Interface relaxation in electrophoretic deposition of polymer chains: Effects of segmental dynamics, molecular weight, and field

Using different segmental dynamics and relaxation, characteristics of the interface growth is examined in an electrophoretic deposition of polymer chains on a three (2+1) dimensional discrete lattice with a Monte Carlo simulation. Incorporation of faster modes such as crankshaft and reptation movements along with the relatively slow kink-jump dynamics seems crucial in relaxing the interface width. As the continuously released polymer chains are driven (via segmental movements) and deposited, the interface width $W$ grows with the number of time steps $t$, $W \propto t^{\beta},$ ($\beta \sim 0.4$--$0.8)$, which is followed by its saturation to a steady-state value $W_s$. Stopping the release of additional chains after saturation while continuing the segmental movements relaxes the saturated width to an equilibrium value ($W_s \to W_r$). Scaling of the relaxed interface width $W_r$ with the driving field $E$, $W_r \propto E^{-1/2}$ remains similar to that of the steady-state $W_s$ width. In contrast to monotonic increase of the steady-state width $W_s$, the relaxed interface width $W_r$ is found to decay (possibly as a stretched exponential) with the molecular weight.Comment: 5 pages, 7 figure

Supersymmetric version of a hydrodynamic system in Riemann invariants and its solutions

In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and supersymmetric versions of this hydrodynamical model are analyzed through the use of group-theoretical methods applied to partial differential equations involving both bosonic and fermionic variables. More specifically, we compute the Lie superalgebras of both models and perform classifications of their respective subalgebras. A systematic use of the subalgebra structures allow us to construct several classes of invariant solutions, including travelling waves, centered waves and solutions involving monomials, exponentials and radicals.Comment: 30 page

Hydrodynamic Waves in Regions with Smooth Loss of Convexity of Isentropes. General Phenomenological Theory

General phenomenological theory of hydrodynamic waves in regions with smooth loss of convexity of isentropes is developed based on the fact that for most media these regions in p-V plane are anomalously small. Accordingly the waves are usually weak and can be described in the manner analogous to that for weak shock waves of compression. The corresponding generalized Burgers equation is derived and analyzed. The exact solution of the equation for steady shock waves of rarefaction is obtained and discusses.Comment: RevTeX, 4 two-column pages, no figure

Biomechanical Differences Between the Bulgarian Split-Squat and Back Squat

International Journal of Exercise Science 14(1): 533-543, 2021. The Bulgarian split squat (BSS) is a unilateral lower extremity strength exercise; however, the mechanical demands have not been fully elucidated. The purpose of this study was to compare ankle, knee, and hip joint net joint moment impulse (NJMI), work (NJW), peak net joint moment (NJM) and peak displacement between the BSS and traditional bilateral back squat (BS). Following a practice and 1-repetition maximum (1-RM) session, 2x3 BS (70% 1-RM) and BSS (35% 1-RM) were completed by twenty resistance trained males (24.20 ± 2.50 yrs, 1.76 ± 0.06m, 85.3 ± 13.90 kg). Significant squat type x joint interactions were revealed for NJMI (p \u3c 0.001), NJW (p \u3c 0.001), peak NJM (p \u3c 0.001), and peak displacement (p = 0.011). For both squats, hip NJMI, NJW, and peak NJM was significantly greater than both ankle (d = 5.50-9.40) and knee (d = 7.50-8.50). While knee NJMI (d = 2.80) and peak NJM (d = 2.10) during the BSS was statistically less compared to ankle, during BS knee NJMI was statistically greater than ankle (d = 3.00). Ankle and knee NJW were statistically similar during BSS (d = 0.30), whereas knee NJW was statistically greater than ankle during BS (d = 3.20). Comparing between squat types within each joint demonstrated statistically equal peak displacement for the ankle (d = 0.14) and hip (d = 0.11), whereas knee joint peak displacement was significantly less for the BSS compared to BS (d = 0.82). Both the BSS and BS are hip dominant exercises. The BSS may best be used in circumstances to focus on hip extension while minimizing the knee joint demands, such as the early phases of knee rehabilitation or when addressing isolated hip extension deficiencies

