Clean relaying aided cognitive radio under the coexistence constraint

We consider the interference-mitigation based cognitive radio where the primary and secondary users can coexist at the same time and frequency bands, under the constraint that the rate of the primary user (PU) must remain the same with a single-user decoder. To meet such a coexistence constraint, the relaying from the secondary user (SU) can help the PU's transmission under the interference from the SU. However, the relayed signal in the known dirty paper coding (DPC) based scheme is interfered by the SU's signal, and is not "clean". In this paper, under the half-duplex constraints, we propose two new transmission schemes aided by the clean relaying from the SU's transmitter and receiver without interference from the SU. We name them as the clean transmitter relaying (CT) and clean transmitter-receiver relaying (CTR) aided cognitive radio, respectively. The rate and multiplexing gain performances of CT and CTR in fading channels with various availabilities of the channel state information at the transmitters (CSIT) are studied. Our CT generalizes the celebrated DPC based scheme proposed previously. With full CSIT, the multiplexing gain of the CTR is proved to be better (or no less) than that of the previous DPC based schemes. This is because the silent period for decoding the PU's messages for the DPC may not be necessary in the CTR. With only the statistics of CSIT, we further prove that the CTR outperforms the rate performance of the previous scheme in fast Rayleigh fading channels. The numerical examples also show that in a large class of channels, the proposed CT and CTR provide significant rate gains over the previous scheme with small complexity penalties.Comment: 30 page

Quantum Monte Carlo simulations of a particle in a random potential

In this paper we carry out Quantum Monte Carlo simulations of a quantum particle in a one-dimensional random potential (plus a fixed harmonic potential) at a finite temperature. This is the simplest model of an interface in a disordered medium and may also pertain to an electron in a dirty metal. We compare with previous analytical results, and also derive an expression for the sample to sample fluctuations of the mean square displacement from the origin which is a measure of the glassiness of the system. This quantity as well as the mean square displacement of the particle are measured in the simulation. The similarity to the quantum spin glass in a transverse field is noted. The effect of quantum fluctuations on the glassy behavior is discussed.Comment: 23 pages, 7 figures included as eps files, uses RevTeX. Accepted for publication in J. of Physics A: Mathematical and Genera

Numerical evidences of spin-1/2 chain approaching spin-1 chain

In this article, we study the one dimensional Heisenberg spin-1/2 alternating bond chain in which the nearest neighbor exchange couplings are ferromagnetic (FM) and antiferromagnetic (AF) alternatively. By using exact diagonalization and density matrix renormalization groups (DMRG) method, we discuss how the system approaches to the AF uniform spin-1 chain under certain condition. When the ratio of AF to FM coupling strength}$\alpha$ $(\alpha=J_{AF}/J_{F})$ \textit{is very small, the physical quantities of the alternating bond chain such as the spin-spin correlation, the string correlation function and the spin density coincide with that of the AF uniform spin-1 chain. The edge state problem is discussed in the present model with small}$\alpha$\textit{limit. In addition, the Haldane gap of the AF uniform spin-1 chain is 4-times of the gap of the system considered.Comment: 9pages,8page

Understanding the Core-Halo Relation of Quantum Wave Dark Matter, ψ\psiDM, from 3D Simulations

