Cardiorespiratory Fitness and Physical Activity in Pediatric Diabetes: A Systemic Review and Meta-Analysis.

Importance: It is unclear whether cardiorespiratory fitness (CRF) and physical activity are lower among youths with type 1 diabetes (T1D) and type 2 diabetes (T2D) compared with youths without diabetes. Objective: To describe the magnitude, precision, and constancy of the differences in CRF and physical activity among youths with and without diabetes. Data Sources: MEDLINE, Embase, CINAHL, and SPORTDiscus were searched from January 1, 2000, to May 1, 2022, for eligible studies. Study Selection: Observational studies with measures of CRF and physical activity in children and adolescents aged 18 years or younger with T1D or T2D and a control group were included. Data Extraction and Synthesis: Data extraction was completed by 2 independent reviewers. A random-effects meta-analysis model was used to estimate differences in main outcomes. The pooled effect estimate was measured as standardized mean differences (SMDs) with 95% CIs. The Preferred Reporting Items for Systematic Review and Meta-Analyses guideline was followed. Main Outcomes and Measures: The main outcomes were objectively measured CRF obtained from a graded maximal exercise test and subjective or objective measures of physical activity. Subgroup analyses were performed for weight status and measurement type for outcome measures. Results: Of 7857 unique citations retrieved, 9 studies (755 participants) with measures of CRF and 9 studies (1233 participants) with measures of physical activity for youths with T2D were included; for youths with T1D, 23 studies with measures of CRF (2082 participants) and 36 studies with measures of PA (12 196 participants) were included. Random-effects models revealed that directly measured CRF was lower in youths with T2D (SMD, -1.06; 95% CI, -1.57 to -0.56; I2 = 84%; 9 studies; 755 participants) and in youths with T1D (SMD, -0.39; 95% CI, -0.70 to -0.09; I2 = 89%; 22 studies; 2082 participants) compared with controls. Random-effects models revealed that daily physical activity was marginally lower in youths with T1D (SMD, -0.29; 95% CI, -0.46 to -0.11; I2 = 89%; 31 studies; 12 196 participants) but not different among youths with T2D (SMD, -0.56; 95% CI, -1.28 to 0.16; I2 = 91%; 9 studies; 1233 participants) compared with controls. When analyses were restricted to studies with objective measures, physical activity was significantly lower in youths with T2D (SMD, -0.71; 95% CI, -1.36 to -0.05; I2 = 23%; 3 studies; 332 participants) and T1D (SMD, -0.67; 95% CI, -1.17 to -0.17; I2 = 93%; 12 studies; 1357 participants) compared with controls. Conclusions and Relevance: These findings suggest that deficits in CRF may be larger and more consistent in youths with T2D compared with youths with T1D, suggesting an increased risk for cardiovascular disease-related morbidity in adolescents with diabetes, particularly among those with T2D. The findings reinforce calls for novel interventions to empower youths living with diabetes to engage in regular physical activity and increase their CRF.

Variational approach to studying solitary waves in the nonlinear Schrödinger equation with complex potentials.

We discuss the behavior of solitary wave solutions of the nonlinear Schrödinger equation (NLSE) as they interact with complex potentials, using a four-parameter variational approximation based on a dissipation functional formulation of the dynamics. We concentrate on spatially periodic potentials with the periods of the real and imaginary part being either the same or different. Our results for the time evolution of the collective coordinates of our variational ansatz are in good agreement with direct numerical simulation of the NLSE. We compare our method with a collective coordinate approach of Kominis and give examples where the two methods give qualitatively different answers. In our variational approach, we are able to give analytic results for the small oscillation frequency of the solitary wave oscillating parameters which agree with the numerical solution of the collective coordinate equations. We also verify that instabilities set in when the slope dp(t)/dv(t) becomes negative when plotted parametrically as a function of time, where p(t) is the momentum of the solitary wave and v(t) the velocity.

Boosted X waves in nonlinear optical systems.

