Our earlier developed software utility, H-BEE, for estimating the energies of individual hydrogen bonds (HB) in molecular clusters was implemented with three methods. These methods are: the molecular tailoring approach based (MTA-based) one, the first spherical shell (SS1), and the Fragments-in-Fragments. These methods work quite well but are still time-consuming and have certain shortcomings. Herein, our recently proposed method of synergistic cyclic cooperativity (SCC) is implemented as an update (called H-BEE 2.0) to H-BEE. The three-dimensional (3D) molecular cluster is usually made up of small cyclic structures which result from the interconnected network of HBs. Within the SCC method, the energy of a referenced HB is estimated as the sum of the cooperativity contributions (CCs) of these small cyclic structures and its energy in an isolated dimeric species. The SCC is an effective and swift method. The H-BEE 2.0 identifies all possible cyclic structures in an automatic manner and evaluates the CCs of these cycles. The H-BEE 2.0 utility has been extensively tested on a variety of molecular clusters and the results are compared with the earlier implemented methods. It also brings out the finer aspects of the strength of HBs in terms of the nature of cooperativity of small cyclic networks.

PurposeThis study aimed to design and characterize a novel dual-function floating-bioadhesive drug delivery system based on a hollow structure to extend gastroretentive time and enhance the bioavailability of ofloxacin.MethodsHollow spherical shells were fabricated via fluidized-bed coating using a blended polymer film composed of (SuE (Surelease® E-7-19040) and EuN (Eudragit® NE 30D)). The system integrated a hollow spherical shell, a waterproof layer, a drug layer, a release-retarding ethylcellulose (EC) film, and an outer bioadhesive layer. The mechanical properties, in vitro floating and bioadhesive behavior, drug release profile, and in vivo pharmacokinetics were comprehensively evaluated.ResultsThe blended film at a SuE/EuN ratio of 4:4 exhibited optimal mechanical rigidity and strength for the hollow shell. Analysis of the release profile showed a zero-order release for the first 4 h, which was in accordance with the predicted value. The optimized formulation demonstrated excellent buoyancy with a floating rate of 96.3±0.5% and 100% bioadhesion on gastric mucosa. In vivo pharmacokinetic studies in New Zealand rabbits revealed that the test formulation had a prolonged elimination half-life (6.65±0.94 h) and a relative bioavailability of 112.2±14.9% compared to the reference tablet.ConclusionThe developed floating-bioadhesive system successfully combined hollow-structure buoyancy with mucoadhesion to achieve prolonged gastric retention and sustained drug release, offering a feasible approach for gastroretentive drug delivery systems.

Finite element analysis with experimental verification of concrete anisotropic structures for industrial design under hydrostatic pressure

Plant primary cell walls are dynamic supramolecular assemblies composed of layered cellulose, hemicellulose, and pectin, progressively built through synthesis and secretion. However, the specific architectural features and structural components sufficient to endow the mechanical properties of the wall remain unclear. Here, we construct a minimal synthetic spherical shell and compare its structural and mechanical properties to those of a plant single-cell system. To eliminate complexities from intercellular connectivity and developmental history, we exploit the ability of plant protoplasts to regenerate cell walls de novo. Compression tests of regenerating protoplasts between parallel plates reveal that wall stiffness increases with wall thickening over time. Despite differences in assembly pathways, architecture, and composition, the synthetic shell exhibits a similar thickness-dependent modulus and similar material stiffness. The synthetic shell, mainly composed of pectin and cellulose nanofibers, mirrors the mechanical behavior of regenerating primary cell walls, suggesting that these components play a major role in conferring key mechanical properties in the limit of compressive small deformations. Extending this comparative approach should allow similarities and differences in component interactions in controlling wall behavior to be identified.

