Nodal Behavior Research Articles

Dynamical heterogeneity and universality of power-grids

Electric power systems during transient states are extensively investigated using variations of the Kuramoto model to analyze their dynamic behavior. However, the majority of current models fail to capture the physics of power flows and the heterogeneity of the grids under study. This study addresses this gap by comparing the levels of heterogeneity in continent-sized power grids in Europe and North America to reveal the underlying universality and heterogeneity of grid frequencies, electrical parameters, and topological structures. Empirical data analysis of grid frequencies from the Hungarian grid indicates that q-Gaussian distributions best fit simulations, with spatio-temporally correlated noise evident in the frequency spectrum. Comparing European and North American power grids reveals that employing homogeneous transmission capacities to represent power lines can lead to misleading results on stability, and nodal behavior is heterogeneous. Community structures of the continent-sized grids are detected, demonstrating that Chimera states are more likely to occur when studying only subsystems. A topographical analysis of the grids is presented to assist in selecting such subsystems. Finally, synchronization calculations are provided to illustrate the occurrence of Chimera states. The findings underscore the necessity of heterogeneous grid models for dynamic stability analysis of power systems.

Hydraulic Connectiveness Metric for the Analysis of Criticality in Water Distribution Networks

Capturing the criticality of a water distribution network (WDN) is difficult because of its many constituent factors. In terms of operation, the arrangement of demand nodes and how they connect have a significant influence. This study aims to integrate hydraulic and topologic aspects into a single criticality measure by adapting the structural hole influence matrix concept. This method applies the nodal demand to the corresponding pipes to construct a weighted network. The matrix stores each node’s local and global connection information, and the criticality value is then assigned based on the adjacency information. The criticality value can reveal the locations in terms of nodes or pipes that are vital for maintaining a network’s level of service. By analyzing pipe-failure scenarios, the criticality value can be related to the loss of performance. Assessing the nodal criticality change behavior under an increased stress scenario can help uncover the impacted areas. The metric for district metered area (DMA) creation demonstrates its potential as a weighting to be considered. This unified criticality metric enables the evaluation of nodes and pipes in a WDN, thereby enabling resilient and sustainable development planning.

Cluster structures of the 0+ states of CΛ13 with the 3α+Λ four-body orthogonality condition model

We study structures of the ${0}^{+}$ states of $_{\mathrm{\ensuremath{\Lambda}}}^{13}\mathrm{C}$ within the framework of the $\ensuremath{\alpha}+\ensuremath{\alpha}+\ensuremath{\alpha}+\mathrm{\ensuremath{\Lambda}}$ four-body orthogonality condition model with the Gaussian expansion method. We obtain five ${0}^{+}$ states of $_{\mathrm{\ensuremath{\Lambda}}}^{13}\mathrm{C}$ and compare them with the low-lying four ${0}^{+}$ states of $^{12}\mathrm{C}$. We find that the ${0}_{1}^{+}$, ${0}_{2}^{+}$, and ${0}_{4}^{+}$ states correspond to the ${0}_{1}^{+}$, ${0}_{2}^{+}$, and ${0}_{4}^{+}$ states of $^{12}\mathrm{C}$, respectively. We also find that both the ${0}_{3}^{+}$ and ${0}_{5}^{+}$ states have analogous nature to the ${0}_{3}^{+}$ state of $^{12}\mathrm{C}$, where the additional $\mathrm{\ensuremath{\Lambda}}$ particle couples with the $^{8}\mathrm{Be}$ cluster and one $\ensuremath{\alpha}$ cluster, in the ${0}_{3}^{+}$ state of $^{12}\mathrm{C}$, respectively. The former is then shown to have an elongated ${}_{\mathrm{\ensuremath{\Lambda}}}^{9}\mathrm{Be}({0}_{1}^{+})+\ensuremath{\alpha}$ cluster structure with a higher nodal behavior for its relative wave function, and the latter has a dilute three-body gas consisting of $2\ensuremath{\alpha}{+}_{\mathrm{\ensuremath{\Lambda}}}^{5}\mathrm{He}$ clusters.

