Search results for: statistical mechanics

Authors: M. Sikoń, E. Bidzińska

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An attempt to apply EPR (Electron Paramagnetic Resonance) spectroscopy to experimental analysis of the mechanical state of the loaded material is considered in this work. Theory concerns the participation of electrons in transfer of mechanical action. The model of measurement is shown by applying classical mechanics and quantum mechanics. Theoretical analysis is verified using EPR spectroscopy twice, once for the free spacemen and once for the mechanical loaded spacemen. Positive results in the form of different spectra for free and loaded materials are used to describe the mechanical state in continuum based on statistical mechanics. Perturbation of the optical electrons in the field of the mechanical interactions inspires us to propose new optical properties of the materials with mechanical stresses.

Keywords: Cosserat medium, EPR spectroscopy, optical active electrons, optical activity

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Authors: Forrest Kaatz, Adhemar Bultheel

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We use an informational statistical mechanics approach to study the catalytic thermodynamics of platinum and palladium cuboctahedral nanoclusters. Nanoclusters and their adatoms are viewed as chemical graphs with a nearest neighbor adjacency matrix. We use the Morse potential to determine bond energies between cluster atoms in a coordination type calculation. We use adsorbate energies calculated from density functional theory (DFT) to study the adatom effects on the thermodynamic quantities, which are derived from a Hamiltonian. Oxygen radical and molecular adsorbates are studied on platinum clusters and hydrogen on palladium clusters. We calculate the entropy, free energy, and total energy as the coverage of adsorbates increases from bridge and hollow sites on the surface. Thermodynamic behavior versus adatom coverage is related to the structural distribution of adatoms on the nanocluster surfaces. The thermodynamic functions are characterized using a simple adsorption model, with linear trends as the coverage of adatoms increases. The data exhibits size effects for the measured thermodynamic properties with cluster diameters between 2 and 5 nm. Entropy and enthalpy calculations of Pt-O2 compare well with previous theoretical data for Pt(111)-O2, and our Pd-H results show similar trends as experimental measurements for Pd-H2 nanoclusters. Our methods are general and may be applied to wide variety of nanocluster adsorbate systems.

Keywords: catalytic thermodynamics, palladium nanocluster absorbates, platinum nanocluster absorbates, statistical mechanics

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Authors: A. Maghari, V. M. Maleki

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In this paper, we present a quantum statistical mechanical formulation from our recently analytical expressions for partial-wave transition matrix of a three-particle system. We report the quantum reactive cross sections for three-body scattering processes 1 + (2,3)-> 1 + (2,3) as well as recombination 1 + (2,3) -> 2 + (3,1) between one atom and a weakly-bound dimer. The analytical expressions of three-particle transition matrices and their corresponding cross-sections were obtained from the three-dimensional Faddeev equations subjected to the rank-two non-local separable potentials of the generalized Yamaguchi form. The equilibrium quantum statistical mechanical properties such partition function and equation of state as well as non-equilibrium quantum statistical properties such as transport cross-sections and their corresponding transport collision integrals were formulated analytically. This leads to obtain the transport properties, such as viscosity and diffusion coefficient of a moderate dense gas.

Keywords: statistical mechanics, nonlocal separable potential, three-body interaction, faddeev equations

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Authors: Samaneh Farokhirad, Fatemeh Ahmadpoor