We examine the nonlinear structure of gravitationally collapsed objects that form in our simulations of wavelike cold dark matter ($\psi$DM), described by the Schr\"{o}dinger-Poisson (SP) equation with a particle mass $\sim 10^{-22} {\rm eV}$. A distinct gravitationally self-bound solitonic core is found at the center of every halo, with a profile quite different from cores modeled in the warm or self-interacting dark matter scenarios. Furthermore, we show that each solitonic core is surrounded by an extended halo composed of large fluctuating dark matter granules which modulate the halo density on a scale comparable to the diameter of the solitonic core. The scaling symmetry of the SP equation and the uncertainty principle tightly relate the core mass to the halo specific energy, which, in the context of cosmological structure formation, leads to a simple scaling between core mass ($M_c$) and halo mass ($M_h$), $M_c \propto a^{-1/2} M_h^{1/3}$, where $a$ is the cosmic scale factor. We verify this scaling relation by (i) examining the internal structure of a statistical sample of virialized halos that form in our 3D cosmological simulations, and by (ii) merging multiple solitons to create individual virialized objects. Sufficient simulation resolution is achieved by adaptive mesh refinement and graphic processing units acceleration. From this scaling relation, present dwarf satellite galaxies are predicted to have kpc sized cores and a minimum mass of $\sim 10^8 {M_\odot}$, capable of solving the small-scale controversies in the cold dark matter model. Moreover, galaxies of $2\times10^{12} {M_\odot}$ at $z=8$ should have massive solitonic cores of $\sim 2\times10^9 {M_\odot}$ within $\sim 60 {\rm pc}$. Such cores can provide a favorable local environment for funneling the gas that leads to the prompt formation of early stellar spheroids and quasars.Comment: 6 pages, 4 figures, accepted for publication in PR

Reaction Mechanism of Organocatalytic Michael Addition of Nitromethane to Cinnamaldehyde: A Case Study on Catalyst Regeneration and Solvent Effects

The Michael addition of nitromethane to cinnamaldehyde has been computationally studied in the absence of a catalyst and the presence of a biotinylated secondary amine by a combined computational and experimental approach. The calculations were performed at the density functional theory (DFT) level with the M06-2X hybrid functional, and a polarizable continuum model has been employed to mimic the effect of two different solvents: dichloromethane (DCM) and water. Contrary to common assumption, the product-derived iminium intermediate was absent in both of the solvents tested. Instead, hydrating the C1–C2 double bond in the enamine intermediate directly yields the tetrahedral intermediate, which is key for forming the product and regenerating the catalyst. Enamine hydration is concerted and found to be rate-limiting in DCM but segregated into two non-rate-limiting steps when the solvent is replaced with water. However, further analysis revealed that the use of water as solvent also raises the energy barriers for other chemical steps, particularly the critical step of C–C bond formation between the iminium intermediate and nucleophile; this consequently lowers both the reaction yield and enantioselectivity of this LUMO-lowering reaction, as experimentally detected. These findings provide a logical explanation to why water often enhances organocatalysis when used as an additive but hampers the reaction progress when employed as a solvent