8-16-4 graphyne: Square-lattice two-dimensional nodal line semimetal with a nontrivial topological Zak index

An unprecedented graphyne allotrope with square symmetry and nodal line semimetallic behavior has been proposed in the two-dimensional (2D) realm. The emergence of the Dirac loop around the high-symmetry points in the presence of both the inversion and time-reversal symmetries is a predominant feature of the electronic band structure of this system. Besides, the structural stability in terms of the dynamic, thermal, and mechanical properties has been critically established for the system. Following the exact analytical model based on the real-space renormalization group scheme and tight-binding approach, we have inferred that the family of 2D nodal line semimetals with square symmetry can be reduced to a universal four-level system in the low-energy limit. This renormalized lattice indeed explains the underlying mechanism responsible for the fascinating emergence of 2D square nodal line semimetals. Besides, the analytical form of the generic dispersion relation of these systems is well supported by our density-functional theory results. Finally, the nontrivial topological properties have been explored for the predicted system without breaking the inversion and time-reversal symmetry of the lattice. We have obtained that the edge states are protected by the nonvanishing topological index, i.e., Zak phase.

High Multiplicity and Chaos for an Indefinite Problem Arising from Genetic Models

Abstract We deal with the periodic boundary value problem associated with the parameter-dependent second-order nonlinear differential equation u ′′ + c ⁢ u ′ + ( λ ⁢ a + ⁢ ( x ) - μ ⁢ a - ⁢ ( x ) ) ⁢ g ⁢ ( u ) = 0 , u^{\prime\prime}+cu^{\prime}+\bigl{(}\lambda a^{+}(x)-\mu a^{-}(x)\bigr{)}g(u)% =0, where λ , μ > 0 {\lambda,\mu>0} are parameters, c ∈ ℝ {c\in\mathbb{R}} , a ⁢ ( x ) {a(x)} is a locally integrable P-periodic sign-changing weight function, and g : [ 0 , 1 ] → ℝ {g\colon{[0,1]}\to\mathbb{R}} is a continuous function such that g ⁢ ( 0 ) = g ⁢ ( 1 ) = 0 {g(0)=g(1)=0} , g ⁢ ( u ) > 0 {g(u)>0} for all u ∈ ] 0 , 1 [ {u\in{]0,1[}} , with superlinear growth at zero. A typical example for g ⁢ ( u ) {g(u)} , that is of interest in population genetics, is the logistic-type nonlinearity g ⁢ ( u ) = u 2 ⁢ ( 1 - u ) {g(u)=u^{2}(1-u)} . Using a topological degree approach, we provide high multiplicity results by exploiting the nodal behavior of a ⁢ ( x ) {a(x)} . More precisely, when m is the number of intervals of positivity of a ⁢ ( x ) {a(x)} in a P-periodicity interval, we prove the existence of 3 m - 1 {3^{m}-1} non-constant positive P-periodic solutions, whenever the parameters λ and μ are positive and large enough. Such a result extends to the case of subharmonic solutions. Moreover, by an approximation argument, we show the existence of a family of globally defined solutions with a complex behavior, coded by (possibly non-periodic) bi-infinite sequences of three symbols.

What is the Diagnosis?

One image and tracings were obtained during the para-Hisian stimulation maneuver in an electrophysiological study. The question is: is there any retrograde nodal or extranodal conduction behavior?

A reactive algorithm for deducing nodal forwarding behavior in a multihop ad-hoc wireless network in the presence of errors

novel algorithm is presented to deduce individual nodal forwarding behavior from standard end-to-end acknowledgments. The algorithm is based on a well-established mathematical method and is robust to network related errors and nodal behavior changes. The proposed solution was verified in a network simulation, during which it achieved sound results in a challenging multihop ad-hoc network environment.

Electric field induced band tuning, optical and thermoelectric responses in tetragonal germanene: a theoretical approach.

In this article, we have systematically explored the electronic, optical and thermoelectric properties of tetragonal germanene (T-Ge) using first principles calculations. The ground state geometry of pristine T-Ge is buckled and exhibits nodal line semi-metallic behaviour. In addition, we have proposed a tight binding (TB) model Hamiltonian that efficiently explains the emergence of double Dirac points at the Fermi level of T-Ge. Furthermore, a hopping relation has been explored at which both Dirac points merge and then annihilate resulting in a direct band gap at the Γ point. To exploit the buckling of the system, we have employed a transverse electric field, which invariably breaks the sublattice symmetry and removes the degeneracies at the Fermi surface. Furthermore, the band gap at the Dirac points varies linearly with the external electric field strength. Our TB Hamiltonian adequately satisfies the first principles results even in the presence of an external electric field. Moreover, we have found that T-Ge offers efficient tuning of band gaps at the Dirac points compared to other buckled systems viz. hexagonal silicene and germanene. In addition, the optical behaviour of T-Ge has been explained in accordance with the electronic states of the system. The strong optical responses in a low energy region make the material efficient for optical nanodevice applications. Moreover, T-Ge shows relatively better thermoelectric behaviour than graphene. Therefore, the external electric field induced tunable band gap and intriguing low energy optical signals pave the way to choose T-Ge as a smart choice for optoelectronic device applications. Finally we have suggested probable routes for experimental realization of the T-Ge structure.