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Biological membranes are constantly in contact with various filamentous soft nanostructures that either reside on their surface or are being transported between the cell and its environment. In particular, viral infections are determined by the interaction of viruses (such as filovirus) with cell membranes, membrane protein organization (such as cytoskeletal proteins and actin filament bundles) has been proposed to influence the mechanical properties of lipid membranes, and the adhesion of filamentous nanoparticles influence their delivery yield into target cells or tissues. The goal of this research is to integrate the rapidly increasing but still fragmented experimental observations on the adhesion and self-assembly of nanofilaments (including filoviruses, actin filaments, as well as natural and synthetic nanofilaments) on cell membranes into a general, rigorous, and unified knowledge framework. The global outbreak of the coronavirus disease in 2020, which has persisted for over three years, highlights the crucial role that nanofilamentbased delivery systems play in human health. This work will unravel the role of a unique property of all cell membranes, namely flexoelectricity, and the significance of nanofilaments’ flexibility in the adhesion and self-assembly of nanofilaments on cell membranes. This will be achieved utilizing a set of continuum mechanics, statistical mechanics, and molecular dynamics and Monte Carlo simulations. The findings will help address the societal needs to understand biophysical principles that govern the attachment of filoviruses and flexible nanofilaments onto the living cells and provide guidance on the development of nanofilament-based vaccines for a range of diseases, including infectious diseases and cancer.

Keywords: virus nanofilaments, cell mechanics, computational biophysics, statistical mechanics

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Authors: F. Berna Benli, Özgür Keskin

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Lately, many mathematicians have been studied the statistical convergence of a sequence of fuzzy numbers. We know that Lambda-statistically convergence is a kind of convergence between ordinary convergence and statistical convergence. In this paper, we will introduce the new kind of convergence such as λ-levelwise statistical convergence. Then, we will define the concept of the λ-levelwise statistical cluster and limit points of a sequence of fuzzy numbers. Also, we will discuss the relations between the sets of λ-levelwise statistical cluster points and λ-levelwise statistical limit points of sequences of fuzzy numbers. This work has been extended in this paper, where some relations have been considered such that when lambda-statistical limit inferior and lambda-statistical limit superior for lambda-statistically convergent sequences of fuzzy numbers are equal. Furthermore, lambda-statistical boundedness condition for different sequences of fuzzy numbers has been studied.

Keywords: fuzzy number, λ-levelwise statistical cluster points, λ-levelwise statistical convergence, λ-levelwise statistical limit points, λ-statistical cluster points, λ-statistical convergence, λ-statistical limit points

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Authors: Yogesh D. Bansod, Jiri Bursa

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The quantitative study of cell mechanics is of paramount interest since it regulates the behavior of the living cells in response to the myriad of extracellular and intracellular mechanical stimuli. The novel experimental techniques together with robust computational approaches have given rise to new theories and models, which describe cell mechanics as a combination of biomechanical and biochemical processes. This review paper encapsulates the existing continuum-based computational approaches that have been developed for interpreting the mechanical responses of living cells under different loading and boundary conditions. The salient features and drawbacks of each model are discussed from both structural and biological points of view. This discussion can contribute to the development of even more precise and realistic computational models of cell mechanics based on continuum approaches or on their combination with microstructural approaches, which in turn may provide a better understanding of mechanotransduction in living cells.

Keywords: cell mechanics, computational models, continuum approach, mechanical models

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Authors: J. Ismail, F. Zaïri, M. Naït-Abdelaziz, Z. Azari

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In this work, a combined approach of continuum damage mechanics (CDM) and fracture mechanics is applied to model a glass plate behavior under static indentation. A spherical indenter is used and a CDM based constitutive model with an anisotropic damage tensor was selected and implemented into a finite element code to study the damage of glass. Various regions with critical damage values were predicted in good agreement with the experimental observations in the literature. In these regions, the directions of crack propagation, including both cracks initiating on the surface as well as in the bulk, were predicted using the strain energy density factor.