Global-Local Finite Element Analysis

114 σ.Η αναλυτική επίλυση πολύπλοκων προβλημάτων της μηχανικής στις μέρες μας καθίσταται δυσχερής εως αδύνατη χωρίς την εφαρμογή αριθμητικών μεθόδων και τη χρήση ηλεκτρονικού υπολογιστή. Η μέθοδος των πεπερασμένων στοιχείων αποτελεί σήμερα ένα ισχυρό εργαλείο για την επίλυση τέτοιων προβλημάτων και εξελίσσεται με μεγάλη ταχύτητα τόσο σε ακαδημαϊκό όσο και σε επαγγελματικό επίπεδο. Ενδεικτικά, αν και επινοήθηκε και χρησιμοποιήθηκε για τη στατική ανάλυση φορέων, έχει καθολικότερη εφαρμογή σε μια ευρύτερη κατηγορία προβλημάτων του μηχανικού, όπως στη ρευστομηχανική, στη μεταφορά θερμότητας, στην ακουστική, στον ηλεκτρομαγνητισμό και στην εμβιομηχανική. Επιπλέον, η εξέλιξη στων Η/Υ με τις ολοένα μεγαλύτερες δυνατότητες διαχείρισης όγκου δεδομένων αλλά και με την αύξηση της ταχύτητας εκτέλεσης των αριθμητικών πράξεων κατέστησε εφικτή την επίλυση σύνθετων προβλημάτων τα οποία θεωρούνταν απροσπέλαστα πριν μερικά χρόνια. Στην κατηγορία αυτή, των προβλημάτων αυξημένου υπολογιστικού κόστους, ανήκει και η καταστατική περιγραφή πολυφασικών υλικών. Είναι γεγονός ότι το μεγαλύτερο μέρος των παραγώμενων δομικών υλικών σήμερα, παρουσιάζει κάποιο είδος ανομοιογένειας, διακριτή ή μη στην κλίμακα δομικών έργων. Χαρακτηριστικά παραδείγματα αποτελούν τα κράματα μετάλλων, τα πορώδη, τα πολυκρυσταλλικά και τα σύνθετα υλικά στα οποία το μέγεθος, το σχήμα και οι ιδιότητες των συστατικών τους μερών καθορίζουν άμεσα τη συνολική τους μηχανική συμπεριφορά. Διάφορες τεχνικές έχουν αναπτυχθεί για την προσομοίωση και την περιγραφή της απόκρισης ανομοιογενών υλικών. Η παρούσα εργασία επικεντρώνεται στη μέθοδο ομογενοποίησης πολλαπλών κλιμάκων η οποία συνίσταται στην επίλυση δύο εμφωλευμένων προβλημάτων συνοριακών τιμών, για τη μακροκλίμακα και τη μικροκλίμακα αντίστοιχα. Τα βασικά χαρακτηριστικά μιας τέτοιας μεθόδου είναι ότι - Δεν απαιτείται η περιγραφή των καταστατικών νόμων του μακροφορέα. - Παρέχει τη δυνατότητα ενσωμάτωσης μεγάλων παραμορφώσεων και στροφών τόσο στην προσομοίωση της μικροκλίμακας όσο και του μακροφορέα. - Παρέχει τη δυνατότητα λεπτομερούς προσομοίωσης των συστατικών μερών της μικροκλίμακας. - Επιτρέπει οποιαδήποτε τεχνική επίλυσης στην κλίμακα του μικροφορέα. Αναλυτικά, σύμφωνα με τη μέθοδο αυτή. υπολογίζεται το διάνυσμα ανηγμένων παραμορφώσεων σε κάθε υλικό σημείο του μακροφορέα το οποίο στη συνέχεια χρησιμοποιείται για τη μόρφωση των συνοριακών συνθηκών του αντιπροσωπευτικού μικροφορέα στο αντίστοιχο σημείο. Μετά την επίλυση του προβλήματος συνοριακών τιμών της μικροκλίμακας, το διάνυσμα των τάσεων του μακροφορέα υπολογίζεται μέσα από τη διαδικασία ομογενοποίησης του πεδίου των τάσεων και κατά τον τρόπο αυτό υπολογίζεται η σχέση τάσεων ανηγμένων παραμορφώσεων για κάθε υλικό σημείο Ωστόσο, υπάρχουν κάποιοι περιορισμοί στην εφαρμογή της εν λόγω υπολογιστικής τεχνικής. Συγκεκριμένα, παρά το ότι κατά την προσομοίωση λαμβάνονται υπ' όψην οι διάφορες παράμετροι της μικροκλίμακας όπως το ποσοστό όγκου, η κατανομή και η μορφολογία των συστατικών μερών του υλικού, τα αποτελέσματα της μεθόδου είναι ανεξάρτητα από το απόλυτο μέγεθος του αντιπροσωπευτικού όγκου της μικροκλίμακας. Παρ' όλα αυτά, η τεχνική ομογενοποίησης στα πλαίσια ανάλυσης πολλαπλών κλιμάκων αποτελεί ένα σημαντικό εργαλείο για τον υπολογισμό των καταστατικών σχέσεων πολυφασικών υλικών στα οποία είναι αδύνατη η εφαρμογή οποιασδήποτε άλλης μεθόδου.Nowadays, analysis of complicated problems in the domain of mechanics consti- tutes a hard and even impossible task without the implementation of numerical methods and the employment of computational machines. Finite element method is a powerful tool for the solution of such problems and is rapidly developed in an academic and professional sense. Even if it was developed and implemented for structural analysis, it is widely employed in several domains such as in fluid mechanics, heat transfer, acoustics and electromagnetism. Furthermore, the development of computer hardware in terms of data processing, has significantly contributed to the solution of problems that were considered inaccessible a few years ago. Most of the materials produced in industry are heterogeneous on one or another spatial scale. Typical examples include metal alloy systems, porous media and polycrystalline materials and composites. The overall response of these micro heterogeneous materials depends strongly on the size, shape properties and spatial distribution of the microstructural components. Several techniques have been developed for the prediction of the macroscopic behavior of such materials. The present work is concentrated on the first order homogenization technique in the framework of a multi-scale approach which consists of the solution of two nested boundary value problems, for the macro-scale and the micro-scale respectively. Methods of this type - Do not require any constitutive assumption with respect to the overall ma- terial behavior. - Enable the incorporation of large deformations and rotations on both micro and macrolevel. - Provide the possibility to introduce detailed microstructural information. - Allow the use of any modelling technique at the microlevel. Concretely, according to this approach, the macroscopic deformation tensor is calculated for every integration point of the macrostructure and then is used to formulate the kinematic boundary conditions for the associated microstructural representative volume element (RVE). After the solution of the microstructural boundary value problem, the macroscopic stress tensor is computed by averaging the resulting microstructural stress field over the volume of the RVE and as a result, we obtain the stress-strain relation at every macroscopic point. However, there is a major disadvantage of the existing first-order computational homogenization. More specifically, this technique can account for the volume fraction, distribution and morphology of the micro-components however, it cannot take into account the absolute size of the microstructure making it thus impossible to treat microstructural size effects. Nevertheless, computational homogenization provides a significant strategy to obtain micro-macro structure-property relations for materials for which the overall macroscopic response cannot be computed by any other method.Κωνσταντινος Ε. Τατση