On the applicability of the poincaré–Birkhoff twist theorem to a class of planar periodic predator-prey models

This paper studies the existence of subharmonics of arbitrary order in a generalized class of non-autonomous predator-prey systems of Volterra type with periodic coefficients. When the model is non-degenerate it is shown that the Poincare–Birkhoff twist theorem can be applied to get the existence of subharmonics of arbitrary order. However, in the degenerate models, whether or not the twist theorem can be applied to get subharmonics of a given order might depend on the particular nodal behavior of the several weight function-coefficients involved in the setting of the model. Finally, in order to analyze how the subharmonics might be lost as the model degenerates, the exact point-wise behavior of the \begin{document}$ T $\end{document} -periodic solutions of a non-degenerate model is ascertained as a perturbation parameter makes it degenerate.

Robustness of superconducting properties to transition metal substitution and impurity phases in Fe1−xVxSe

We have performed transverse- and zero-field muon spin rotation/relaxation experiments, as well as magnetometry measurements, on samples of Fe1-xVxSe and their Li+NH3 intercalates Li0.6(NH2)0.2(NH3)0.8 Fe1-x Vx Se. We examine the low vanadium substitution regime: x = 0.005, 0.01, and 0.02. The intercalation reaction significantly increases the critical temperature (Tc) and the superfluid stiffness for all x. The nonintercalated samples all exhibit Tc = 8.5 K while the intercalated samples all show an enhanced Tc > 40 K. Vanadium substitution has a negligible effect on Tc, but seems to suppress the superfluid stiffness for the nonintercalated samples and weakly enhance it for the intercalated materials. The optimal substitution level for the intercalated samples is found to be x = 0.01, with Tc = 41 K and {\lambda}_{ab}(0) = 0.18 {\mu}m. The nonintercalated samples can be modeled with either a single d-wave superconducting gap or with an anisotropic gap function based on recent quasiparticle imaging experiments, whereas the intercalates display multigap nodal behavior which can be fitted using s + d- or d + d-wave models. Magnetism, likely from iron impurities, appears after the intercalation reaction and coexists and competes with the superconductivity. However, it appears that the superconductivity is remarkably robust to the impurity phase, providing an avenue to stably improve the superconducting properties of transition metal substituted FeSe.

An integrated overview of AV node physiology

The atrioventricular (AV) node generates half of the AV delay needed for blood pumping and filters atrial impulses that could otherwise induce life-threatening ventricular arrhythmias. It is also a pacemaker and a key target in the treatment of cardiac arrhythmias. The special roles of the AV node primarily arise from its slow conduction, long refractory period, and cellular automaticity. However, efforts to establish the dynamics of these properties and their interaction led to many controversies. In fact, the AV node's behavior is so complex that it seems to escape broadly applicable rules. This review summarizes progresses made in resolving these issues and in integrating the multiple roles of the AV node within a common functional model. Presented evidence shows that the rate-dependent conduction and refractory properties of the AV node can be reliably characterized and reconciled from nodal responses to S1 S2 S3 protocols. It also supports the concept that dual pathways constitute a feature of the normal AV node and account for its overall conduction and refractory properties. In this model, the posterior extension and compact node provide the core of the slow and fast pathway, respectively. The transitional tissues and lower nodal bundle provide a common proximal and distal pathway, respectively. These pathways would also support bidirectional conduction. The dual pathway involvement can also be extended to widely variable AV nodal responses, such as Wenckebach cycles, hysteresis, and ventricular response to atrial fibrillation. In brief, the intricate AV nodal behavior may obey a limited set of accessible and definable rules.

High Pressure Crystal Structure and Electrical Properties of a Single Component Molecular Crystal [Ni(dddt)2] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate).