Analytical vibro-acoustic model of laminated spherical shell is developed in order to study the vibrational characteristics of human eyeball considering intraocular pressure (IOP) effect. Eyeball layers are assumed to be viscoelastic with frequency- and IOP-dependent properties, filled with compressible inviscid internal fluid. Love's first approximation theory, along with the method of stress function, is used to formulate the governing equations of motion for a laminated spherical shell. The wave equation models the internal acoustic domain, and fluid-solid interaction is accounted for by enforcing velocity and stress continuity condition at the interface. The coupled system frequency equations are derived using the modal expansion method in conjunction with the orthogonality property of mode shapes. The analytical results are validated with the available literature and compared with the finite element simulations. The effects of different parameters including elastic modulus, eyeball thickness and radius, IOP variation, and frequency- and pressure-dependent properties on natural frequencies and damping characteristics are studied. It is observed that multi-layer modelling reduces natural frequencies slightly, whereas incorporating frequency- and IOP-dependent viscoelastic properties significantly increase them, demonstrating the critical importance of viscoelastic modelling for accurate eyeball biomechanics.

Integrating machine learning or deep learning models into autonomous underwater vehicles often requires extra steps with an accuracy trade-off, and the scarcity of training datasets makes it inconvenient. This work introduces a reduced-order identification approach for thin spherical shells using sparse hydrophone measurements. Because these impedances are unique to a given scatterer, the central hypothesis is that they provide strong identification potential. The method begins by using established techniques to analytically reconstruct the scattered field from hydrophone measurements. From this field, the surface pressures and velocities corresponding to each spherical harmonic are obtained and used to compute the in vacuo mechanical impedance. The method's effectiveness is then evaluated using synthetic data with added noise. Results demonstrate that Modal Mechanical Impedance Estimation can approximate the first two modal mechanical impedances with absolute percentage error less than 10% in the low-frequency range (ka ≤ 2.1) with only 10 hydrophones. Its performance is limited by directivity due to increasing frequency. By enabling efficient computation without any training phase, the proposed method stands out as a promising candidate for real-time and low-energy applications.

Be stars are currently viewed as B-type stars surrounded by a disc fuelled by the star itself during episodic excretion events. The origin of these events is poorly understood. This study aims to determine whether surface equatorial Kelvin waves can be unstable and therefore can play a role in triggering the Be phenomenon. We first derived an analytical expression for gravito-inertial modes in the shallow water framework. We then numerically investigated the evolution of equatorial Kelvin modes as the system parameters varied. We extended the study to thick-layer configurations with a constant-density fluid. We then analysed the stability of these modes under differential rotation and viscous effects. We show that equatorial Kelvin waves still exist in a spherical shell of finite thickness, but their equatorial confinement is weaker. At low azimuthal wave numbers, Kelvin waves lie in the inertial-wave frequency band and therefore exhibit specificities of inertial waves, such as shear layers associated with singularities of the Poincaré equation. These shear layers constitute new dissipative structures for Kelvin waves. When a radial (shellular) differential rotation is imposed, we show that equatorial Kelvin waves can be destabilised, provided that differential rotation and viscosity are in an appropriate range. We trace back the non-monotonic behaviour of the instability growth rate to the rise of a critical layer where the fluid azimuthal velocity equals the phase speed of the surface waves. This study provides new insights into the behaviour of equatorial Kelvin waves in astrophysics, particularly in rapidly rotating stars. The results reinforce the idea that gravito-inertial waves, and more specifically the equatorial Kelvin waves, can be unstable and thus constitute key components in the mechanisms leading to the Be phenomenon.

