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Search results for: WAVEPACKETS IN QUANTUM MECHANICS

  • Biomimetic torene shells

    Publication

    - MATHEMATICS AND MECHANICS OF SOLIDS - Year 2023

    The genome inside the eukaryotic cells is guarded by a unique shell structure, called the nuclear envelope (NE), made of lipid membranes. This structure has an ultra torus topology with thousands of torus-shaped holes that imparts the structure a high flexural stiffness. Inspired from this biological design, here we present a novel ‘‘torene’’ architecture to design lightweight shell structures with ultra-stiffness for engineering...

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  • Estimation of fracture toughness and shear yield stress of orthotropic materials in cutting with rotating tools

    Publication

    - ENGINEERING FRACTURE MECHANICS - Year 2017

    The cutting force is an energetic effect of splitting material, and might be considered from a point of view of modern fracture mechanics. Forecasting of the shear plane angle in cutting broaden possibilities for modelling of the cutting process even for thin uncut chips. Such mathematical model has been developed here for description of the orthotropic materials’ cutting on the base of fracture theory, and includes work of separation...

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  • Prediction of fracture toughness in fibre-reinforced concrete, mortar, and rocks using various Machine learning techniques

    Publication

    Machine Learning (ML) method is widely used in engineering applications such as fracture mechanics. In this study, twenty different ML algorithms were employed and compared for the prediction of the fracture toughness and fracture load in modes I, II, and mixed-mode (I-II) of various materials, including fibre-reinforced concrete, cement mortar, sandstone, white travertine, marble, and granite. A set of 401 specimens of “Brazilian...

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  • A Novel Approach to Fully Nonlinear Mathematical Modeling of ‎Tectonic Plates

    Publication

    - Journal of Applied and Computational Mechanics - Year 2023

    The motion of the Earth's layers due to internal pressures is simulated in this research with an efficient mathematical model. The Earth, which revolves around its axis of rotation and is under internal pressure, will change the shape and displacement of the internal layers and tectonic plates. Applied mathematical models are based on a new approach to shell theory involving both two and three-dimensional approaches. It is the...

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  • Process zone in the Single Cantilever Beam under transverse loading. - Part II: Experimental

    Publication

    - THEORETICAL AND APPLIED FRACTURE MECHANICS - Year 2011

    This paper describes an experimental arrangement to evaluate stress/strain fields in the process zone of asymmetric adhesively bonded joints. A transparent polycarbonate flexible beam was bonded to an aluminium alloy rigid block with an epoxy adhesive in a Single Cantilever Beam (SCB) configuration. The flexible adherend was loaded in the direction parallel to the initial crack front at constant rate. To monitor strains induced...

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  • Experimentally feasible semi-device-independent certification of four-outcome positive-operator-valued measurements

    Publication

    - PHYSICAL REVIEW A - Year 2019

    Recently the quantum information science community devoted a lot of attention to the theoretical and practical aspects of generalized measurements, the formalism of all possible quantum operations leading to acquisition of classical information. On the other hand, due to imperfections present in quantum devices, and limited thrust to them, a trend of formulating quantum information tasks in a semi-device-independent manner emerged....

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  • Universal construction of genuinely entangled subspaces of any size

    Publication

    We put forward a simple construction of genuinely entangled subspaces – subspaces supporting only genuinely multipartite entangled states – of any permissible dimensionality for any number of parties and local dimensions. The method uses nonorthogonal product bases, which are built from totally nonsingular matrices with a certain structure. We give an explicit basis for the constructed subspaces. An immediate consequence of our...

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  • A continual model of a damaged medium used for analyzing fatigue life of polycrystalline structural alloys under thermal–mechanical loading

    Publication
    • I. Volkov
    • L. Igumnov
    • F. dell'Isola
    • S. Litvinchuk
    • V. Eremeev

    - CONTINUUM MECHANICS AND THERMODYNAMICS - Year 2020

    The main physical laws of thermal–plastic deformation and fatigue damage accumulation processes in polycrystalline structural alloys under various regimes of cyclic thermal–mechanical loading are considered. Within the framework of mechanics of damaged media, a mathematical model is developed that describes thermal–plastic deformation and fatigue damage accumulation processes under low-cycle loading. The model consists of three...