Keywords: finite element modeling, continuum damage mechanics, indentation, cracks

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Authors: Ven. Bhikkhu Ananda

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Mind emerged from the quantum field. The practice of mediation can take one to the state of enlightenment. During meditation, the change in the very behaviour of electrons, protons, and photons and their fields, known to be quantum fields, create mental states. This could well be expressed in the mathematical language of quantum mechanics. This paper qualifies and quantifies mental states created during meditation and is explained by quantum mechanics. In meditation, phenomenology can be seen as the process of enlightenment. In this process, the emptiness shown in Buddhist philosophy and the emptiness of quantum fields is compared. The methodologies used here are mindfulness meditation and metta mediation (compassion meditation ). The research findings suggest not only quantumness and change are consciousness, but well-founded behaviour of an individual in the society, which can amplify the positive behaviour caused by mental states, and that emptiness and impermanence of phenomenon are based on dependent arisings. The presence of quantum coherence indicates that quantum mechanics has a role in the evolution of the pure mind and the phenomenology created thereof in mediation.

Keywords: meditation, mental states, quantum mechanics, enlightenment

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Authors: Jianguo Chen, Fenggang Zang, Yu Yang, Liangang Zheng

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Reactor Pressure Vessel (RPV) is an important security barrier in nuclear power plant. Crack like defects may be produced on RPV during the whole operation lifetime due to the harsh operation condition and irradiation embrittlement. During the severe loss of coolant accident, thermal shock happened as the injection of emergency cooling water into RPV, which results in re-pressurization of the vessel and very high tension stress on the vessel wall, this event called Pressurized Thermal Shock (PTS). Crack on the vessel wall may propagate even penetrate the vessel, so the safety of the RPV would undergo great challenge. Many assumptions in structure integrity evaluation make the result of deterministic fracture mechanics very conservative, which affect the operation lifetime of the plant. Actually, many parameters in the evaluation process, such as fracture toughness and nil-ductility transition temperature, have statistical distribution characteristics. So it is necessary to assess the structural integrity of RPV subjected to PTS event by means of Probabilistic Fracture Mechanics (PFM). Structure integrity evaluation methods of RPV subjected to PTS event are summarized firstly, then evaluation method based on probabilistic fracture mechanics are presented by considering the probabilistic characteristics of material and structure parameters. A comprehensive analysis example is carried out at last. The results show that the probability of crack penetrates through wall increases gradually with the growth of fast neutron irradiation flux. The results give advice for reactor life extension.

Keywords: fracture toughness, integrity evaluation, pressurized thermal shock, probabilistic fracture mechanics, reactor pressure vessel

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Authors: Momoh Omeiza Sheidu

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Finite element method as a method of providing solutions to problems in computational bio mechanics provides a framework for modeling the function of tissues that integrates structurally from cell to organ system and functionally across the physiological processes that affect tissue mechanics or are regulated by mechanical forces. In this paper, we present an integrative finite element strategy for solution to problems in tissue bio mechanics as a case study.

Keywords: finite element, biomechanics, modeling, computational biomechanics

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Authors: Petros Roussos

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The present study focused on students' statistical reasoning related to Null Hypothesis Statistical Testing and p-values. Its objective was to test the hypothesis that neither the place (classroom, at a distance, online) nor the medium that actually supports the learning (ICT, internet, books) has an effect on understanding of statistical concepts. In addition, it was expected that students' attitudes towards statistics would not predict understanding of statistical concepts. The sample consisted of 385 undergraduate and postgraduate students from six state and private universities (five in Greece and one in Cyprus). Students were administered two questionnaires: a) the Greek version of the Survey of Attitudes Toward Statistics, and b) a short instrument which measures students' understanding of statistical significance and p-values. Results suggest that attitudes towards statistics do not predict students' understanding of statistical concepts, whereas the medium did not have an effect.