Physics in Riemann's mathematical papers

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann's mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann's philosophical points of view, we review some ideas on the same subjects emitted by Riemann's predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle. The final version of this paper will appear in the book: From Riemann to differential geometry and relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Intersubband absorption linewidth in GaAs quantum wells due to scattering by interface roughness, phonons, alloy disorder, and impurities

We calculate the intersubband absorption linewidth in quantum wells (QWs) due to scattering by interface roughness, LO phonons, LA phonons, alloy disorder, and ionized impurities, and compare it with the transport energy broadening that corresponds to the transport relaxation time related to electron mobility. Numerical calculations for GaAs QWs clarify the different contributions of each individual scattering mechanism to absorption linewidth and transport broadening. Interface roughness scattering contributes about an order of magnitude more to linewidth than to transport broadening, because the contribution from the intrasubband scattering in the first excited subband is much larger than that in the ground subband. On the other hand, LO phonon scattering (at room temperature) and ionized impurity scattering contribute much less to linewidth than to transport broadening. LA phonon scattering makes comparable contributions to linewidth and transport broadening, and so does alloy disorder scattering. The combination of these contributions with significantly different characteristics makes the absolute values of linewidth and transport broadening very different, and leads to the apparent lack of correlation between them when a parameter, such as temperature or alloy composition, is changed. Our numerical calculations can quantitatively explain the previously reported experimental results.Comment: 17 pages, including 15 figure

On the Nature of the Cosmological Constant Problem

General relativity postulates the Minkowski space-time to be the standard flat geometry against which we compare all curved space-times and the gravitational ground state where particles, quantum fields and their vacuum states are primarily conceived. On the other hand, experimental evidences show that there exists a non-zero cosmological constant, which implies in a deSitter space-time, not compatible with the assumed Minkowski structure. Such inconsistency is shown to be a consequence of the lack of a application independent curvature standard in Riemann's geometry, leading eventually to the cosmological constant problem in general relativity. We show how the curvature standard in Riemann's geometry can be fixed by Nash's theorem on locally embedded Riemannian geometries, which imply in the existence of extra dimensions. The resulting gravitational theory is more general than general relativity, similar to brane-world gravity, but where the propagation of the gravitational field along the extra dimensions is a mathematical necessity, rather than being a a postulate. After a brief introduction to Nash's theorem, we show that the vacuum energy density must remain confined to four-dimensional space-times, but the cosmological constant resulting from the contracted Bianchi identity is a gravitational contribution which propagates in the extra dimensions. Therefore, the comparison between the vacuum energy and the cosmological constant in general relativity ceases to be. Instead, the geometrical fix provided by Nash's theorem suggests that the vacuum energy density contributes to the perturbations of the gravitational field.Comment: LaTex, 5 pages no figutres. Correction on author lis

Reconstructing a Z' Lagrangian using the LHC and low-energy data

We study the potential of the LHC and future low-energy experiments to precisely measure the underlying model parameters of a new Z' boson. We emphasize the complimentary information obtained from both on- and off-peak LHC dilepton data, from the future Q-weak measurement of the weak charge of the proton, and from a proposed measurement of parity violation in low-energy Moller scattering. We demonstrate the importance of off-peak LHC data and Q-weak for removing sign degeneracies between Z' couplings that occur if only on-peak LHC data is studied. A future precision measurement of low-energy Moller scattering can resolve a scaling degeneracy between quark and lepton couplings that remains after analyzing LHC dilepton data, permitting an extraction of the individual Z' couplings rather than combinations of them. We study how precisely Z' properties can be extracted for LHC integrated luminosities ranging from a few inverse femtobarns to super-LHC values of an inverse attobarn. For the several example cases studied with M_Z'=1.5 TeV, we find that coupling combinations can be determined with relative uncertainties reaching 30% with 30 fb^-1 of integrated luminosity, while 50% is possible with 10 fb^-1. With SLHC luminosities of 1 ab^-1, we find that products of quark and lepton couplings can be probed to 10%.Comment: 36 pages, 17 figure