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  • Method for universal detection of two-photon polarization entanglement

    Publication
    • K. Bartkiewicz
    • P. Horodecki
    • K. Lemr
    • A. Miranowicz
    • K. Życzkowski

    - PHYSICAL REVIEW A - Year 2015

    Detecting and quantifying quantum entanglement of a given unknown state poses problems that are fundamentally important for quantum information processing. Surprisingly, no direct (i.e., without quantum tomography) universal experimental implementation of a necessary and sufficient test of entanglement has been designed even for a general two-qubit state. Here we propose an experimental method for detecting a collective universal...

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  • Objectivity in the non-Markovian spin-boson model

    Publication

    - PHYSICAL REVIEW A - Year 2017

    Objectivity constitutes one of the main features of the macroscopic classical world. An important aspect of the quantum-to-classical transition issue is to explain how such a property arises from the microscopic quantum theory. Recently, within the framework of open quantum systems, there has been proposed such a mechanism in terms of the so-called spectrum broadcast structures. These are multipartite quantum states of the system...

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  • New approaches to cutting resistance estimation of wood cutting process with circular-saw blades

    Publication

    - Year 2013

    Theoretical and experimental determination of values of cutting resistance belongs to the basic and simultaneously the most developed field of mechanics of this process. Energetic effects of wood sawing process are mainly calculated on the basis of the specific cutting resistance which, in wood cutting, is a function on a lot of factors. In this paper new method for calculation of cutting resistance is described. The latter method...

  • Monitoring of the Process of System Information Broadcasting in Time

    One of the problems of quantum physics is how a measurement turns quantum, noncopyable data, towards copyable classical knowledge. We use the quantum state discrimination in a central system model to show how its evolution leads to the broadcasting of the information, and how orthogonalization and decoherence factors allow us to monitor the distance of the state in question to the one perfectly broadcasting information, in any...

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  • Hidden Tensor Structures

    Publication

    - ENTROPY - Year 2024

    Any single system whose space of states is given by a separable Hilbert space is automatically equipped with infinitely many hidden tensor-like structures. This includes all quantum mechanical systems as well as classical field theories and classical signal analysis. Accordingly, systems as simple as a single one-dimensional harmonic oscillator, an infinite potential well, or a classical finite-amplitude signal of finite duration...

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  • Characterizing the Performance of <span class="sc">xor</span> Games and the Shannon Capacity of Graphs

    Publication

    - PHYSICAL REVIEW LETTERS - Year 2014

    In this Letter we give a set of necessary and sufficient conditions such that quantum players of a two-party xor game cannot perform any better than classical players. With any such game, we associate a graph and examine its zero-error communication capacity. This allows us to specify a broad new class of graphs for which the Shannon capacity can be calculated. The conditions also enable the parametrization of new families of games...

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  • Designing effective educational games - a case study of a project management game

    This paper addresses the issues of designing effective educational games. We aim at investigating how the cognitive, behavioral and emotional aspects of the games influence their educational effectiveness. The results were obtained with an observational user experience study extended with affect analysis carried out for a project management game GraPM. We analyzed the...

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  • Konzetrationslöschung durch Energieübertragung bei der Lumineszenz von Lösungen

    Publication
    • C. Bojarski
    • J. Kuśba
    • G. Obermüller

    - Year 1971

    The absorption spectra and quantum yields of the fluorescence of rhodamine 6 G are investigated in two different water-glycerol mixtures as a function of the rhodamine concentration. The observed concentration quenching is attributed to the formation of rhodamine dimers and the decrease in quantum yield is compared with theoretical concepts about concentration quenching by energy transfer to the dimers.

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  • Vibrational Quenching of Optically Pumped Carbon Dimer Anions

    Publication
    • M. Nötzold
    • R. Wild
    • C. Lochmann
    • T. Rahim
    • S. P. Melath
    • K. Dulitz
    • B. P. Mant
    • J. Franz
    • F. A. Gianturco
    • R. Wester

    - PHYSICAL REVIEW LETTERS - Year 2023

    Careful control of quantum states is a gateway to research in many areas of science such as quantum information, quantum-controlled chemistry, and astrophysical processes. Precise optical control of molecular ions remains a challenge due to the scarcity of suitable level schemes, and direct laser cooling has not yet been achieved for either positive or negative molecular ions. Using a cryogenic wire trap, we show how the internal...