Keywords: attitudes towards statistics, blended learning, e-learning, statistical reasoning

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Authors: Ahmad Almajid

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The idea of unifying quantum mechanics with general relativity is still a dream for many researchers, as physics has only two paths, no more. Einstein's path, which is mainly based on particle mechanics, and the path of Paul Dirac and others, which is based on wave mechanics, the incompatibility of the two approaches is due to the radical difference in the initial assumptions and the mathematical nature of each approach. Logical thinking in modern physics leads us to two problems: - In quantum mechanics, despite its success, the problem of measurement and the problem of wave function interpretation is still obscure. - In special relativity, despite the success of the equivalence of rest-mass and energy, but at the speed of light, the fact that the energy becomes infinite is contrary to logic because the speed of light is not infinite, and the mass of the particle is not infinite too. These contradictions arise from the overlap of relativistic and quantum mechanics in the neighborhood of the speed of light, and in order to solve these problems, one must understand well how to move from relativistic mechanics to quantum mechanics, or rather, to unify them in a way different from Dirac's method, in order to go along with God or Nature, since, as Einstein said, "God doesn't play dice." From De Broglie's hypothesis about wave-particle duality, Léon Brillouin's definition of the new proper time was deduced, and thus the quantum Lorentz factor was obtained. Finally, using the Euler-Lagrange equation, we come up with new equations in quantum mechanics. In this paper, the two problems in modern physics mentioned above are solved; it can be said that this new approach to quantum mechanics will enable us to unify it with general relativity quite simply. If the experiments prove the validity of the results of this research, we will be able in the future to transport the matter at speed close to the speed of light. Finally, this research yielded three important results: 1- Lorentz quantum factor. 2- Planck energy is a limited case of Einstein energy. 3- Real quantum mechanics, in which new equations for quantum mechanics match and exceed Dirac's equations, these equations have been reached in a completely different way from Dirac's method. These equations show that quantum mechanics is a limited case of relativistic mechanics. At the Solvay Conference in 1927, the debate about quantum mechanics between Bohr, Einstein, and others reached its climax, while Bohr suggested that if particles are not observed, they are in a probabilistic state, then Einstein said his famous claim ("God does not play dice"). Thus, Einstein was right, especially when he didn't accept the principle of indeterminacy in quantum theory, although experiments support quantum mechanics. However, the results of our research indicate that God really does not play dice; when the electron disappears, it turns into amicable particles or an elastic medium, according to the above obvious equations. Likewise, Bohr was right also, when he indicated that there must be a science like quantum mechanics to monitor and study the motion of subatomic particles, but the picture in front of him was blurry and not clear, so he resorted to the probabilistic interpretation.

Keywords: lorentz quantum factor, new, planck’s energy as a limiting case of einstein’s energy, real quantum mechanics, new equations for quantum mechanics

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Authors: Muna Tabuni

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The paper contains an investigation of the notion of Q algebras. A brief introduction to quantum mechanics is given, in that systems the state defined by a vector in a complex vector space H which have Hermitian inner product property. H may be finite or infinite-dimensional. In quantum mechanics, operators must be hermitian. These facts are saved by Lie algebra operators but not by those of quantum algebras. A Hilbert space H consists of a set of vectors and a set of scalars. Lie group is a differentiable topological space with group laws given by differentiable maps. A Lie algebra has been introduced. Q-algebra has been defined. A brief introduction to BCI-algebra is given. A BCI sub algebra is introduced. A brief introduction to BCK=BCH-algebra is given. Every BCI-algebra is a BCH-algebra. Homomorphism maps meanings are introduced. Homomorphism maps between two BCK algebras are defined. The mathematical formulations of quantum mechanics can be expressed using the theory of unitary group representations. A generalization of Q algebras has been introduced, and their properties have been considered. The Q- quantum algebra has been studied, and various examples have been given.

Keywords: Q-algebras, BCI, BCK, BCH-algebra, quantum mechanics

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Authors: M. Blokh

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Method of combined teaching laws of classical mechanics and hydrostatics in non-inertial reference frames for undergraduate students is proposed. Pressure distribution in a liquid (or gas) moving with acceleration is considered. Combined effect of hydrostatic force and force of inertia on a body immersed in a liquid can lead to paradoxical results, in a motion of pendulum in particular. The body motion under Stokes force influence and forces in rotating reference frames are investigated as well. Problems and difficulties in student perceptions are analyzed.