The even-even superheavy nuclei with 104 ≤ Z ≤ 126 and N ≤ 258 have been investigated using a microscopic five-dimensional collective Hamiltonian (5DCH) based on constrained triaxial relativistic Hartree-Bogoliubov calculations with the PC-PK1 density functional. The 5DCH approach effectively captures the characteristic of isospin dependence of nuclear binding energies, two-nucleon separation energies, and α -decay energies across isotopic chains and demonstrates consistent accuracy as Z increases, underscoring the model’s predictive power. The collective potentials, average quadrupole deformations, and characteristic collective observables: E ( 2 1 + ) , R 42 , and B ( E 2 ; 2 1 + → 0 1 + ) reveal a shape transition from well-prolate deformation around N = 150 and N = 210 to medium-deformed γ -soft shape around N = 176 and N = 246 , and finally to a spherical shape near N = 184 and N = 258 for the isotopic chains with 104 ≤ Z ≤ 118. Oblate deformations are favored for Z ≥ 120 isotopes around N = 178 . Remarkably, for a substantial range of transitional superheavy nuclei with N ≳ 184 and N ≳ 240, no 0 + states bounded by the fission saddles are predicted within their very shallow potential wells due to quantum shape fluctuations (QSFs). Additionally, sharp variations predicted for two-neutron separation energies S 2 n and α -decay energies Q α at N = 184 and 258 in mean-field calculations are significantly reduced and shifted to N = 182 and 256 in the 5DCH calculations, which is caused by the rapid evolution of the dynamical correlation energies related to QSFs around the nuclear spherical shells.

ABSTRACT Al‐doped lithium lanthanum zirconate (Li 7 La 3 Zr 2 O 12 , LLZO) is a promising solid electrolyte material for all‐solid‐state lithium batteries due to its high ionic conductivity and thermal stability. Flame‐based synthesis is an effective method for synthesizing nanoscale LLZO particles. In the present study, we propose a combined spray‐drying and flame‐based synthesis (SD‐FS) process for producing cubic‐phase LLZO, using a rotating‐plane premixed stagnation flame (RPSF) apparatus with cost‐effective feedstocks (including nitrate salt, water, and ethanol), followed by sintering processes to obtain a high‐performance LLZO solid electrolyte. The combined SD‐FS mechanism and the effect of sintering methods on the ionic conductivity of final LLZO solid electrolytes are investigated. Experiments and mathematical models reveal that the fed droplets undergo the stages of solvent evaporation, spherical shell precipitation, precursor melting and evaporation, nucleation, and collision, ultimately forming nanoparticles. The nano‐sized morphology and the hot‐pressing sintering, which involves a high pressure (40 MPa) with heating (1473 K for 2 h), are proven beneficial to the ionic conductivity of the sintered electrolyte pellets. Al‐doped LLZO SSE pellets with an ionic conductivity of 4.7 × 10 ‒4 S·cm ‒1 are synthesized using ethanol‐blended nitrate aqueous solution as the precursor and employing the hot‐pressing method as the sintering process.

Dissolution of a strained spherical shell embedded in a matrix

We construct a novel effective field theory for a compact body coupled to gravity, whose key feature is that the dynamics of gravitational perturbations is explicitly determined by known solutions in black hole perturbation theory in four dimensions. In this way, the physics of gravitational perturbations in curved space are already encoded in the effective field theory, thus bypassing the need for the higher-order calculations that constitute a major hurdle in standard approaches. Concretely, we model the compact body as a spherical shell, whose finite size regulates short-distance divergences in four dimensions and whose tidal responses are described by higher-dimensional operators. As an application, we consider scalar perturbations and derive new results for scalar Love numbers through O(G^{9}) for Schwarzschild black holes and for generic compact bodies. Finally, our analysis reveals an intriguing structure of the scalar black-hole Love numbers in terms of the Riemann zeta function, which we conjecture to hold to all orders.