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  • Increased Certification of Semi-device Independent Random Numbers using Many Inputs and More Postprocessing

    Publication
    • P. A. Mironowicz
    • A. Tavakoli
    • A. Hameedi
    • B. Marques
    • M. Pawłowski
    • M. Bourennane

    - NEW JOURNAL OF PHYSICS - Year 2016

    Quantum communication with systems of dimension larger than two provides advantages in information processing tasks. Examples include higher rates of key distribution and random number generation. The main disadvantage of using such multi-dimensional quantum systems is the increased complexity of the experimental setup. Here, we analyze a not-so-obvious problem: the relation between randomness certification and computational requirements...

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  • Report of Eurocode 7 application for pile foundation design in Poland

    Publication

    The EC7 rules of geotechnical design are in use in Poland for several years, even though there is no National annex. With regard to pile foundations, there are valid EC7 recommendations concerning design approaches, load partial coefficients, correlation coefficients and capacity partial coefficients. Polish designers can be quite flexible when it comes to choose a method for static, bearing capacity and settlement calculations....

  • Entangled rendezvous: a possible application of Bell non-locality for mobile agents on networks

    Publication

    Rendezvous is an old problem of assuring that two or more parties, initially separated, not knowing the position of each other, and not allowed to communicate, are striving to meet without pre-agreement on the meeting point. This problem has been extensively studied in classical computer science and has vivid importance to modern and future applications. Quantum non-locality, like Bell inequality violation, has shown that in many...

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  • Multidimensional Monitoring System of State Machines

    Publication

    - Year 2017

    Technical systems are more complex every day as their electronics and mechanics. Technical advances tend to be autonomous in its performance and perform an auto-diagnosis that allows determining an abnormality existence in a component or subsystem and deciding if the system has to be stopped or not.

  • Bound on Bell inequalities by fraction of determinism and reverse triangle inequality

    Publication
    • P. Joshi
    • K. Horodecki
    • M. Horodecki
    • P. Horodecki
    • R. Horodecki
    • B. Li
    • S. Szarek
    • T. Szarek

    - PHYSICAL REVIEW A - Year 2015

    It is an established fact that entanglement is a resource. Sharing an entangled state leads to nonlocal correlations and to violations of Bell inequalities. Such nonlocal correlations illustrate the advantage of quantum resources over classical resources. In this paper, we quantitatively study Bell inequalities with 2 × n inputs. As found in Gisin et al. [Int. J. Quantum. Inform. 05, 525 (2007)], quantum mechanical correlations...

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  • Bell-Type Inequalities from the Perspective of Non-Newtonian Calculus

    Publication

    A class of quantum probabilities is reformulated in terms of non-Newtonian calculus and projective arithmetic. The model generalizes spin-1/2 singlet state probabilities discussed in Czachor (Acta Physica Polonica:139 70–83, 2021) to arbitrary spins s. For s → ∞ the formalism reduces to ordinary arithmetic and calculus. Accordingly, the limit “non-Newtonian to Newtonian” becomes analogous to the classical limit of a quantum theory

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  • Towards Resource Theory of Coherence in Distributed Scenarios

    Publication

    - Physical Review X - Year 2017

    The search for a simple description of fundamental physical processes is an important part of quantum theory. One example for such an abstraction can be found in the distance lab paradigm: if two separated parties are connected via a classical channel, it is notoriously difficult to characterize all possible operations these parties can perform. This class of operations is widely known as local operations and classical communication....

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  • Framework for gamification of specialized subjects within engineering studies

    Publication

    - Year 2017

    Gamification is a relatively new term forged along with the occurrence of new information technology, especially easy access to internet and smartphones. Gamification is a use of game mechanics, to modify the behavior of people in non-games situations to increase the involvement of individuals. The method is based on the pleasure that comes from overcoming the obstacles to reach next achievable level, which consists of challenges,...

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  • Numerical Simulation of two dimensional flow past a bridge cross section

    Publication

    - Year 2013

    This work presents some numerical results concerning application of CFD in civil engineering problems. Selected theoretical aspects of fluid mechanics are elucidated. In the second part of the paper a cross section of upper footbridge of the Bella Sky Hotel in Copenhagen is analysed numerically in the field of wind action.