Keywords: hydrodynamics, mechanics, non-inertial reference frames, teaching

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Authors: Neha Bhardwaj

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In this paper, we consider positive linear operators and study the Voronovskaya type result of the operator then obtain an error estimate in terms of the higher order modulus of continuity of the function being approximated and its A-statistical convergence. Also, we compute the corresponding rate of A-statistical convergence for the linear positive operators.

Keywords: Poisson distribution, Voronovskaya, modulus of continuity, a-statistical convergence

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Authors: Lukanda Kalobo

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In South Africa, the High School Mathematics Curriculum provides teachers with specific aims and skills to be developed which involves the understanding about the measures of central tendency. The exploration begins with the definitions of statistical literacy, measurement of central tendency and a discussion on why statistical literacy is essential today. It furthermore discusses the statistical literacy basics involved in understanding the concepts of measures of central tendency. The statistical literacy test on the measures of central tendency, was used to collect data which was administered to 78 first year students direct from high schools. The results indicated that students seemed to have forgotten about the statistical literacy in understanding the concepts of measure of central tendency after completing their high school study. The authors present inferences regarding the alignment between statistical literacy and the understanding of the concepts about the measures of central tendency, leading to the conclusion that there is a need to provide in-service and pre-service training.

Keywords: conceptual understanding, mean, median, mode, statistical literacy

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Authors: Mustapha Majid

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Gone were the days when technicians/mechanics will have to spend too much time trying to identify a mechanical fault and rectify the problem. Now the emphasis is on the use of Automobile diagnosing Equipment through the use of computers and special software. An investigation conducted at Tamale Metropolis and Accra in the Northern and Greater Accra regions of Ghana, respectively. Methodology for data gathering were; questionnaires, physical observation, interviews, and newspaper. The study revealed that majority of mechanics lack computer skills which can enable them use diagnosis tools such as Exhaust Gas Analyzer, Scan Tools, Electronic Wheel Balancing machine, etc.

Keywords: diagnosing, local garages and modern garages, lack of knowledge of diagnosing posing an existential threat, training of local mechanics

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Authors: Ahmet Kaya

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Incoming cash flows and outgoing claims play an important role to determine how is companies’ profit or loss. In this matter, ruin probability provides to describe vulnerability of the companies against ruin. Quantum mechanism is one of the significant approaches to model ruin probability as stochastically. Using the Hamiltonian method, we have performed formalisation of quantum mechanics < x|e-ᵗᴴ|x' > and obtained the transition probability of 2x2 and 3x3 matrix as traditional and eigenvector basis where A is a ruin operator and H|x' > is a Schroedinger equation. This operator A and Schroedinger equation are defined by a Hamiltonian matrix H. As a result, probability of not to be in ruin can be simulated and calculated as stochastically.

Keywords: ruin probability, quantum mechanics, Hamiltonian technique, operator approach

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Authors: Paulo Castro, J. R. Croca, M. Gatta, R. Moreira

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Owing to the development of quantum mechanics, we will contextualize the foundations of the theory on the Fourier analysis framework, thus stating the unavoidable philosophical conclusions drawn by Niels Bohr. We will then introduce an alternative way of describing the undulatory aspects of quantum entities by using gaussian Morlet wavelets. The description has its roots in de Broglie's realistic program for quantum physics. It so happens that using wavelets it is possible to formulate a more general set of uncertainty relations. A set from which it is possible to theoretically describe both ends of the behavioral spectrum in reality: the indeterministic quantum trajectorial foam and the perfectly drawn Newtonian trajectories.

Keywords: philosophy of quantum mechanics, quantum realism, morlet wavelets, uncertainty relations, determinism

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Authors: Aathira H.

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Digital games can act as catalysts for educational transformation in the current scenario. Children and adolescence acquire this digital knowledge quickly and hence digital games can act as one of the most effective media for technology-mediated learning. Mobile gaming industries have seen the rise of a new trending genre of games, i.e., “Merge games” which is currently thriving in the market. This paper analysis on how gamifying historic and cultural narratives with merge mechanics can be an effective way to educate school children. Through the study of how merge mechanics in games have currently emerged as a trend., this paper argues how it can be integrated with a strong narrative which can convey history in an engaging way for education.

