization of the chaotic eigenstates. Consequently, the total spectrum is well described by the Berry-Robnik-Brody (BRB) distribution. (ii) The entropy localization measure A (also the normalized inverse participation ratio) has a bimodal universal distribution, where the narrow peak at small A encompasses the regular eigenstates, theoretically well understood, while the peak at larger A comprises the chaotic eigenstates, and is well described by the beta distribution. (iii) Thus the BRB energy level spacing distribution captures two effects: the divided phase space dictated by the classical Berry-Robnik parameter ρ2 measuring the relative size of the largest chaotic region, in agreement with the Berry-Robnik picture, and the localization of chaotic PH functions characterized by the level repulsion (Brody) parameter β. (iv) Examination of the PH functions shows that they are supported either on the classical invariant tori in the regular islands or on the chaotic sea, where they are only weakly localized. With increasing energy the localization of chaotic states decreases, as the PH functions tend towards uniform spreading over the classical chaotic region, and correspondingly β tends to 1.

Preferred Mode Choice Model for Commuter Purpose Based on Multinominal Logit Model

As a quasi-public traffic mode, more and more attention has been paid to the commuter bus to ease the traffic congestion. To get the travel behaviors of the commuters to which the commuter bus is available, The RP and SP survey about the travel behavior of commuters were carried out and the influencing factors of mode choice are discussed. The commuting mode combinations were found to exist during the decision-making process and there exist the preferred mode and secondary mode for each individual for one trip mode choice. The preferred mode choice model is established based on the multinomial logit mode. The results show that gender, month income, vehicle ownership, commuter cost, and commuter time have marked influences on the result of preferred mode choice for commuter purpose. The goodness of fit parameter ρ2 and goodness-of fit index adjusted by freedom ρ2 of the preferred mode choice model are 0.407 and 0.369 respectively, which implies that the forecast accuracy of the model is high. The VOT of the respondents in the survey is 29.9RMB/h and the results can provide a good reference for designing and optimizing of the commuter bus.

Subleading Isgur–Wise function of Λb→Λc1 using QCD sum rules

Subleading Isgur–Wise form factor τ(v·v′) at O(1/mQ) for Λb→Λc11/2,3/2 weak transition is calculated by using the QCD sum rules in the framework of the heavy quark effective theory (HQET), where Λ1/2c1 and Λ3/2c1 are the orbitally excited charmed baryon doublet with JP=(1−/2,3−/2). We consider the subleading contributions from the weak current matching in the HQET. The interpolating currents with transverse covariant derivative are adopted for Λ1/2c1 and Λ3/2c1 in the analysis. The slope parameter ρ2 in linear approximation of τ is obtained to be ρ2=2.76 and the interception to be τ(1)=−1.27 GeV.

Utility of NMR T2 distributions, connection with capillary pressure, clay effect, and determination of the surface relaxivity parameter ρ2

Nuclear magnetic resonance magnetization decays are now used routinely to determine reservoir properties of economic significance to the oil and gas industry. Although individual features of relaxation time distributions are subject to degradation in the presence of measurement noise, integrated and average measures of those distributions are remarkably stable. Properties such as porosity, producible porosity, hydraulic permeability, and the capillary pressure curve can be measured rapidly and continuously. Laboratory comparisons of NMR T 2 distributions with two different capillary pressure measurements enable the surface relaxivity parameter ρ 2 to be determined for sandstones. Comparison with relaxivities of synthetic materials having well-defined surface areas strongly suggests that the NMR-effective internal surface area of rocks is closely connected with the hydraulic radius, and, surprisingly, is not greatly affected by the presence of clay, which dominates the pore space surface area as measured by gas adsorption.

Exact tests and confidence intervals for ratio of variance components in unbalanced two-and three-stage nested designs

For the unbalanced two-stage nested design an exact size σ test for H0 : ρ≤ρ0 exists, where the variance component component in the first sampling stage σ2 e the error variance in the second stage. Using Wald's procudure one can construct and exact (1-σ) confidence interval for the ratio ρ of the variance components. For the three-stage nested design there are two interesting ratios of variance components where are the variance components in the first stage and second stage respectively, and is the error variance. The construction of exact size σ tests and (1-σ) confidence intervals for ρ2 is no problem using the same procedure as for the two-stage nested design. In the balanced three-stage nested design an exact size σ test is well known for H0: ρ ≥ ρ10 against H1:ρ ≥ ρ10 exists but depends also on the parameter ρ2. In the unbalanced three-stage nested design even the test for H1: ρ ≥ ρ10 exists but depends also on the parameter ρ2. In the unbalanced three-stage nested design even the test for H0:ρ1 = 0 ...

Studies on rare-earth compounds. Part I. The magnetic anisotropy of and crystal field in cerous magnesium nitrate, Ce2Mg3(NO3)12,24H2O

The average magnetic susceptibility and magnetic anisotropy of cerous magnesium nitrate over the temperature range 80–300 K are reported. These results, together with the previously reported g-values, have been interpreted in terms of a point-charge crystal-field model with the inclusion of an orbital reduction parameter k. Values of the radial parameters ρ2, ρ4 and ρ6 for both a 12- and 6-co-ordinate model have been determined. The value of k required by both models is in the range 0·93–0·96. The possible reasons for this parameter being less than unity are discussed.

Single-crystal magnetic properties of lanthanide complexes. Part IV. Tri-iodohexakis(antipyrine)neodymium(III)

The principal magnetic moments of crystals of tri-iodohexakis(antipyrine)neodymium(III)(antipyrine is 2,3-dimethyl-1-phenyl-Δ3-pyrazolin-5-one) have been measured in the temperature range 300–90 K. These are interpreted within a free-ion f3,4l term as basis, perturbed by a crystal field of D3d symmetry. The point-charge potential leads to second-, fourth-, and sixth-order radial parameters ρ2, ρ4, and ρ6, and θ, the effective angle subtended by any metal–oxygen bond and the three-fold symmetry axis. Mean moments fix ρ4 and ρ6 as 700 ± 200 cm–1 and 425 ± 50 cm–1, respectively. Magnetic anisotropies set ranges for A20〈r2〉, related to the coefficient of the second-order potential, as 140–220 cm–1 at 300 K and 200–350 cm–1 at 100 K. These ranges depend on ρ2, a property not shared by the magnetic properties of the cerium, terbium, or ytterbium analogues.