Dielectric and magnetic spherical hollow shells are employed in many applications as standard building units. These structures are commonly subjected to size reduction to obtain a high surface area/volume ratio, a property that is in favor of specific applications. However, the size reduction enhances the importance of physical mechanisms that originate from surfaces, such as the depolarization effect. Here we tackle the problem of dielectric and magnetic spherical hollow shells, consisting of a linear, homogeneous and isotropic parent material, subjected to an external potential, Uext(r), of any spatial form (either dc (static) or ac of low-frequency (quasistatic limit)). By applying the method-of-linear-recursive-solution (MLRS) to the Laplace equation, we calculate analytically the internal, Uint(r), and total, Utot(r), potentials in respect to the external one, Uext(r). From Uint(r) and Utot(r) we calculate all relevant scalar and vector physical entities of interest. The MLRS unveils straightforwardly the existence of two distinct depolarization factors, Nl=l/(2l+1) and Nl+1=(l+1)/(2l+1), both depending on the degree, l, however not on the order, m, of the mode of the external potential, Uext(l,m)(r). These depolarization factors, Nl and Nl+1, originate from the outer, r=b, and inner, r=a, surfaces and are accompanied by two extrinsic susceptibilities, χe,lext=χe/(1+Nlχe) and χe,l+1ext=χe/(1+Nl+1χe), respectively. Importantly, Nl+Nl+1=1, irrespective of the degree, l, as it should. The properties of spherical hollow shells are investigated through analytical modeling and detailed simulations, with emphasis on application-relevant scenarios including resonance phenomena in scattering, quantitative materials characterization, and shielding/distortion. The generic MLRS strategy provides a flexible and reliable route for analyzing depolarization processes in other dielectric and magnetic building-unit geometries encountered in practice.

This study introduces a refined multi-objective optimization framework using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). It strategically positions solid stiffening rings in spherical sandwich shells to enhance a defined set of natural frequencies. The NSGA-II employs fast non-dominated sorting, crowding distance assignment, and elitist selection to maintain solution diversity and convergence. This method efficiently explores the design space, balancing conflicting objectives to produce a well-distributed Pareto front. Optimized configurations offer potential for aerospace applications, including lightweight satellite structures and high-performance pressure vessels that demand superior modal characteristics. The sandwich shells consist of Graphene Platelet-Reinforced Nanocomposite (GPLRC) face sheets and a porous core. The model is based on First-Order Shear Deformation Theory (FSDT) and Sanders’ strain relations for deep shells, with linear elasticity for each layer. Stiffening rings are modeled as artificial circumferential springs. The 2D Ritz method with a combination of Chebyshev and trigonometric polynomials minimizes the system’s Lagrangian to derive the governing equations. Solving the eigenvalue problem provides the natural frequencies. This NSGA-II-based approach delivers a robust Pareto front of optimal ring placements, advancing frequency-based optimization in spherical sandwich shell structures. Results demonstrate that the optimized configurations achieve significant frequency enhancement, confirming the effectiveness of the proposed approach in structural vibration control.

Inflation and instability responses of an incompressible transversely isotropic hyperelastic spherical shell: Role of constitutive models

It has been demonstrated that rotational-vortex geomorphology is not only a science but also the leading, longest-lasting, and most persistent global factor in shaping the rapidly rotating Earth. It manifested itself from the initial stage of Earth's growth as an accretionary planet, and the ellipsoid of the Proto-Earth was inherited from the growing core of a rapidly rotating counterclockwise spiral vortex that orbited the Sun. The vortex core, thanks to a complex, multilayered, and multi-faceted set of turbulent processes occurring there, transformed into a layered, rapidly rotating planet–Earth–composed of spherical shells. Rotation served as the primary and main global cause of dynamic shaping processes occurring in the lithosphere, as well as those associated with the planet's hydrosphere and atmosphere. A key consequence of the rotational effect and spiral vortices is their indirect influence on terrestrial shaping through the organic life they enabled, including humans. The origin of life is the active and complex interaction between lithospheric vortices and the vortex structures of the Earth's liquid outer core. The vortex structures of the liquid core have been and remain the generators of alternating electric and magnetic fields.