Keywords: game-based learning, merge mechanics, historical narratives, gaming innovations

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Authors: R. Pravin Kumar, L. Roopa

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Enzymes are molecular machines used in various industries such as pharmaceuticals, cosmetics, food and animal feed, paper and leather processing, biofuel, and etc. Nevertheless, this has been possible only by the breath-taking efforts of the chemists and biologists to evolve/engineer these mysterious biomolecules to work the needful. Main agenda of this enzyme engineering project is to derive screening and selection tools to obtain focused libraries of enzyme variants with desired qualities. The methodologies for this research include the well-established directed evolution, rational redesign and relatively less established yet much faster and accurate insilico methods. This concept was initiated as a Receptor Rependent-4Dimensional Quantitative Structure Activity Relationship (RD-4D-QSAR) to predict kinetic properties of enzymes and extended here to study transaminase by a 7D QSAR approach. Induced-fit scenarios were explored using Quantum Mechanics/Molecular Mechanics (QM/MM) simulations which were then placed in a grid that stores interactions energies derived from QM parameters (QMgrid). In this study, the mutated enzymes were immersed completely inside the QMgrid and this was combined with solvation models to predict descriptors. After statistical screening of descriptors, QSAR models showed > 90% specificity and > 85% sensitivity towards the experimental activity. Mapping descriptors on the enzyme structure revealed hotspots important to enhance the enantioselectivity of the enzyme.

Keywords: QMgrid, QM/MM simulations, RD-4D-QSAR, transaminase

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Authors: Vladimir S. Timofeev

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In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique, author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation

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Authors: Petar Sarajcev, Josip Vasilj, Damir Jakus

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This paper presents a novel statistical description of the counterpoise effective length due to lightning surges, where the (impulse) effective length had been obtained by means of regressive formulas applied to the transient simulation results. The effective length is described in terms of a statistical distribution function, from which median, mean, variance, and other parameters of interest could be readily obtained. The influence of lightning current amplitude, lightning front duration, and soil resistivity on the effective length has been accounted for, assuming statistical nature of these parameters. A method for determining the optimal counterpoise length, in terms of the statistical impulse effective length, is also presented. It is based on estimating the number of dangerous events associated with lightning strikes. Proposed statistical description and the associated method provide valuable information which could aid the design engineer in optimising physical lengths of counterpoises in different grounding arrangements and soil resistivity situations.

Keywords: counterpoise, grounding conductor, effective length, lightning, Monte Carlo method, statistical distribution

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Authors: Jihye Jeon

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This paper analyzes the conceptual framework of three statistical methods, multiple regression, path analysis, and structural equation models. When establishing research model of the statistical modeling of complex social phenomenon, it is important to know the strengths and limitations of three statistical models. This study explored the character, strength, and limitation of each modeling and suggested some strategies for accurate explaining or predicting the causal relationships among variables. Especially, on the studying of depression or mental health, the common mistakes of research modeling were discussed.

Keywords: multiple regression, path analysis, structural equation models, statistical modeling, social and psychological phenomenon

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Authors: I-Ling Chang, Jer-An Chen

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The elastic properties and fracture of two-dimensional graphene were calculated purely from the atomic bonding (stretching and bending) based on molecular mechanics method. Considering the representative unit cell of graphene under various loading conditions, the deformations of carbon bonds and the variations of the interlayer distance could be realized numerically under the geometry constraints and minimum energy assumption. In elastic region, it was found that graphene was in-plane isotropic. Meanwhile, the in-plane deformation of the representative unit cell is not uniform along armchair direction due to the discrete and non-uniform distributions of the atoms. The fracture of graphene could be predicted using fracture criteria based on the critical bond length, over which the bond would break. It was noticed that the fracture behavior were directional dependent, which was consistent with molecular dynamics simulation results.