  • Collective Uncertainty Entanglement Test

    Publication

    - PHYSICAL REVIEW LETTERS - Year 2011

    For a given pure state of a composite quantum system we analyze the product of its projections onto aset of locally orthogonal separable pure states. We derive a bound for this product analogous to theentropic uncertainty relations. For bipartite systems the bound is saturated for maximally entangled statesand it allows us to construct a family of entanglement measures, we shall call collectibility. As thesequantities are experimentally...

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  • Optoelectronic and non-linear optical properties of Lu-doped AgGaGe3Se8 crystallites

    Publication
    • I. Kityk
    • G. Myronchuk
    • M. Lelonek
    • P. Goring
    • L. Piskach
    • B. Vidrynsky
    • A. Ryzhuk
    • A. Fedorchuk
    • J. Jedryka

    - OPTICAL AND QUANTUM ELECTRONICS - Year 2020

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  • NO-BROADCASTING OF NON-SIGNALLING BOXES VIA OPERATIONS WHICH TRANSFORM LOCAL BOXES INTO LOCAL ONES

    Publication
    • P. Joshi
    • A. Grudka
    • K. Horodecki
    • M. Horodecki
    • P. Horodecki
    • R. Horodecki

    - QUANTUM INFORMATION & COMPUTATION - Year 2013

    We deal with families of probability distributions satisfying non-signalling condition, called non-signalling boxes and consider a class of operations that transform local boxes into local ones (the one that admit LHV model). We prove that any operation from this class cannot broadcast a bipartite non-local box with 2 binary inputs and outputs. We consider a function called anti-Robustness which can not decrease under these operations....

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  • Lattice-commensurate skyrmion texture in a centrosymmetric breathing kagome magnet

    Publication
    • M. Hirschberger
    • B. G. Szigeti
    • M. Hemmida
    • M. M. Hirschmann
    • S. Esser
    • H. Ohsumi
    • Y. Tanaka
    • L. Spitz
    • S. Gao
    • K. Kolincio... and 8 others

    - npj Quantum Materials - Year 2024

    Skyrmion lattices (SkL) in centrosymmetric materials typically have a magnetic period on the nanometer-scale, so that the coupling between magnetic superstructures and the underlying crystal lattice cannot be neglected. We reveal the commensurate locking of a SkL to the atomic lattice in Gd3Ru4Al12 via high-resolution resonant elastic x-ray scattering (REXS). Weak easy-plane magnetic anisotropy, demonstrated here by a combination...

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  • Shrinking-shifting and amplifying-shifting device using transformation optics

    Publication

    - OPTICAL AND QUANTUM ELECTRONICS - Year 2022

    Based on transformation optics (TO), this paper uses geometric divisions and linear coordinate transformations to design “shrinking-shifting—and reshaping”, and “amplifying-shifting—and reshaping” devices. The proposed devices can reshape the sizes and locations of the wrapped-objects inside the core-region. The shrinking-shifting device shrinks the larger object into a smaller one and shifts it to different location, whereas the...

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  • The role of low-energy electrons in the charging process of LISA test masses

    Publication
    • S. Taioli
    • M. Dapor
    • F. Dimiccoli
    • M. Fabi
    • V. Ferroni
    • C. Grimani
    • M. Villani
    • W. J. Weber

    - CLASSICAL AND QUANTUM GRAVITY - Year 2023

    The estimate of the total electron yield is fundamental for our understanding of the test-mass charging associated with cosmic rays in the Laser Interferometer Space Antenna (LISA) Pathfinder mission and in the forthcoming gravitational wave observatory LISA. To unveil the role of low energy electrons in this process owing to galactic and solar energetic particle events, in this work we study the interaction of keV and sub-keV...

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  • Refined theoretical study of radiative association: Cross sections and rate constants for the formation of SiN

    Publication
    • M. Gustafsson
    • S. Antipov
    • J. Franz
    • G. Nyman

    - JOURNAL OF CHEMICAL PHYSICS - Year 2012

    Radiative association of silicon mononitride (SiN) in its two lowest molecular electronic states is studied through quantum and classical dynamics. Special attention is paid to the behavior of the cross section at high collision energies. A modified expression for the semiclassical cross section is presented which excludes transitions to continuum states. This gives improved agreement with quantum mechanical perturbation theory...

