The existence of a positive solution to a Kirchhoff type problem on RN is proved by using variational methods, and the new result does not require usual compactness conditions. A cut-off functional ...is utilized to obtain the bounded Palais–Smale sequences.
The variational method complemented with the use of explicitly correlated Gaussian basis functions is one of the most powerful approaches currently used for calculating the properties of few-body ...systems. Despite its conceptual simplicity, the method offers great flexibility, high accuracy, and can be used to study diverse quantum systems, ranging from small atoms and molecules to light nuclei, hadrons, quantum dots, and Efimov systems. The basic theoretical foundations are discussed, recent advances in the applications of explicitly correlated Gaussians in physics and chemistry are reviewed, and the strengths and weaknesses of the explicitly correlated Gaussians approach are compared with other fewbody techniques.
Using variational methods, we establish the existence of infinitely many solutions to an elliptic problem driven by a Choquard term and a singular nonlinearity. We further show that if the problem ...has a positive solution, then it is bounded a.e. in the domain Ω and is Hölder continuous.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
The accelerated progress in manufacturing noisy, intermediate-scale quantum (NISQ) computing hardware has opened the possibility of exploring its application in transforming approaches to solving ...computationally challenging problems. The important limitations common among all NISQ computing technologies are the absence of error correction and the short coherence time, which limit the computational power of these systems. Shortening the required time of a single run of a quantum algorithm is essential for reducing environment-induced errors and for the efficiency of the computation. We have investigated the ability of a variational version of adiabatic state preparation (ASP) to generate an accurate state more efficiently compared to existing adiabatic methods. The standard ASP method uses a time-dependent Hamiltonian, connecting the initial Hamiltonian with the final Hamiltonian. In the current approach, a navigator Hamiltonian is introduced which has a non-zero amplitude only in the middle of the annealing process. Both the initial and navigator Hamiltonians are determined using variational methods. A Hermitian cluster operator, inspired by coupled-cluster theory and truncated to single and double excitations/de-excitations, is used as a navigator Hamiltonian. A comparative study of our variational algorithm (VanQver) with that of standard ASP, starting with a Hartree-Fock Hamiltonian, is presented. The results indicate that the introduction of the navigator Hamiltonian significantly improves the annealing time required to achieve chemical accuracy by two to three orders of magnitude. The efficiency of the method is demonstrated in the ground-state energy estimation of molecular systems, namely, H2, P4, and LiH.
In this manuscript we study the existence and multiplicity of solutions for a singular equation involving Orlicz-Sobolev spaces. The approach is based on sub-supersolutions and variational methods.
In this paper, we study a generalized quasilinear Choquard equation−εpΔpu+V(x)|u|p−2u=εμ−N(∫RNQ(y)F(u(y))|x−y|μ)Q(x)f(u)in RN, where Δp is the p-Laplacian operator, 1<p<N, V and Q are two continuous ...real functions on RN, 0<μ<N, F(s) is the primate function of f(s) and ε is a positive parameter. Under suitable assumptions on p,μ and f, we establish a new concentration behavior of solutions for the quasilinear Choquard equation by variational methods. The results are also new for the semilinear case p=2.
Traditional analytic homogenization methods of granular micromechanics limit the maximum predicted effective Poisson’s ratio to at most 1/4 for strain-driven constitutive models. However, this ...prediction disagrees with both the experimental evidence and discrete element method (DEM) simulations of many granular materials. To resolve this problem, a novel data-driven and volume-constrained homogenization of nonlinear granular elasticity is proposed with only the incompressible-limit upper bound on Poisson’s ratio of 1/2. Due to the volume constraint, the proposed formulation bears similarity to techniques in state-based peridynamics and, likewise, classical mixed finite elements. The new multiscale model is designed to be particularly advantageous for machine learning of effective moduli from DEM simulations (and other data sources) informed by the packings’ topology, specifically the average number of intergranular contacts per grain (the coordination number). Self-consistent elastic solutions for structured granular packings supplement DEM data in model training in order to cover a larger parameter space, demonstrating the flexibility of the method. The homogenization approach is further developed to capture glass bead packs’ semi-Hertzian nonlinearity. The designed utility for data-driven modeling is exemplified in the training of a micromechanically-sensitive input-convex neural network (ICNN) constitutive model applied in finite element analysis of an illustrative boundary value problem.
•Data-driven approach incorporates emulator models into granular micromechanics.•DEM simulations and self-consistent solutions inform predictions.•Volume-constrained formulation defines micro-to-macro static/kinematic relations.•Removes unphysical limit on Poisson’s ratio of 1/4 for kinematic-based methods.•Extended to capture monodisperse glass bead packs’ elastic nonlinearity.
In this paper, we study the existence of multiple normalized solutions for a Choquard equation involving fractional p-Laplacian in RN. With the help of variational methods, minimization techniques, ...and the Lusternik–Schnirelmann category, the existence of multiple normalized solutions is obtained for the above problem.
We propose a decentralized variant of Monte Carlo tree search (MCTS) that is suitable for a variety of tasks in multi-robot active perception. Our algorithm allows each robot to optimize its own ...actions by maintaining a probability distribution over plans in the joint-action space. Robots periodically communicate a compressed form of their search trees, which are used to update the joint distribution using a distributed optimization approach inspired by variational methods. Our method admits any objective function defined over robot action sequences, assumes intermittent communication, is anytime, and is suitable for online replanning. Our algorithm features a new MCTS tree expansion policy that is designed for our planning scenario. We extend the theoretical analysis of standard MCTS to provide guarantees for convergence rates to the optimal payoff sequence. We evaluate the performance of our method for generalized team orienteering and online active object recognition using real data, and show that it compares favorably to centralized MCTS even with severely degraded communication. These examples demonstrate the suitability of our algorithm for real-world active perception with multiple robots.
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