Single-component molecular conductors form an important class of materials showing exotic quantum phenomena, owing to the range of behavior they exhibit under physical stimuli. We report the effect of high pressure on the electrical properties and crystal structure of the single-component crystal [Ni(dddt)2] (where dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate). The system is isoelectronic and isostructural with [Pd(dddt)2], which is the first example of a single-component molecular crystal that exhibits nodal line semimetallic behavior under high pressure. Systematic high pressure four-probe electrical resistivity measurements were performed up to 21.6 GPa, using a Diamond Anvil Cell (DAC), and high pressure single crystal synchrotron X-ray diffraction was performed up to 11.2 GPa. We found that [Ni(dddt)2] initially exhibits a decrease of resistivity upon increasing pressure but, unlike [Pd(dddt)2], it shows pressure-independent semiconductivity above 9.5 GPa. This correlates with decreasing changes in the unit cell parameters and intermolecular interactions, most notably the π-π stacking distance within chains of [Ni(dddt)2] molecules. Using first-principles density functional theory (DFT) calculations, based on the experimentally-determined crystal structures, we confirm that the band gap decreases with increasing pressure. Thus, we have been able to rationalize the electrical behavior of [Ni(dddt)2] in the pressure-dependent regime, and suggest possible explanations for its pressure-independent behavior at higher pressures.

Control Across Scales by Positive and Negative Feedback

Feedback is a key element of regulation, as it shapes the sensitivity of a process to its environment. Positive feedback upregulates, and negative feedback downregulates. Many regulatory processes involve a mixture of both, whether in nature or in engineering. This article revisits the mixed-feedback paradigm, with the aim of investigating control across scales. We propose that mixed feedback regulates excitability and that excitability plays a central role in multiscale neuronal signaling. We analyze this role in a multiscale network architecture inspired by neurophysiology. The nodal behavior defines a mesoscale that connects actuation at the microscale to regulation at the macroscale. We show that mixed-feedback nodal control provides regulatory principles at the network scale, with a nodal resolution. In this sense, the mixed-feedback paradigm is a control principle across scales.

WNBLI - A Multifarious Liability Examination for Wireless Sensor Networks

Wireless communications has completely revolutionized the living environment, just as personal computers forever altered the way of working in the 1980’s and the Internet dramatically changed the obtainment and accessing way of information in the 1990’s. Wireless sensor networks are evolving to a new level. The Failure liability is a very prominent problem in Wireless Sensor Network (WSN) research. Failure liable nodes behave in different form and this faulty behavior is referred to as multifarious faults or heterogeneous faults in WSN. This paper presents a Multifarious Failure liability Investigation protocol called Wireless Nodal Behavior and Liability Investigation (WNBLI) protocol for wireless sensor networks. The proposed WNBLI protocol consists of three vital phases, such as Association phase, Apprehension phase and Assortment phase. The performance of the proposed Wireless Nodal Behavior and Liability Investigation protocol is evaluated using network simulator.

Fully gapped d-wave superconductivity in CeCu2Si2

The nature of the pairing symmetry of the first heavy fermion superconductor CeCu2Si2 has recently become the subject of controversy. While CeCu2Si2 was generally believed to be a d-wave superconductor, recent low-temperature specific heat measurements showed evidence for fully gapped superconductivity, contrary to the nodal behavior inferred from earlier results. Here, we report London penetration depth measurements, which also reveal fully gapped behavior at very low temperatures. To explain these seemingly conflicting results, we propose a fully gapped [Formula: see text] band-mixing pairing state for CeCu2Si2, which yields very good fits to both the superfluid density and specific heat, as well as accounting for a sign change of the superconducting order parameter, as previously concluded from inelastic neutron scattering results.

Abstract 17: Patterns of neck nodal metastases and recurrence in human papilloma virus-associated oropharyngeal squamous cell carcinoma after neck dissection