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  • BJS-03 DO WE NEED FIXATION OF THE MESH IN LAPAROENDOSCOPIC TECHNIQUES FOR M3 INGUINAL DEFECTS? AN EXPERIMENTAL STUDY

    Publication

    - BRITISH JOURNAL OF SURGERY - Year 2022

    The authors conducted a research experiment to verify the hypothesis that it is possible to preserve the mesh in the operating field in large direct hernias (M3) without the need to use fixing materials. The results showed that mesh fixation is not the only alternative to preventing recurrence in complex defects and that the type of implant seems to be a key factor from the point of view of mechanics and biophysics.

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  • SAWING PROCESS AS A NEW ALTERNATIVE WAY OF DETERMINING SOME WOOD PROPERTIES

    Publication

    - Year 2015

    Cutting forces (power) could be considered from a point of view of modern fracture mechanics. The developed cutting model, derived from fracture mechanics, includes work of separation (fracture toughness) in addition to plasticity and friction, and also dullness of the cutting edge described by the cutting edge radius. Moreover, forecasting of the shear plane angle for the cutting models, broaden possibilities of energetic effects...

  • A New Quaternion Encryption Scheme for Image Transmission

    Publication

    Quaternions are hypercomplex number of rank 4. They are often applied to mechanics in three-dimensional space and considered as one of the best ways to represent rotations. In this paper a new encryption scheme, based on the rotation of data vector in three-dimensional space around another quaternion (key) is proposed. A computer-based simulation was created to analyze the potential of the proposed encryption technique.

  • Linear game non-contextuality and Bell inequalities—a graph-theoretic approach

    Publication

    - NEW JOURNAL OF PHYSICS - Year 2016

    We study the classical and quantum values of a class of one-and two-party unique games, that generalizes the well-known XOR games to the case of non-binary outcomes. In the bipartite case the generalized XOR(XOR-d) games we study are a subclass of the well-known linear games. We introduce a 'constraint graph' associated to such a game, with the constraints defining the game represented by an edge-coloring of the graph. We use the...

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  • Robust amplification of Santha-Vazirani sources with three devices

    Publication

    - PHYSICAL REVIEW A - Year 2015

    We demonstrate that amplification of arbitrarily weak randomness is possible using quantum resources. We present a randomness amplification protocol that involves Bell experiments. We find a Bell inequality which can amplify arbitrarily weak randomness and give a detailed analysis of the protocol involving it. Our analysis includes finding a sufficient violation of Bell inequality as a function of the initial quality of randomness....

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  • PHOTON LUMINESCENCE STUDIES OF TETRAHYDROFURAN FOLLOWING TRIHYDROGEN CATIONS IMPACT IN THE 20–1000 EV ENERGY RANGE

    Publication

    Photon emission arising during tetrahydrofuran (C4H8O, THF) fragmentation initiated by H3 + ion impact has been studied experimentally. Luminescence fragmentation spectra and the relative emission cross-sections of the excited fragments have been measured using collision-induced emission spectroscopy in the 20–1000 eV energy range. The main features in the spectra are the H Balmer series lines, whose intensities decrease with increasing...

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  • Sudden death of effective entanglement

    Publication

    - PHYSICAL REVIEW A - Year 2010

    Sudden death of entanglement is a well-known effect resulting from the finite volume of separable states. We study the case when the observer has a limited measurement capability and analyze the effective entanglement (i.e., entanglement minimized over the output data). We show that in the well-defined system of two quantum dots monitored by single-electron transistors, one may observe a sudden death of effective entanglement when...

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  • An innovative approach to the forecasting of energetic effects while wood sawing

    Publication

    - Year 2013

    In the classical approach, energetic effects (cutting forces and cutting power) of wood sawing process are generally calculated on the basis of the specific cutting resistance, which is in the case of wood cutting the function of more or less important factors. On the other hand, the cutting forces (power) problem may be tackled with an innovative, up-to-date fundamental analysis of the mechanics of sawing based on modern fracture...

  • A compartment model of alveolar–capillary oxygen diffusion with ventilation–perfusion gradient and dynamics of air transport through the respiratory tract

    This paper presents a model of alveolar–capillary oxygen diffusion with dynamics of air transport through the respiratory tract. For this purpose electrical model representing the respiratory tract mechanics and differentia equations representing oxygen membrane diffusion are combined. Relevant thermodynamic relations describing the mass of oxygen transported into the human body are proposed as the connection between these models,...