X waves are spatiotemporal optical waves with intriguing superluminal and subluminal characteristics. Here we theoretically show that for a given initial carrier frequency of the system localized waves with genuine superluminal or subluminal group velocity can emerge from initial X waves in nonlinear optical systems with normal group velocity dispersion. Moreover, we show that this temporal behavior depends on the wave detuning from the carrier frequency of the system and not on the particular X-wave biconical form. A spatial counterpart of this behavior is also found when initial X waves are boosted in the plane transverse to the direction of propagation, so a fully spatiotemporal motion of localized waves can be observed.

Soliton theory of two-dimensional lattices: the discrete nonlinear schrödinger equation.

We theoretically investigate the motion of collective excitations in the two-dimensional nonlinear Schrödinger equation with cubic nonlinearity. The form of these excitations for a broad range of parameters is derived. Their evolution and interaction is numerically studied and the modulation instability is discussed. The case of saturable nonlinearity is revisited.

Thermal diffusion of Boussinesq solitons.

We consider the problem of the soliton dynamics in the presence of an external noisy force for the Boussinesq type equations. A set of ordinary differential equations (ODEs) of the relevant coordinates of the system is derived. We show that for the improved Boussinesq (IBq) equation the set of ODEs has limiting cases leading to a set of ODEs which can be directly derived either from the ill-posed Boussinesq equation or from the Korteweg-de Vries (KdV) equation. The case of a soliton propagating in the presence of damping and thermal noise is considered for the IBq equation. A good agreement between theory and simulations is observed showing the strong robustness of these excitations. The results obtained here generalize previous results obtained in the frame of the KdV equation for lattice solitons in the monatomic chain of atoms.

Solitons in anharmonic chains with negative group velocity.

We consider the problem of the soliton dynamics in anharmonic chains with nearest-neighbor interactions and negative group velocity. By using the quasicontinuum approach we derive analytic expressions for envelope solitons. We observe that these solitons are stable under collisions and, moreover, in the absence of losses they can propagate with nearly any desired velocity. Energy loss effects are discussed by considering the presence of Stokes and hydrodynamical damping. Numerical simulations are performed showing a good agreement with the theory.

Nondissipative diffusion of lattice solitons out of thermal equilibrium.

We perform Langevin dynamics simulations for pulse solitons on atomic chains with anharmonic nearest-neighbor interactions. After switching off noise and damping after a sufficiently long time, the solitons are only influenced by the thermal phonon bath which had been created by the noise. The soliton diffusion constant D is considerably smaller than before the switch-off, and it is proportional to the square of the temperature T , in contrast to the diffusion due to the noise which is proportional to T . We derive a diffusion equation for a soliton which is scattered elastically in an ensemble of phonons and derive general expressions for D and for the drift velocity v(d) . These expressions can be evaluated for the case of the Toda lattice for which the soliton shift due to the phonon scattering is known explicitly. D is indeed proportional to T2 and agrees well with the simulation results, while v(d) is much smaller than the soliton velocity and cannot be measured in the simulations due to the large fluctuations of the soliton position. We express D in terms of soliton characteristics which are known also for solitons on other anharmonic chains in the continuum limit: namely, velocity, amplitude, and width. The results agree well with the simulations if the soliton shape is the same as in the Toda case. If the shape is different, only an estimate of the order of magnitude can be given.

Thermal diffusion of supersonic solitons in an anharmonic chain of atoms.

We study the nonequilibrium diffusion dynamics of supersonic lattice solitons in a classical chain of atoms with nearest-neighbor interactions coupled to a heat bath. As a specific example we choose an interaction with cubic anharmonicity. The coupling between the system and a thermal bath with a given temperature is made by adding noise, delta correlated in time and space, and damping to the set of discrete equations of motion. Working in the continuum limit and changing to the sound velocity frame we derive a Korteweg-de Vries equation with noise and damping. We apply a collective coordinate approach which yields two stochastic ODEs which are solved approximately by a perturbation analysis. This finally yields analytical expressions for the variances of the soliton position and velocity. We perform Langevin dynamics simulations for the original discrete system which confirm the predictions of our analytical calculations, namely, noise-induced superdiffusive behavior which scales with the temperature and depends strongly on the initial soliton velocity. A normal diffusion behavior is observed for solitons with very low energy, where the noise-induced phonons also make a significant contribution to the soliton diffusion.