Abstract Background: The aim of this study is to address the paucity of data on the potentially unique patterns of neck nodal metastases in HPV-positive oropharyngeal squamous cell carcinoma (HPV+OPSCC). Methods: The neck dissection (ND) specimens of varying levels of HPV+OPSCC patients at University of California-San Francisco from 2010-2016 were reviewed for the numbers and frequencies of clinically evident and occult nodes by neck level, and for those with extra-capsular spread (ECS). Smoking history (>10 pack-years), T status, and local, regional and distal recurrences were also assessed for possible associations with nodal metastatic behavior. Results: Sixty HPV+OPSCC patients underwent primary site trans-oral robotic surgery and 65 NDs, of which 21 (32%) were elective. Forty-three (65%) NDs were in non-smokers. Overall, the mean number of positive nodes per ND was 2.5 (range 1-9). The frequencies of at least one pathologically positive node for neck levels 1b, 2, 2a, 2b, 3, 4, and 5 were 0% (0/41), 67.7% (44/65), 43% (23/53), 13% (7/53), 27.7% (18/65), 7% (4/54), and 8% (2/23), respectively. All positive level 5 positive nodes were clinically evident preoperatively. Five of 21 (24%) elective NDs had occult disease only in levels 2A, 2B, and 3, with a mean number of positive nodes of 1.8 (range 1-3). Three of 21 (14%) elective NDs had nodes with ECS. Six of 44 (13%) therapeutic NDs had occult nodes outside the known preoperative distribution in levels 2b, 3 and 4. There were no occult 2a nodes. Smoking history, primary site, and T status were not statistically significantly associated with a differing metastatic nodal behavior. Twenty-three of 60 and 18 of 60 patients underwent adjuvant radiation and adjuvant chemoradiation, respectively. Thirteen of the 19 patients who only underwent surgery had positive lymph nodes, of which five had N1 disease and four had N2b disease. All four of N2b disease patients refused adjuvant therapy and none have had a recurrence as of follow-up (mean 28 months, range 3-51). The overall mean follow-up was 29.1 months (range 2-76 months), with 72% of patients having at least 12 months. One of 65 (1.5%) NDs developed a neck recurrence in the skin overlying level 2 in a patient in the therapeutic ND cohort who had undergone chemoradiation for ECS. No undissected neck levels developed metastatic nodal disease. Two of 60 (3%) patients developed local recurrence. No patients developed distant metastases. One patient in the cohort died of an unrelated cause. There have been no cancer-related deaths. Conclusions: For HPV+OPSCC, therapeutic NDs should encompass any levels bearing suspicious nodes and levels 2a, 2b, 3, and 4, while elective NDs should be performed and encompass at least levels 2a, 2b, and 3. ECS may be present in occult nodes. For HPV+OPSCC, these selective ND plans, followed by the indicated adjuvant treatment, is associated with a low neck recurrence rate. Citation Format: Madeleine P. Strohl, Steven J. Wang, Patrick K. Ha, Jonathan R. George, Chase M. Heaton, Ivan H. El-Sayed, Jon Mallen St Clair, William R. Ryan. Patterns of neck nodal metastases and recurrence in human papilloma virus-associated oropharyngeal squamous cell carcinoma after neck dissection [abstract]. In: Proceedings of the AACR-AHNS Head and Neck Cancer Conference: Optimizing Survival and Quality of Life through Basic, Clinical, and Translational Research; April 23-25, 2017; San Diego, CA. Philadelphia (PA): AACR; Clin Cancer Res 2017;23(23_Suppl):Abstract nr 17.

NMR study of quasi-one-dimensional Ta<sub>4</sub>Pd<sub>3</sub>Te<sub>16</sub>

Low-dimensional systems often display rich physical phenomena, such as charge density wave (CDW), spin density wave (SDW), and superconductivity. Many superconductors were found at low dimensions where the superconductivity coexists with or adjoins another ordered state and has an unconventional nature. The high transition temperature (<italic>T</italic>_C) superconductivity has been realized in two-dimensional copper oxides and iron pnictides, where the superconducting phase is located in the vicinity of magnetic and nematic orders. This raises an interest in finding unconventional superconductivity in low-dimensional materials. Ta₄Pd₃Te₁₆ with a quasi-one-dimensional crystal structure was discovered to be superconducting with <italic>T</italic>_C∼4.6 K. It consists of PdTe₂ chains, TaTe₃ chains, and Ta₂Te₄ double chains along the crystallographic <italic>b</italic> axis. Band structure calculations indicate that Ta₄Pd₃Te₁₆ is an s-wave superconductor with pairing from phonons associated with the Te-Te p bonding and a Fermi-surface associated with Te p bands. Although scanning tunneling microscopy (STM) found that the superconducting gap structure in this system is more likely anisotropic without nodes, nodal gap behaviors were claimed by thermal conductivity and specific heat measurements. STM study suggested that the system is in the vicinity of an ordered state that shows a periodic modulation. This suggestion is consistent with the observation that the magnetoresistance shows an <italic>H</italic>-linear behavior without saturation up to 50 T. In this paper, we report nuclear magnetic resonance and nuclear quadrupole resonance investigations on Ta₄Pd₃Te₁₆. The spin-lattice relaxation rate (1/<italic>T</italic>₁) divided by the temperature, 1/<italic>T</italic>₁<italic>T</italic>, of ¹²⁵Te is almost a constant and obeys the Korringa relationship as in a normal metal, but 1/<italic>T</italic>₁<italic>T</italic> of ¹⁸¹Ta increases dramatically below 80 K. These results indicate strong electric-field-gradient (EFG) fluctuations, since ¹⁸¹Ta has a nuclear spin <italic>I</italic>=7/2 with a large nuclear quadrupole moment that couples to EFG, but ¹²⁵Te with spin <italic>I</italic>=1/2 can only relax by magnetic interactions. Upon cooling, both the full width at half maximum of the spectra and 1/<italic>T</italic>₁<italic>T</italic> show a sudden change at <italic>T</italic>=20 K, indicating a CDW transition takes place at <italic>T</italic>_CDW=20 K. This is consistent with the electronic structure calculation which implies that Ta₄Pd₃Te₁₆ prefers the CDW rather than the SDW. In the superconducting state, a Hebel-Slichter coherence peak appears in the temperature dependence of 1/<italic>T</italic>₁ of ¹²⁵Te just below <italic>T</italic>_C, which indicates that Ta₄Pd₃Te₁₆ is a fully gapped superconductor. 1/<italic>T</italic>₁ can be fitted by using a BCS gap with <inline-formula><mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mrow><mml:mi>Δ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy=false>)</mml:mo><mml:mo>=</mml:mo><mml:mn>1.76</mml:mn><mml:msub><mml:mi other=0>k</mml:mi><mml:mtext other=1>B</mml:mtext></mml:msub> <mml:msub><mml:mi other=0>T</mml:mi><mml:mtext other=1>C</mml:mtext> </mml:msub></mml:mrow></mml:math></inline-formula>. Although Ta₄Pd₃Te₁₆ is a multiband system, the main contribution to the DOS is from Te p orbitals. Therefore, the full gap derived from the ¹²⁵Te NMR is consistent with the suggestion from the band calculation that Ta₄Pd₃Te₁₆ should be an s-wave superconductor mediated by phonons associated with the Te-Te bonding if there are no spin fluctuations. Due to coexistence of CDW and superconducting, strong EFG fluctuations eliminate the coherence peak in the temperature dependence of 1/<italic>T</italic>₁ of ¹⁸¹Ta.