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  • An Innovative Approach to the Forecasting of Energetic Effects While Wood Sawing

    Publication

    - Drvna Industrija - Year 2014

    In the classical approach, energetic effects (cutting forces and cutting power) of wood sawing process are generally calculated on the basis of the specifi c cutting resistance, which is in the case of wood cutting the function of more or less important factors. On the other hand, the cutting forces (power) problem may be tackled with an innovative, up-to-date fundamental analysis of the mechanics of sawing based on modern fracture mechanics....

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  • Report for the Short Term Scientific Mission within COST Action FP1101: development of the in-field sensor for estimation of fracture toughness and shear strength by measuring cutting forces

    Publication

    - International Wood Products Journal - Year 2017

    Knowledge on the fracture properties of materials is essential to assure structural integrity and proper design of mechanical connections in timber constructions. Measurement of this property is, however, a very challenging task. The linear fracture mechanics is usually used for its assessment assisted with experimental data acquired by means of various techniques, usually of destructive nature. The cutting force is an energetic...

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  • Professor Jan Kruszewski-Majewski (1929-2012)

    In this obituary, we present the life and achievements of an outstanding Polish scientist, Professor Jan Kruszewski-Majewski, who passed away in 2012. Professor Jan Kruszewski-Majewski was one of the pioneers in introducing modern numerical methods in mechanics. He created and developed an original, Polish method of modellings called the rigid finite element method. He was ont only an outstanding scientist, but also a person of...

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  • Quaternion Encryption Method for Image and Video Transmission

    Quaternions are hyper-complex numbers of rank 4. They are often applied to mechanics in 3D space and are considered to be one of the best ways of representing rotations. In this paper a quaternion encryption method, based on algorithm by Nagase et al. (2004) has been proposed. According to a computer-based simulation the results of the performed research yield a high level of security, which is additionally strengthened by the...

  • Optymalne ciśnienie kondensacji w odwróconym obiegu Braytona

    Publication
    • P. Ziółkowski

    - Year 2013

    Motywacją do podjęcia niniejszej pracy jest potrzeba rozwijania obiegów termodynamicznych charakteryzujących się niskoemisyjnością, takich jak podwójny obieg Braytona z zastosowaniem oksyspalania. Celem przeprowadzonej analizy termodynamicznej było znalezienie optymalnego ciśnienia kondensacji w odwróconym obiegu Braytona. W artykule przybliżono również zagadnienie kondensacji oraz przedstawiono wyniki obliczeń numerycznych wykonanych...

  • A Comprehensive Experimental and Theoretical Study on the[{(η5-C5H5)2Zr[P(µ-PNEt2)2P(NEt2)2P]}2O Crystalline System

    Publication

    - MOLECULES - Year 2021

    The structure of tetraphosphetane zirconium complex C52H100N8OP10Zr21 was determined by single crystal X-ray diffraction analysis. The crystal belongs to the monoclinic system, space group P21/c, with a = 19.6452(14), b = 17.8701(12), c = 20.7963(14)Å, α = γ = 90°, β = 112.953(7)°, V = 6722.7(8)Å3, Z = 4. The electronic structure of the organometallic complex has been characterized within the framework of Quantum Chemical Topology....

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  • Dirac fermions and possible weak antilocalization in LaCuSb2

    Publication
    • J. Chamorro
    • A. Topp
    • Y. Fang
    • M. J. Winiarski
    • C. R. Ast
    • M. Krivenkov
    • A. Varykhalov
    • B. J. Ramshaw
    • L. Schoop
    • T. McQueen

    - APL Materials - Year 2019

    Layered heavy-metal square-lattice compounds have recently emerged as potential Dirac fermion materials due to bonding within those sublattices. We report quantum transport and spectroscopic data on the layered Sb square-lattice material LaCuSb2. Linearly dispersing band crossings, necessary to generate Dirac fermions, are experimentally observed in the electronic band structure observed using angle-resolved photoemission spectroscopy,...

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  • Reexamination of the decoherence of spin registers

    Publication

    - PHYSICAL REVIEW A - Year 2019

    We revisit the decoherence process of a multiqubit register interacting with a thermal bosonic bath. We generalize the previous studies by considering not only the register’s behavior but also a part of its environment. In particular, we are interested in information flow from the register to the environment, which we describe using recently introduced multipartite quantum state structures called spectrum broadcast structures....

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