Keywords: energy minimization, fracture, graphene, molecular mechanics

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Authors: Queen Suraajini Rajendran, Sai Hung Cheung

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Statistical down scaling models are required to connect the global climate model outputs and the local weather variables for climate change impact prediction. For reliable climate change impact studies, the uncertainty associated with the model including natural variability, uncertainty in the climate model(s), down scaling model, model inadequacy and in the predicted results should be quantified appropriately. In this work, a new approach is developed by the authors for statistical classification, statistical down scaling and uncertainty assessment and is applied to Singapore rainfall. It is a robust Bayesian uncertainty analysis methodology and tools based on coupling dependent modeling error with classification and statistical down scaling models in a way that the dependency among modeling errors will impact the results of both classification and statistical down scaling model calibration and uncertainty analysis for future prediction. Singapore data are considered here and the uncertainty and prediction results are obtained. From the results obtained, directions of research for improvement are briefly presented.

Keywords: statistical downscaling, global climate model, climate change, uncertainty

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Authors: Rishikesh Yadav, Ramakanta Meher, Vishnu Narayan Mishra

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The main aim of this article is to investigate the statistical convergence of the summation of integral type operators and to obtain the weighted statistical convergence. The rate of statistical convergence by means of modulus of continuity and function belonging to the Lipschitz class are also studied. We discuss the convergence of the defined operators by graphical representation and put a better rate of convergence than the Szasz-Mirakjan-Kantorovich operators. In the last section, we extend said operators into bivariate operators to study about the rate of convergence in sense of modulus of continuity and by means of Lipschitz class by using function of two variables.

Keywords: The Szasz-Mirakjan-Kantorovich operators, statistical convergence, modulus of continuity, Peeters K-functional, weighted modulus of continuity

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Authors: Andrey Egorov

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A product of the specific Lagrangian and the entropy factor is defined. Its positive definiteness is stated for the proper coupling constant. The passage from statistical mechanics to quantum field theory is performed by Wick rotation. The Green function (a convolution of the spectral amplitude and the propagator) is positive. Masses of quasiparticles are computed as residues. The role of the zeta derivative at zeta zeros is then highlighted, and the correspondent low bound is obtained.

Keywords: mass gap, positive definite kernels, quantum fields, Riemann zeta zeros

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Authors: Navid Zarif Karimi, Hossein Heidary, Giangiacomo Minak, Mehdi Ahmadi

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In this paper analytical model based on the mechanics of oblique cutting, linear elastic fracture mechanics (LEFM) and bending plate theory has been presented to determine the critical feed rate causing delamination in drilling of composite materials. Most of the models in this area used LEFM and bending plate theory; hence, they can only determine the critical thrust force which is an incorporable parameter. In this model by adding cutting oblique mechanics to previous models, critical feed rate has been determined. Also instead of simplification in loading condition, actual thrust force induced by chisel edge and cutting lips on composite plate is modeled.

Keywords: composite material, delamination, drilling, thrust force

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Authors: Shahriar Shahbazpanahi, Alaleh Kamgar

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So far, the conventional experimental and theoretical analysis in fracture mechanics have been applied to study concrete flexural- cracked beams, which are strengthened using fiber reinforced polymer (FRP) composite sheets. However, there is still little knowledge about the shear capacity of a side face FRP- strengthened shear-cracked beam. A numerical analysis is herein presented to model the fracture mechanics of a four-point RC beam, with two inclined initial notch on the supports, which is strengthened with side face FRP sheets. In the present study, the shear crack is forced to conduct by using an initial notch in supports. The ABAQUS software is used to model crack propagation by conventional cohesive elements. It is observed that the FRP sheets play important roles in preventing the propagation of shear cracks.

Keywords: crack, FRP, shear, strengthening

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