Radiating and non-radiating sources in elasticity

In this work, we study the inverse source problem of a fixed frequency for the Navier's equation. We investigate that nonradiating external forces. If the support of such a force has a convex or non-convex corner or edge on their boundary, the force must be vanishing there. The vanishing property at corners and edges holds also for sufficiently smooth transmission eigenfunctions in elasticity. The idea originates from the enclosure method: The energy identity and new type exponential solutions for the Navier's equation.Comment: 17 page

Switchable genome editing via genetic code expansion

Multiple applications of genome editing by CRISPR-Cas9 necessitate stringent regulation and Cas9 variants have accordingly been generated whose activity responds to small ligands, temperature or light. However, these approaches are often impracticable, for example in clinical therapeutic genome editing in situ or gene drives in which environmentally-compatible control is paramount. With this in mind, we have developed heritable Cas9-mediated mammalian genome editing that is acutely controlled by the cheap lysine derivative, Lys(Boc) (BOC). Genetic code expansion permitted non-physiological BOC incorporation such that Cas9 (Cas9BOC) was expressed in a full-length, active form in cultured somatic cells only after BOC exposure. Stringently BOC-dependent, heritable editing of transgenic and native genomic loci occurred when Cas9BOC was expressed at the onset of mouse embryonic development from cRNA or Cas9BOC transgenic females. The tightly controlled Cas9 editing system reported here promises to have broad applications and is a first step towards purposed, spatiotemporal gene drive regulation over large geographical ranges

Varied Signature Splitting Phenomena in Odd Proton Nuclei

Varied signature splitting phenomena in odd proton rare earth nuclei are investigated. Signature splitting as functions of $K$ and $j$ in the angular momentum projection theory is explicitly shown and compared with those of the particle rotor model. The observed deviations from these rules are due to the band mixings. The recently measured $^{169}$Ta high spin data are taken as a typical example where fruitful information about signature effects can be extracted. Six bands, two of which have not yet been observed, were calculated and discussed in detail in this paper. The experimentally unknown band head energies are given