Theory of the coplanar-waveguide Penning trap

A novel planar Penning trap is presented, which results from the projection of the well-known three-dimensional cylindrical trap onto the surface of a chip. The introduced trap is also a coplanar-waveguide cavity, similar to those used in circuit quantum electrodynamics experiments with superconducting two-level systems. It opens up the possibility of integrating a single trapped electron, or geonium atom, into quantum circuits. The trap is an elliptical Penning trap, with the magnetic field parallel to the chip's surface. A design procedure is described, which permits the compensation of electric anharmonicities up to sixth order. This should render possible the observation of a single trapped electron and the accurate measurement of its eigenfrequencies, a sine qua non requirement for a useful planar geonium technology

Randomly Spread CDMA: Asymptotics via Statistical Physics

This paper studies randomly spread code-division multiple access (CDMA) and multiuser detection in the large-system limit using the replica method developed in statistical physics. Arbitrary input distributions and flat fading are considered. A generic multiuser detector in the form of the posterior mean estimator is applied before single-user decoding. The generic detector can be particularized to the matched filter, decorrelator, linear MMSE detector, the jointly or the individually optimal detector, and others. It is found that the detection output for each user, although in general asymptotically non-Gaussian conditioned on the transmitted symbol, converges as the number of users go to infinity to a deterministic function of a "hidden" Gaussian statistic independent of the interferers. Thus the multiuser channel can be decoupled: Each user experiences an equivalent single-user Gaussian channel, whose signal-to-noise ratio suffers a degradation due to the multiple-access interference. The uncoded error performance (e.g., symbol-error-rate) and the mutual information can then be fully characterized using the degradation factor, also known as the multiuser efficiency, which can be obtained by solving a pair of coupled fixed-point equations identified in this paper. Based on a general linear vector channel model, the results are also applicable to MIMO channels such as in multiantenna systems.Comment: To be published in IEEE Transactions on Information Theor

One-Shot Mutual Covering Lemma and Marton's Inner Bound with a Common Message

By developing one-shot mutual covering lemmas, we derive a one-shot achievability bound for broadcast with a common message which recovers Marton's inner bound (with three auxiliary random variables) in the i.i.d.~case. The encoder employed is deterministic. Relationship between the mutual covering lemma and a new type of channel resolvability problem is discussed.Comment: 6 pages; extended version of ISIT pape

A statistical theory of polymer network degradation

A statistical theory was proposed for the degradation (random scission of chains) of a network having f-functional nodes in the case where all chains contain equireactive groups and a chain scission event does not create new groups or suppress more than one group. Closedform relations were established between the conversion ratio of the degradation process and the crosslink density. Emphasis was put on the value of the conversion ratio for which the gel disappears. Some limited cases already considered in the literature were recovered, but a general solution was proposed for networks having any number of reactive groups per chain, be it uniform or not, and for conversion ratios up to the degelation point. The results were applied successfully to recent experiments regarding the hydrolysis of a polyester

Mutual Information and Minimum Mean-square Error in Gaussian Channels

This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given the output. That is, the derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input statistics. This relationship holds for both scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE estimation. This fundamental information-theoretic result has an unexpected consequence in continuous-time nonlinear estimation: For any input signal with finite power, the causal filtering MMSE achieved at SNR is equal to the average value of the noncausal smoothing MMSE achieved with a channel whose signal-to-noise ratio is chosen uniformly distributed between 0 and SNR

Plastisol Gelation and Fusion Rheological Aspects

This study deals with the rheological aspects of poly-vinyl chloride (PVC) plastisol gelation and fusion processes in foamable formulations. Here, such processes are simulated by temperature-programmed experiment (5 K min−1) in which complex viscosity components are continuously recorded. Nineteen samples based on a PVC-VAC (vinyl acetate 95/5) copolymer with 100 phr plasticizer have been studied, differing only by the plasticizer structure. The sample shear modulus increases continuously with temperature until a maximum, long time after the end of the dissolution process as characterized by DSC. The temperature at the maximum varies between 345 and 428 K with a clear tendency to increase almost linearly with the plasticizer molar mass, and to vary with the flexibility and the degree of branching of the plasticizer molecule. The shear modulus increase is interpreted in terms of progressive “welding” of swelled particles by polymer chain reptation. The plasticizer nature would mainly affect the friction parameter of chain diffusio

Characterising the impact of surface integrity on the fatigue behaviour of forged components

The present study focusses on analysing and modelling the influence on fatigue behaviour of the surface of a hot-forged C70 connecting rod which undergoes a shot-blasting treatment. The shot-blasting heavily affects the surface and thus the fatigue properties. In addition, the forging process introduces large defects which also have an effect on the fatigue strength. So as to be able to determine which aspects of the surface integrity are the most influential in fatigue, various surface states were thoroughly characterised and then tested in high cycle fatigue in bending. The various aspects studied are the surface roughness and large defects, residual stresses, microstructure and hardness

WHEN CHEAPER IS BETTER: FEE DETERMINATION IN THE MARKET FOR EQUITY MUTUAL FUNDS

In this paper, we develop a model of the market for equity mutual funds that captures three key characteristics of this market. First, there is competition among funds. Second, fund managers' ability is not observed by investors before making their investment decisions. And third, some investors do not make optimal use of all available information. The main results of the paper are that 1) price competition is compatible with positive mark-ups in equilibrium; and 2) worse-performing funds set fees that are greater or equal than those set by better-performing funds. These predictions are supported by available empirical evidence.