Singly and doubly scandium-doped aluminum clusters ScmAln−m+/0/− with m = 1–2 and n = 3–15 are systematically investigated using density functional theory (DFT) with the PBE functional and the def2-TZVP basis set. Incorporation of scandium atoms significantly enhances the thermodynamic stability of aluminum clusters, following the trend of Sc2Aln−2+/0/− > ScAln−1+/0/− > Aln+/0/−. Structural evolution of these systems is constructed from three building units, including a three-atom triangle, a six-atom octahedron and a thirteen-atom icosahedron. Owing to the isovalent nature of Sc and Al, the doped clusters exhibit extensive delocalization of valence electrons, giving rise to metal aromaticity that spans all structural centers. The bonding network consists of unpolarized Al–Al interactions combined with polarized Alδ+–Scδ− or Alδ+–Alδ- bonds, where Sc atoms primarily act as electron acceptors. Progressive electron filling across charge states reveals the 20- and 40-electron shell closure tendencies for the six- and thirteen-atom clusters, respectively. The six-atom clusters show a progressive tendency to achieve the [(1S)2(1P)6(2S)2(1D)10] electron shell, whereas the thirteen-atom clusters tend toward the [(1S)2(1P)6(2S)2(1D)10(2P)6(1F)14] configuration, corresponding to their octahedral and icosahedral structures, respectively. These spherical shell fillings account for the exceptional stability, well-ordered electronic structures, and synchronization between electronic and geometric features observed in both cluster families.

SummaryIn this investigation, we have examined the fundamental problem of streaming motion in a liquid-filled sphere undergoing lateral oscillations. Such motion can be externally created, or exists in spacecrafts where g -jitter is well known. The important point here is that for spatially constant liquid density, such an internal problem is degenerate, when no non-trivial oscillatory flow and hence no streaming occur. However, this totally changes in the presence of some density stratification, which may be due to compositional and/or thermal non-uniformities. To clarify the phenomenon in simplest possible terms, we here just consider a constant volumetric heating source within the liquid and isothermal container walls. Proceeding with oscillatory displacement of the spherical shell, we assume a high-frequency limit relative to the viscous and thermal times, and a small displacement amplitude relative to the container (sphere) size. Treating the oscillations as a perturbation to an otherwise stationary shell, two steady streaming contributions are revealed. One is driven in the bulk of the liquid, which is atypical in the incompressible-liquid limit. The other classically originates in the Stokes layer at the boundary also engaging the bulk by viscosity. Even if the former is asymptotically greater here, it does not turn out to be practical to outright disregard the latter. The reason is the particularly low prefactor values arising in the former, which is typical for the internal problem. The streaming pattern consists of two or four axially symmetric vortices, which are dependent on the result of the competition between the two contributions.

Searching stable orbits in BiER4BP with variable eccentricity for exploring the stable drift dynamics of Dyson sphere shells

Studying physical mechanisms and common geometric principles underlying known spherical packings is crucial for the rational design of synthetic nanocontainers. Here we model the growth of small spherical shells containing n ≤ 72 identical particles that have their own curvature and interact with each other via the Lennard-Jones potential. The shell assembly is assumed to be nonequilibrium and sequential: at each step, a new particle is attached to the most energetically favorable position, after which the system relaxes. Along with well-known structures of the smallest icosahedral viral protein shells, the proposed mechanism generates a wide range of shells exhibiting square-triangular surface order. Most of such shells are the models of synthetic or natural protein complexes that have octahedral or tetrahedral symmetries and perform various functions. We compare the obtained structures with those resulting from the equilibrium assembly and corresponding to global energy minima. Also, we consider the temperature-dependent stochastic assembly and use the double-minimum Lennard-Jones-Gauss potential to mimic anisotropic particle interactions.

Abstract Latitudinal variations in heat transport shape the thermal and magnetic evolution of rapidly rotating planets, stars, and icy moons. Although global simulations have revealed strong equatorial–polar contrasts, a predictive scaling theory has been lacking. Here we use rotating Rayleigh‐Bénard convection with tilted rotation and gravity axes to model dynamics at different latitudes in the geostrophic regime. We derive scaling relations for convective length scales and the Nusselt number that explain the latitude dependence of heat transfer. At high latitudes, near onset and above onset; at low latitudes, . These relations, validated against direct numerical simulations in spherical shells, unify local and global models. The results provide the first predictive framework for latitude‐dependent rotating thermal convection, with implications for Earth's core, gas giants, stellar interiors, and ocean circulation in icy moons.