Electronic Structure Problem of Alkaline Earth Metals

Purpose: The present study is to resolve the problem in electronic structure of alkaline earth metals bydifferent calculations and conceptual theories. Methodological concept: All discovered alkaline earth metals occur in nature. Experiments have beenconducted to attempt the synthesis of element 120, the next potential member of the group, but they have allmet with failure. The electronic structure of alkaline earth metals determines all their physical properties.Effective electron Eigen value problem of the singly charged alkaline earth metal ion with a single valenceelectron. This valence electron moves in one particle model potential to reproduce the valence excitationenergies of the monocation. Results: The radial degree of freedom of the electronic wave function in a finite element basis set from thesolution of the one electron problem. Using the Lanczos-based package ARPACK, we calculate-for eachvalid combination of angular momentum quantum numbers l and j-the first 18 eigen functions outside thecore shells. In other words, solutions associated with inner shells are skipped. Thus, the selected valence-electron solutions display correct nodal behavior.

Coupling of 2D discretized Peridynamics with a meshless method based on classical elasticity using switching of nodal behaviour

PurposeThe paper aims to use a switching technique which allows to couple a nonlocal bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions (MLEBF) method, based on classical continuum mechanics, to solve planar problems.Design/methodology/approachThe coupling has been achieved in a completely meshless scheme. The domain is divided in three zones: one in which only Peridynamics is applied, one in which only the meshless method is applied and a transition zone where a gradual transition between the two approaches takes place.FindingsThe new coupling technique generates overall grids that are not affected by ghost forces. Moreover, the use of the meshless approach can be limited to a narrow boundary region of the domain, and in this way, it can be used to remove the “surface effect” from the Peridynamic solution applied to all internal points.Originality/valueThe current study paves the road for future studies on dynamic and static crack propagation problems.

Multiple positive solutions to elliptic boundary blow-up problems

We prove the existence of multiple positive radial solutions to the sign-indefinite elliptic boundary blow-up problem{Δu+(a+(|x|)−μa−(|x|))g(u)=0,|x|<1,u(x)→∞,|x|→1, where g is a function superlinear at zero and at infinity, a+ and a− are the positive/negative part, respectively, of a sign-changing function a and μ>0 is a large parameter. In particular, we show how the number of solutions is affected by the nodal behavior of the weight function a. The proof is based on a careful shooting-type argument for the equivalent singular ODE problem. As a further application of this technique, the existence of multiple positive radial homoclinic solutions toΔu+(a+(|x|)−μa−(|x|))g(u)=0,x∈RN, is also considered.